12.1 COUNTING PARTICLES OF MATTER

I. A. STOICHIOMETRY- THE STUDY OF RELATIONSHIPS BETWEEN MEASURABLE QUANTITIES, SUCH AS MASS, VOLUME, AND THE # OF ATOMS IN A CHEMICAL REACTION.

B. THE NUMBER OF PARTICLES (ATOMS, MOLECULES, OR IONS) IN MACROSCOPIC MATTER CONTROLS THE CONSUMPTION AND FORMATION OF SUBSTANCES IN CHEMICAL REACTIONS.

1. HELPS COUNT LARGE NUMBERS OF PARTICLES.

II. DETERMINING MASS FOR MOLECULES, FORMULA UNITS AND MOLES

A. MOLECULAR MASS

Molecular mass of a covalent compound is the mass in atomic mass units of one molecule. Generally atomic masses will be rounded to tenths. For those elements with masses less than ten, masses will be rounded to hundredths unless more significant digits are suggested by the data of the problem.

EXAMPLE

Find the molecular mass of vitamin A, one of the fat-soluble vitamins. Its molecular formula is C₂₀H₃₀O.

Solving Process:

carbon 20 X 12.0 u = 240 u

hydrogen 30 X 1.01 u = 30.3 u

oxygen 1 X 16.0 u = 16.0 u

Molecular mass = 286 u

B. FORMULA MASS

Ionic compounds do not exist in the form of molecules. The formula mass of

an ionic compound is the mass in atomic mass units of one formula unit. Both the molecular and formula masses are calculated in the same manner. It is possible to calculate masses without first determining whether the substance is ionic or molecular.

Formula mass is a more general term than molecular mass. Formula mass may be used in referring to all compounds. Molecular mass should be used only to refer to molecular compounds.

EXAMPLE

Determine the formula mass of calcium phosphate, Ca₃(PO₄)₂.

Solving Process:

calcium 3 X 40.1 u = 120.3 u

phosphorus 2 X 31.0 u = 62.0 u

oxygen 8 X 16.0 u = 128.0 u

Formula mass = 310.3 u

C. MOLAR MASS- THE MASS OF ONE MOLE OF A PURE SUBSTANCE*

1. MOLAR MASS= MASS IN GRAMS OF THE AVERAGE ATOMIC MASS.

2. FOUND ON THE PERIODIC TABLE

3. MUST KNOW FORMULA

CAN ALSO BE CALLED GFM (GRAM FORMULA MASS)

1. Calculate the formula or molecular mass of each of the following compounds.

a. H2SO4

b. NaOH

c. NH4NO3

d. Fe(CH3COO)3

e. C3H5N3O3, nitroglycerin

f. Al(NO3)3

g. C63H84N14O14PCo, vitamin B12

h. SO2

2. Aspirin can be used to decrease pain and fever. Calculate the molecular mass of 2-acetyloxybenzoic acid (aspirin) that has the following structural formula.

3. Calculate the mass in grams of 0.354 mol of each of the following.

a. ammonia gas, NH3

b. platinum metal, Pt

c. cholesterol, C27H46O

d. iron(II) ferricyanide, Fe3(Fe(CN)6)2

4. Calculate the number of moles in 50.0 g of each of the following.

a. borazon, BN

b. thallium(I) sulfate, Tl2SO4

c. calcium propanoate, Ca(C3H5O2)2

d. penicillin G, C16H18N2O4S

5. Calculate the number of atoms, molecules, or ions for each of the following.

a. 2.00 mol Na atoms

b. 46.0 g Na atoms

c. 3.00 mol K⁺

d. 68.0 g H2S molecules

III. THE AVOGADRO CONSTANT

As stated earlier, the mass of a single atom or molecule is so small it cannot

be measured easily. Laboratory quantities require many millions of atoms. If we express the international atomic masses of elements in grams, the masses can be readily measured in the laboratory.

Since atomic masses are relative quantities, the atomic mass in grams of one

element contains the same number of atoms as the atomic mass in grams of any other element. It has been found that the atomic mass in grams of any element contains 6.02 X 10²³ atoms. This number is called Avogadro’s constant, and is abbreviated NA. Another name for this quantity is the mole.

IV. THE MOLE

A. THE GROUP OR UNIT OF MEASURE USED TO COUNT NUMBERS OF ATOMS, MOLECULES, OR FORMULA UNITS OF A SUBSTANCE

1. ABBREVIATED- MOL

B. The mole is the SI unit for amount of substance, and its symbol is mol. It represents both a formula mass and a number of formula units. Just as one million equals 1 x 10⁶ things, one dozen equals 12 things, and one gross equals 144 things, one mole is 6.02 X 10²³ things. Depending on the substance, the mass of the mole will be different. The mole is an important quantitative unit used in most chemical calculations. It is always understood to refer to one formula mass in grams, one atomic mass in grams, or one molecular mass in grams.

Counting Things: Moles

An element that is diatomic (such as nitrogen) can be measured as one mole

of molecules or as one mole of atoms. Note the difference in Table 12-1.

These relationships are important in a number of different chemical calculations.

They will be used in this chapter and in subsequent chapters.

Conversion ratios are used to convert from one unit (such as grams) to a different unit (such as moles). Since the atomic mass in grams of an element = 1 mole

of the element = 6.02 X 10²³ atoms of an element, four conversion factors can be written.

The actual form used depends upon the units desired in the answer.

EXAMPLE

Calculate the mass in grams of 2.23 mol of nitrogen molecules.

Solving Process:

To convert from moles to grams, use the conversion ratio 28.0 g N₂/mol N₂. This ratio gives the answer in grams by dividing out the unit mol.

EXAMPLE

Find the number of atoms in 16.0 g sulfur.

Solving Process:

Convert from grams to moles of sulfur, then from moles of sulfur to atoms of sulfur.

This conversion will involve two ratios.

Counting Atoms

EXAMPLE

Determine the number of atoms in 2.23 mol nitrogen molecules, N₂.

Solving Process:

The number of molecules in a mole is given by the Avogadro constant. To obtain atoms, this number must be multiplied by two, since N₂ is diatomic.

6. Calculate the mass in grams of each of the following.

a. 6.02 X 10²³ atoms of Na

b. 3.01 X 10²³ formula units of Sr(OH)2

c. 1.20 X 10²⁴ molecules of CO2

d. 1.50 X 10²³ ions of Na⁺

12.2 USING MOLES

MASS-MASS RELATIONSHIPS

Stoichiometry is the study of quantitative relationships in chemical reactions. A basic idea used in solving stoichiometric problems is the mole concept. If you are given the mass of one substance and know the balanced equation, you can calculate the reactants needed or the products produced because the equation shows relative number of moles of reactants and products.

Moles and Particles

A general procedure for mass-mass problems uses the following steps.

1. Write a balanced equation.

Identify the known and calculate its molar mass.

2. Convert from mass of given material to moles.

(1MOLE OF KNOWN / MOLAR MASS OF KNOWN)

3. Determine the mole ratio from the coefficients of the balanced equation and convert from moles of given material to moles of required material.

(COEFFICIENT {MOLES} OF UNKNOWN / COEFFICIENT{MOLES} OF KNOWN)

4. Express the moles of required material in grams.

(MOLAR MASS OF UNKNOWN / 1 MOLE OF UNKNOWN)

The setup for a mass-mass calculation follows the format given below.

(start with grams given)-> (grams to moles)-> (use mole ratio)-> (moles to grams)-> (end with grams required)

Solving Mass-Mass Problems

EXAMPLE

Calculate the mass of HCl needed to react with 10.0 g Zn.

Solving Process:

Step 1. Begin with the balanced equation.

Zn(s) + 2HCl(aq)à ZnCl₂(aq) + H₂(g)

Step 2. Convert grams of zinc to moles.

Step 3. Determine the mole ratio that exists between Zn and HCl and convert

from moles Zn to moles HCl.

1 mole Zn reacts with 2 moles HCl

Step 4. Convert moles of HCl to grams of HCl.

grams HCl =

= 11.2 g HCl

Note that the conversion ratios are chosen and arranged so all the units divide out except the desired unit, in this case, grams of HCl. Since all the ratios are equal to 1,multiplying by one of them, or by all of them, changes only the units of the answer.

EXAMPLE

Calculate the mass of O₂ produced if 2.50 g KClO₃ are completely decomposed by heating.

Solving Process:

Step 1. Write the balanced equation.

2KClO₃(s)à 2KCl(s) + 3O₂(g)

Step 2. Convert mass of KClO₃ to moles.

Step 3. Determine the mole ratio that exists between KClO₃ and O₂.

2 moles KClO₃ yields 3 moles O₂

Step 4. Convert moles of O₂ to grams.

grams O₂

Solve the following problems. The reactions may not be balanced.

1. If 20.0 g of magnesium react with excess hydrochloric acid, how many grams of magnesium chloride are produced?

Mg(s) + HCl(aq) à MgCl₂(aq) + H₂(g)

2. How many grams of chlorine gas must be reacted with excess sodium iodide if 10.0 g of sodium chloride are needed?

NaI(aq) + Cl₂(g) à NaCl(aq) + I₂(s)

3. How many grams of oxygen are produced in the decomposition of 5.00 g of potassium chlorate?

KClO₃(s)à KCl(s) + O₂(g)

4. What mass of copper is required to replace silver from 4.00 g of silver nitrate dissolved in water?

Cu(s) + AgNO₃(aq) à Cu(NO₃)₂(aq) + Ag(s)

5. If excess ammonium sulfate reacts with 20.0 g of calcium hydroxide, how many grams of ammonia are produced?

(NH₄)₂SO₄(aq) + Ca(OH)₂(s) à CaSO₄(s) + NH₃(s) + H₂O(l)

6. If excess sulfuric acid reacts with 30.0 g of sodium chloride, how many

grams of hydrogen chloride are produced?

NaCl(aq) + H₂SO₄(aq) à HCl(g) + Na₂SO₄(aq)

7. How much silver phosphate is produced if 10.0 g of silver acetate react with excess sodium phosphate?

AgCH₃COO(aq) + Na₃PO₄(aq) à Ag₃PO₄(s) + NaCH₃COO(aq)

8. How many grams of sodium hydroxide are needed to completely neutralize 25.0 g of sulfuric acid?

NaOH(aq) + H₂SO₄(aq) à Na₂SO₄(s) + H₂O(g)

Assume the volumes given are at STP unless other conditions are specified.

AVOGADRO’S PRINCIPLE AND MOLAR VOLUME

What is the relationship between the mass of a gas and its volume? Avogadro’s principle states that equal volumes of all gases, measured under the same conditions of pressure and temperature, contain the same number of particles or moles. One mole of any gas has a mass equal to its molecular mass.

For example:

1 mole N₂ = 28.0 g N₂ = 6.02 X 10²³ molecules of N₂

1 mole CO₂ = 44.0 g CO₂ = 6.02 X 10²³ molecules of CO₂

The volume of one mole of a gas at STP is the molar volume of the gas. One mole of a gas at STP occupies 22.4 liters (L). This volume is the same for all gases at STP. The mass and volume of any gas are related as follows.

1 mole of any gas = molecular mass = 22.4 L

STP: STANDARD TEMPERATURE AND PRESSURE FOR A GAS

TEMPERATURE = 0.00 ^oC = 273 K

PRESSURE = 1 ATMOSPHERE = 101 kPa

Mole Relationships

EXAMPLE

How many grams of carbon dioxide, CO₂, will occupy a volume of 500.0 mL at STP?

Solving Process:

The conversion equalities are

1 mol CO₂ = 22.4 L CO₂ (STP)

1 mol CO₂ = 44.0 g CO₂

= 0.982 g

9. Calculate the number of moles contained in each of the following gas

volumes.

a. 5.00 X 10⁴ mL H₂

b. 1.000 X 10³ mL N₂

c. 6500 mL SO₂

d. 15 000 mL NH₃

e. 2500 mL O₂

f. 2.000 X 10³ mL CO₂

10. Calculate the mass of each of the following volumes of gas.

a. 2.00 X 10⁴ L CH₄

b. 1500.0 mL Cl₂

c. 70.0 mL SO₃

d. 3.000 X 10² L N₂O

e. 3.0 X 10³ L N₂

f. 3500.0 mL H₂S

11. Calculate the volume in L of each of the following.

a. 4.0 mol Br₂

b. 200.0 g H₂S

c. 25.5 g SO₂

d. 600.0 g Cl₂

e. 2.50 mol NH₃

f. 50.0 g NO₂

g. 7.00 mol O₂

h. 10.0 g HCl

MASS-GAS VOLUME PROBLEMS

Many chemical reactions involve gases. It is often necessary to know the volume of gas involved with a known mass of material in a reaction. Problems of this type are similar to mass-mass problems, however one additional piece of information is needed. In mass-volume problems, mass is changed to moles of the desired substance and then converted to volume using the relationship:

1 mole of any gas = 22.4 L of that gas at STP

The reverse calculation may also be done. Volume is changed to moles and

moles are changed to mass.

EXAMPLE

Calculate the volume of oxygen produced at STP by the decomposition of 10.0 g of potassium chlorate, KClO₃.

Solving Process:

Write the balanced equation.

2KClO₃(s)à 2KCl(s) + 3O₂(g)

Start with the known mass of KClO₃ given in the problem and convert to volume of oxygen at STP.

Assume that all volumes are at STP.

12. How many mL of hydrogen are produced if 4.00 g zinc react with excess hydrochloric acid?

Zn(s) + 2HCl(aq) à ZnCl₂(aq) + H₂(g)

13. If excess chlorine gas reacts with a solution containing 20.0 g of potassium bromide, how many milliliters of bromine gas can be produced?

2KBr(aq) + Cl₂(g) à 2KCl(aq) + Br₂(g)

14. How many grams of copper(II) oxide can be reduced to copper metal with 10.0 L of H₂?

CuO(s) + H₂₍g) à Cu(s) + H₂O(g)

15. Calculate the mL of oxygen that can be produced by the electrolysis of 5.00 g of water.

2H₂O(l) à 2H₂(g) + O₂(g)

16. In the reaction between aluminum and oxygen, how many grams of aluminum are required to react with 5.00 L of oxygen?

4Al(s) + 3O₂(g) à 2Al₂O₃(s)

EXAMPLE

A student performs an experiment involving the reaction of magnesium metal

with hydrochloric acid to form hydrogen gas. From the given data, calculate the mass of magnesium.

1. volume of hydrogen gas formed 42.0 mL

2. temperature of hydrogen 20.0°C

3. pressure 99.3 kPa

4. vapor pressure of water 2.3 kPa

5. pressure of dry hydrogen (99.3 - 2.3) 97.0 kPa

VOLUME-VOLUME PROBLEMS

It is possible to calculate the volume of a gas in a reaction when the volume of another gas in the reaction is known. Two methods can be used in solving these volume-volume problems. The first method is the same as the mass-mass or mass-volume method.

Use the following steps.

Step 1. Convert the given volume to moles.

Step 2. From the balanced equation, convert the moles of given substance to moles of required substance.

Step 3. Convert the moles of required substance back to its volume.

In each case, the temperature and pressure must be taken into consideration.

Two methods of solving for gas volume are given. The second method usually involves only an inspection and simple mental calculation. It can be used easily when the temperature and pressure remain constant.

EXAMPLE

If 6.00 L of oxygen are available to burn carbon disulfide, CS₂, how many L of carbon dioxide are produced? The products of the combustion of carbon disulfide are carbon dioxide and sulfur dioxide.

Solving Process:

Balance the equation for this reaction.

CS₂(l) + 3O₂(g) à CO₂(g) + 2SO₂(g)

Convert 6.00 L O₂ to L of CO₂.

Therefore, 6.00 L O₂ will produce 2.00 L CO₂. Note that the changes to and from moles divide out.

Alternate Method: Temperature and Pressure Constant

The balanced equation indicates the relative number of moles of reactant and product.

The coefficients also indicate the relative volumes of the gases at constant temperature and pressure. The relationship is a result of the principle stated in Avogadro’s hypothesis: equal volumes of gases at the same temperature and pressure contain the same number of particles. If the gases are measured at the same temperature and pressure then 3 volumes O₂:1 volume CO₂ or 3 L O₂:1 L CO₂. The volume of CO₂ will be one-third the volume of O₂. Since the O₂ volume is 6.00 L, the CO₂ volume is 2.00 L. Conversion ratios could be used as follows.

17. In the electrolysis of water, 75.0 mL of oxygen gas are produced. How many mL of hydrogen are produced?

2H₂O(l) à 2H₂(g) + O₂(g)

18. If an electric discharge produces 20.0 mL of ozone, O₃, how many milliliters of oxygen are required?

3O₂(g) à 2O₃(g)

19. Ammonia can be produced by the Haber process. If 60.0 L of NH₃ are produced, how many L of hydrogen and nitrogen are necessary?

3H₂(g) + N₂(g) à 2NH₃(g)

20. How many mL of chlorine gas are required to produce 50.0 mL of hydrogen chloride gas?

H₂(g) + Cl₂(g) à 2HCl(g)

21. The residue from the complete decomposition of potassium chlorate is found to contain 1.80 g of potassium chloride. Determine the following:

a. grams of KClO₃ originally present

b. grams of oxygen produced

c. milliliters of oxygen at STP

LIMITING REACTANTS

Many reactions continue until one of the reactants is consumed. The reactant

that is used up first is called the limiting reactant. The other reactant is said to be in excess. When discussing limiting reactants, we will deal only with nonreversible reactions. It is possible to determine whether a material is in excess or is deficient in a reaction by experiment or by calculation.

Limiting reactant problems are most easily solved by comparing the moles of

the reactants present using the following steps.

Step 1. Write a balanced equation.

Step 2. Change both given quantities to moles.

Step 3. From the balanced equation, determine the moles of required substance that each given quantity will produce.

Step 4. Complete the problem using the quantity that yields the lesser amount of product. This reactant is the limiting reactant.

EXAMPLE

If 40.0 g of H₃PO₄ react with 60.0 g of MgCO₃, calculate the volume of CO₂ produced at STP.

Solving Process:

Step 1. Write the balanced equation.

2H₃PO₄(aq) + 3MgCO₃(s) à Mg₃(PO₄)₂(s) + 3CO₂(g) + 3H₂O(l)

Step 2. Change grams of reactant to moles of reactant.

Step 3. From the balanced equation determine the moles of CO₂ that will be

produced by each reactant.

The limiting reactant produces the lesser amount of product, so in this

case, H₃PO₄ is the limiting reactant.

Step 4. Use the limiting reactant to complete the problem.

Therefore, 40.0 g of H₃PO₄ will produce 13.7 L of CO₂ measured at standard temperature and pressure.

The same approach for finding limiting reactants can also be used in mass-mass or volume-volume problems.

22. If 20.0 g of NaOH react with 30.0 g of H₂SO₄ to produce Na₂SO₄, which reactant is limiting?

2NaOH(aq) + H₂SO₄(aq) à Na₂SO₄(aq) + 2H₂O(l)

23. If 5.00 g of copper metal react with a solution containing 20.0 g of AgNO₃ to produce silver metal, which reactant is limiting?

Cu(s) + 2AgNO₃(aq) à Cu(NO₃)₂(aq) + 2Ag(s)

24. What reactant is limiting if 3.00 L of Cl₂ at STP react with a solution containing 25.0 g of NaBr to produce Br₂?

25. If 20.0 g of KOH react with 15.0 g of (NH₄)2SO₄, calculate the L of NH₃ produced at STP.

26. Magnesium acetate can be prepared by a reaction involving 15.0 g of

iron(III) acetate with either 10.0 g of MgCrO₄ or 15.0 g of MgSO₄. Which

reaction will give the greatest yield of Mg(CH₃COO)₂? How many grams of Mg(CH₃COO)₂ will be produced?

2Fe(CH₃COO)₃(aq) + 3MgCrO₄(s) à3Mg(CH₃COO)₂(aq) + Fe₂(CrO₄)₃(s)

2Fe(CH₃COO)₃(aq) + 3MgSO₄(s) à 3Mg(CH₃COO)₂(aq) + Fe₂(SO₄)₃(s)

NONSTANDARD CONDITIONS

Gas volume changes dramatically when pressure or temperature change.

The molar volume is 22.4 L only at STP. If the experimental conditions are different from STP in a problem, it is still necessary to calculate the gas volume at STP.

The secret to success in these problems is to remember that the central step

(moles of given to moles of unknown) must take place at STP. Thus, if you are given a volume of gas at other than STP, you must convert to STP before performing the moles to moles step in the solving process. On the other hand, if you are requested to find the volume of a gas at conditions other than STP, you must convert the volume after the moles to moles step.

EXAMPLE

How many grams of ammonium sulfate must react with excess sodium hydroxide to produce 408 mL of ammonia measured at 27°C and 98.0 kPa?

Solving Process:

Write the balanced equation.

(NH₄)₂SO₄(s) + 2NaOH(aq) à Na₂SO₄(aq) + 2NH₃(g) + 2H₂O(l)

Convert 408 mL NH₃ at 27°C and 98.0 kPa to STP and then convert to g of

(NH₄)₂SO₄. Since the temperature decreases, the volume decreases and the absolute temperature ratio is

EXAMPLE

What volume of hydrogen collected over water at 27°C and 97.5 kPa is produced by the reaction of 3.00 g of Zn with an excess of sulfuric acid? The vapor pressure of water at 27°C is 3.6 kPa.

Solving Process:

Step 1. Write the balanced equation.

Zn(s) + H₂SO₄(aq) à ZnSO4(aq) + H₂(g)

Step 2. Convert from grams of Zn to liters of dry H2 at 27°C and 97.5 kPa. Then convert to liters of H₂ at STP by using the absolute temperature and pressure ratios.

Step 3. The liters of H₂ at STP must be converted to the conditions given in the problem. As the temperature is increased, the volume will increase, so

the absolute temperature ratio is

Step 4. As pressure is decreased volume will increase, so the pressure ratio is

This ratio must be corrected for the vapor pressure of water, which is

3.6 kPa at this temperature. The corrected ratio is

27. If 14.7 g of sodium peroxide (Na₂O₂) react with water to produce sodium hydroxide and oxygen gas, how many L of oxygen are produced at 22°C and 1.12 X 10⁵ Pa?

28. How many L of chlorine gas measured at 18.5°C and 98.0 kPa can be produced by the electrolysis of 62.3 g NaCl to give sodium metal and chlorine gas?

29. How many L of nitrogen measured at 21.5°C and 9.55 X 10⁴ Pa are required to react with excess calcium carbide, CaC₂, to produce 100.0 g of calcium cyanamid, CaCN₂, and carbon?

30. How many grams of iron metal must react with excess steam to produce 10.0 L of hydrogen collected over water at 20.0°C and 9.90 X 10⁴ Pa? The other product is iron(II,III) oxide, Fe₃O₄ (Fe₃O₄ is actually FeO ^. Fe₂O₃).

IDEAL GAS EQUATION

The ideal gas equation combines the four physical variables (pressure, volume, temperature, and number of particles) for gases into one equation. Remember that an ideal gas is composed of point masses that do not take up space, and these masses are not attracted to each other at all. All real gases deviate somewhat from the gas laws since the molecules of real gases are not point masses (they take up space) and they attract one another.

The ideal gas equation is PV = nRT, where P is the pressure in kilopascals. V

is the volume in cubic decimeters and T is the temperature in kelvin. The n represents the number of moles of a gas. With these units, the value of the constant R is 8.31 L ^. kPa/mol ^. K. There are other values of R depending upon the units used to derive R.

We can use the ideal gas equation to determine the molecular mass (M) of

a gas. The number of moles (n) of any species is equal to its mass (m) divided by the molecular mass (M). Thus, the ideal gas equation can also be written as follows.

How many moles of gas will a 1250-mL flask hold at 35.0°C and a pressure of 95.4 kPa?

Solving Process:

The ideal gas equation can be solved for the number of moles, n, of a substance.

Before we can substitute the known values into the ideal gas equation, 35.0°C must be converted to 308.2 K. We get the following expression.

The solution is 0.0466 mol. Note that all other units in the problem divide out.

EXAMPLE

A flask has a volume of 258 mL. A gas with mass 1.475 g is introduced into the flask at a temperature of 302.0 K and a pressure of 9.86 X 10⁴ Pa. Calculate the molecular mass of the gas using the ideal gas equation.

Solving Process:

The number of moles, n, of a substance is equal to mass, m, divided by the molecular mass, M. Therefore, the ideal gas equation may be written

Remember that the units of volume, pressure, temperature, and quantity of gas must be consistent with the value of R.

31. What is the molecular mass of sulfur dioxide, SO₂, if 300.0 mL of the gas has a mass of 0.855 g at STP?

32. A sample of hydrogen iodide, HI, has a mass of 2.28 g and occupies

400.0 mL at STP. What is the molecular mass of this compound?

33. If 0.179 g of methane, CH₄, occupy 0.250 L, what is the molecular mass of methane if the volume is given at standard conditions?

34. From the volume, temperature, and pressure, calculate the number of moles for each gas listed using the ideal gas equation.

a. 750.0 mL O₂ at 27°C and 99.0 kPa

b. 3.00 L CO₂ at -15°C and 103.0 kPa

35. Calculate the volume each gas will occupy under the conditions listed using the ideal gas equation.

a. 3.00 mol H₂ at 24°C and 100.5 kPa

b. 150.0 g Cl₂ at -12.5°C and 98.5 kPa

36. The density of a sample of phosphorus trifluoride, PF₃, is 3.90 g/L. What is the molecular mass of this gas at STP?

MASS PERCENTS

The mass percent of elements in a compound gives the relative amount of

each element present. The percent of an element in a compound is determined by the following equation.

To calculate mass percent:

(a) calculate the total mass for each element,

(b) calculate the formula mass for the entire compound,

(c) divide the total mass of each element by the formula mass of the compound, and

(d) multiply by 100%.

EXAMPLE

Find the mass percent of nitrogen in ammonium nitrate, NH₄NO₃, an important source of nitrogen in fertilizers.

Solving Process:

Calculate the formula mass; then find the percentage.

37. Calculate the mass percent of each element of the following compounds.

a. Fe₂O₃

b. Ag₂O

c. HgO

d. Na₂S

38. Determine the mass percent of sodium in sodium sulfate, Na₂SO₄.

39. Urea, CO(NH₂)₂, and ammonia, NH₃, are two compounds used as a source of nitrogen in fertilizers. Calculate the mass percent of nitrogen in each.

40. Calculate the percentage of each of the following in the compound sodium sulfate decahydrate, Na₂SO₄ ^.10 H₂O.

a. Na

b. S

c. O

d. H₂O

MOLECULAR AND EMPIRICAL FORMULAS

The empirical formula of a compound is the smallest whole number ratio

of the number of atoms of each element in the substance. The molecular formula gives the actual number of atoms in the molecule. For instance, CH₂ is the empirical formula for the series of molecular compounds C₂H₄, C₃H₆, C₄H₈, and so on.There is a definite relationship between the empirical and the molecular formula.

Note that the molecular formula is always a whole number multiple of the

empirical formula. As can be seen in Table 12-2 the empirical formula and the molecular formula are not always the same.

41. Write the empirical formula for each of the following.

a. C₆H₆ (benzene)

b. C₂H₂ (ethyne)

c. C₆H₁₂O₆ (glucose)

d. C₄H₁₀ (butane)

e. P₄O₁₀

f. SO₃

g. N₂O₄

h. NO₂

i. Ag₂C₄H₄O₆

j. K₂S₄

EMPIRICAL FORMULAS

Earlier, we used the formula of a compound to determine its mass percents.

Now we reverse the procedure and determine the empirical formula from the

mass percents. The elements in compounds combine in simple whole number ratios of atoms. To determine an empirical formula, masses of elements are converted to moles and then a ratio of moles is determined.

EXAMPLE

Determine the empirical formula for sodium sulfite. Sodium sulfite contains

36.5% sodium, 25.4% sulfur, and 38.1% oxygen.

Solving Process:

A percentage indicates a part of one hundred. Therefore, the percentage composition data indicates that there are 36.5 g Na, 25.4 g S, and 38.1 g O in 100 g of compound.

Step 1. Find the number of moles.

Step 2. Determine the ratio of moles.

EXAMPLE

What is the empirical formula of a compound that contains 53.73% Fe and

46.27% S?

Solving Process:

There are 53.73 g Fe and 46.27 g S in 100 g of compound.

Step 1. Find the number of moles.

In the previous example problem, the relative numbers of atoms were small

whole numbers and we could write the formula directly from them. The ratio 1 to 1.5 must be expressed in terms of whole numbers, since a fractional part of an atom does not exist. By multiplying both numbers in the ratio by two, we obtain two atoms Fe and three atoms S. The empirical formula is Fe₂S₃.

42. Calculate the empirical formula for compounds with the following compositions.

a. Fe 63.5%, S 36.5%

b. Mn 63.1%, S 36.9%

c. K 26.6%, Cr 35.4%, O 38.0%

43. Calculate empirical formulas for the following two compounds containing sodium, sulfur, and oxygen.

a. Na 32.4%, S 22.6%, O 45.0%

b. Na 29.1%, S 40.5%, O 30.4%

44. Calculate the empirical formulas for the following three iron ores.

a. Fe 77.7%, O 22.3%

b. Fe 72.4%, O 27.6%

c. Fe 70.0%, O 30.0%

MOLECULAR FORMULAS

The molecular formula indicates not only the ratio of the atoms of the elements in a compound but also the actual number of atoms of each element in one molecule of the compound.

The molecular formula calculation is the same as the empirical formula calculation, except that the molecular mass is used in an additional step. Remember, the molecular formula is always a whole number multiple of the empirical formula.

EXAMPLE

An organic compound is found to contain 92.25% carbon and 7.75% hydrogen.

If the molecular mass is 78 u, what is the molecular formula?

Solving Process:

Determine the empirical formula.

45. There are two oxides of phosphorus. Both oxides can exist in different forms depending on the temperature and the pressure. Calculate the empirical and molecular formulas from the following data.

a. P 56.4%, O 43.6%, molecular mass 220 u

b. P 43.7%, O 56.3%, molecular mass 284 u

46. The formula mass of a compound is 92 u. Analysis of the compound shows that there are 0.608 g of nitrogen and 1.388 g of oxygen. What is the molecular formula of this compound?

SECTION REVIEW

1. Molten iron and carbon monoxide are produced in a blast furnace by the reaction of iron(III) oxide and coke (carbon). If 25.0 kg of pure Fe₂O₃ are used, how many moles of iron can be produced?

2. Ammonia gas produced as a by-product in an industrial reaction can be reacted with sulfuric acid in order that the gas does not escape into the atmosphere. The product, ammonium sulfate, can be used as a fertilizer. Determine how many kilograms of acid are required to produce 1000.0 kg of (NH₄)₂SO₄.

3. Coal gasification is a process that is carried out industrially in a series of steps. The net reaction involves coal (carbon) reacting with water to form methane, CH₄, and carbon dioxide. How many kilograms of methane can be produced from 1.00 X 10³ kg of coal?

4. A source of acid rain is automobile exhaust. Nitric oxide, formed in an internal combustion engine, reacts with oxygen in the air to produce nitrogen dioxide. The NO₂ reacts with water to form nitric acid. It is determined that the average car produces 1.00 X 10⁴ L of exhaust gas per mile driven. Assume that the average concentration of NO₂ in auto exhaust is 0.10 ug/L and that traffic surveys have shown an average of 2.00 X 10⁶ vehicle miles driven per day. From this data, determine the kilograms of nitric acid that could be produced annually.

2NO₂ + H₂Oà HNO₂ + HNO₃

5. Photosynthesis is a complex process composed of many steps. The initial reactants are carbon dioxide and water and the final products are glucose and oxygen gas. If a plant needs to make 30.0 g of glucose, C₆H₁₂O₆, through the process of photosynthesis, how many grams of water are required?

6. One mole of He has a mass of 4.0026 g and 1.000 L of He (at STP) has a mass of 0.1787 g. Calculate the molar volume of helium.

7. What is the molecular mass of a gas if 5.75 g of the gas occupy a volume of 3.50 L? The pressure was recorded as 9.525 X 10⁴ Pa and the temperature is 52°C.

8. How many milliliters of hydrogen at STP are produced by the reaction of 0.750 g of sodium metal with excess water?

2Na(s) + 2H₂O(l) à 2NaOH(aq) + H₂(g)

9. What mass of magnesium will react with excess hydrochloric acid to produce 5.00 X 10² mL of H₂ at STP?

Mg(s) + 2HCl(aq) à MgCl₂(aq) + H₂(g)

10. When lead(II) sulfide is burned in air, lead(II) oxide and sulfur dioxide are produced. If 20.0 L of sulfur dioxide were produced, how many liters of oxygen gas were required to react with the lead(II) sulfide?

2PbS(s) + 3O₂(g) à 2PbO(s) + 2SO₂(g)

11. In a reaction involving carbon monoxide and iron(III) oxide, the products are iron metal and carbon dioxide. If 84.75 L of carbon dioxide are produced, how many L of carbon monoxide are required?

12. Hydrogen burns to give water. If 200.0 mL of H2 reacts with 150.0 mL of O₂, what volume of water vapor is produced? How many milliliters of gas remain unreacted and what gas remains? Assume that all volumes are measured at any given temperature above the normal boiling point of water.

13. How many grams of sodium hydrogen carbonate, NaHCO₃, must be heated to produce 2.50 L of carbon dioxide measured at 22.5°C and 97.5 kPa? The other products are sodium carbonate and water.

14. If 3.20 g of aluminum react with excess hydrochloric acid, how many mL of hydrogen collected over water at 20.0°C and 99.5 kPa are produced?

15. A sample of gas has a mass of 1.248 g and occupies 300.0 mL at STP. What is the molecular mass of this gas?

16. From the volume, temperature, and pressure data given, calculate the number of moles and the mass in grams for each gas listed using the ideal gas equation.

a. 2000.0 mL NH₃ at 10.0°C and 105.0 kPa

b. 5.00 L SO₂ at 21.0°C and 100.0 kPa

17. Calculate the volume each gas will occupy under the conditions listed using the ideal gas equation.

a. 5.00 mol CH₄ at 27.0°C and 97.2 kPa

b. 200.0 g NH₃ at 12.0°C and 104.5 kPa

18. The sugar substitute sodium benzosulfimide (sodium saccharin) has a sweetness of about 500 times that of sucrose. Calculate the percentage of sodium and carbon in the sweetener. Its formula is

19. Copper phthalocyanine is a complex organic molecule possessing a brilliant greenish blue color. Millions of pounds are produced yearly to color products such as plastics, automobile finishes, rubber goods, and printing inks.

Determine the percent carbon in copper phthalocyanine that has the formula Cu(C₈H₄N₂)₄.

20. Write the empirical formula for each of the following.

a. C₆H₁₄

b. CO₂

c. N₂F₄

d. C₃H₆Cl₂

e. C₅H₁₀O₂

f. P₃N₃Cl₆

21. Two compounds are analyzed and found to contain:

a. 0.89 g K, 1.18 g Cr, 1.27 g O

b. 1.03 g K, 0.69 g Cr, 0.84 g O

Determine the empirical formulas for these two compounds.

22. A fat is composed, in part, of long chains of carbon and hydrogen atoms. In a reaction with a strong base, a fat forms a soap and glycerol. What is the empirical formula of a fat containing 76.5% C, 11.3% O and 12.2% H, if it has a molecular mass of 847 u?

23. Citric acid, an organic acid found in lemons and other citrus fruits, contains 37.5% carbon, 58.3% oxygen, and 4.20% hydrogen. What is the empirical formula of citric acid if it has a molecular mass of 192 u?