A chemical equation is a statement of experimental fact. It gives on the side the reactants and on the right side the products of the reaction. Because no atoms are produced or destroyed in a nonnuclear chemical reaction, the equa-tion must be so balanced that every atom originally present in the reactants is accounted for in the products. This means that the combined weight of the reaction products is exactly equal to the combined weight of the original reactants.
All of the important stoichiometric calculations that relate the weights and volumes of starting materials to the weights and volumes of products typically involve just three simple steps.
Find how many moles correspond to the given quantity of some sub-stance in the reaction.
2. Use the balanced chemical equation to find, from the number of moles of the given substance, the number of moles of the substance sought in the calculation.
3. Convert the number of moles of the substance sought to the units requested in the statement of the problem.
three steps are illustrated in the following problems.
174 Stolchlometry II: Calculations Based on Chemical Equations
PROBLEM:
Oxygen is prepared by heating
(a) What weight of is obtained from 3.00 g
(b) What is the volume of measured at standard conditions?
(c) What volume does the occupy if collected over water at 730 and
SOLUTION:
The first step is to write the balanced equation for the reaction (if it is not given).
This step requires knowledge of the experimental facts. We note in the text that, when is decomposed by heating, the products are and so we start with the unbalanced equation
KCl +
(The A symbol indicates that heating is necessary.) To account for the three moles of oxygen atoms in we need moles of in the products:
KCl +
This is now a balanced equation, but we prefer to eliminate fractional numbers of moles, so we multiply all terms by 2, getting the final equation
2KC1 +
We now examine the problem, asking two questions: (a) what is given, and (b) what is sought? We see (a) that the weight of used is given, and (b) that we seek the amount of produced. We then proceed with the three steps listed earlier.
From the weight of given, compute the number of moles that are given.
Moles of given =
122.6 mole
2. From the moles of given, compute the number of moles of pro-duced. The chemical equation shows that 3 moles of are produced from 2 moles of Therefore,
Moles of produced = (
= 0.0368 moles
3. From the moles of produced, express the amount of in the units specified in the statement of the problem, as follows.
(a) Weight of = (0.0368 moles 32.0
=
(b) The volume of will be given by the ideal gas law (see p 159). For standard conditions, T = 273.2 K and P = 760.0 torr, so
Calculations Based on Chemical Equations 175
(0.0368 moles) (273 K)
\ /
760
0.825 liters at standard conditions
(c) The volume of will again be given by the ideal gas law, but the partial pressure of must be used (not the combined pressures of and water vapor). The partial pressure of is calculated from law, using the vapor pressure of (24 torr) from Table
= 730 torr - 24 torr = 706 torr
(0.0368 K)
P 706 torr
= 0.969 liters
PROBLEM:
Chlorine is prepared by the reaction
+ lONaCl + + + +
or
+ IOC1- + + +
What weights of (a) pure NaCl and (b) 90.0% pure are needed to prepare 500 ml of gas measured dry at 25°C and 730 torr?
SOLUTION:
We follow the three simple steps.
From the volume of that we are given (to compute the moles of that are given, using the ideal gas equation.
PV (730 liter) =
mole K
= 0.0196 moles given
2. From the moles of given, compute the number of moles of NaCl and required. The chemical equation shows that moles of NaCl and 2 moles of are required for 5 moles of therefore the needed
j (0.0196 moles = 0.0392 moles 10 moles
5 moles
moles of = (0.0196 moles = 0.00784 moles
3. From the moles of NaCl and required, express these quantities in the units specified in the statement of the problem.
176 II Based on Chemical Equations
(a) Weight of pure = (0 0392 moles 5
= 2 29 g NaCl
(b) If x = the required grams of 90 0% pure you can see that 0 g must contain 0 00784 moles of That
0 g = ( 00784 moles 141 9
= 1 g pure
mole
x = = 1 23 g impure
PROBLEM:
(a) What volume of oxygen at 20°C and 750 needed to burn 3 00 liters of propane, also at and 750
(b) What volume of 0% by volume) would be required under the same The products of combustion are solely and
SOLUTION:
First, you must have a balanced chemical equation on to base your calcula-tion Because the three C atoms of are converted to and the 8H atoms are converted to you can readily see that the 10 oxygen atoms needed
much and must come from Therefore,
+ +
Second, you must realize that, when the two substances you are interested are both gases you can make a much simpler calculation than that involved the
"three simple steps You recall (see p 160) that equal volumes of gases under the same conditions of temperature and pressure contain the same number of moles (or molecules) The chemical equation shows that you need 5 moles of per mole of you need 5 times the volume of as the volume of under the same conditions Therefore,
(a) Volume of = ( (3 00 liters
\ 1 mole
= liters of
(b) If V = the required volume of (also a gas) that 0% you can see that 0 210V liters of must provide 15 0 liters of That
0 210V = 15 0 liters
V = liters of
Based on Equations 177
PROBLEM:
Sulfur dioxide is prepared by heating iron pyrites, in the presence of air. The reaction is
+ +
(a) How many tons of can be obtained from 20.0 tons of
(b) What volume of air, in cubic feet at 0.90 and 77°F, is required for the
SOLUTION:
First, you need to know that it is not necessary to convert tons to grams to moles, and then at the end reconvert moles to grams to tons. You recall that the atomic weight scale (inside back cover) is a relative atomic weight scale habitually used with gram as the mass unit. For problems like this where tons (or or oz, or whatever) are involved, it is easier to use ton as the mass unit and to use ton molecular weights (ton-moles) instead of gram molecular weights (moles). We still use the three-step approach.
From the weight of given, compute the number of ton-moles that are given.
Ton-moles of given = = ton-moles
I20.0
ton-mole
2. From the ton-moles of given, compute the number of ton-moles of produced and the ton-moles of required. The chemical equation shows that 8 ton-moles of are produced and ton-moles of are required for every 4 ton-moles of Therefore,
8 ton-moles \
ton-moles of SO, produced = ton-moles
ton-moles
= 0.333 ton-moles
ton-moles of required = ton-moles
ton-moles
= 0.458 ton-moles
3. From the ton-moles of produced, express the amounts of in the units specified in the statement of the problem.
(a) Weight of = (0.333 ton-moles ' ° ton-mole
= 21.3 tons produced
(b) The volume of (or air) must be calculated from the ideal gas equation, where the gas constant R is always on a per basis (that is, a
basis). The simplest approach in this case is to first convert 0.458 ton-moles of to gram moles (just plain moles), and then use the ideal gas equation.
178 Calculations Based on Chemical Equations
Moles of = (0 458 moles
ton-mole
= 4 16 x 10° moles
The ideal gas equation the liters of at the specified conditions
= 25°C, and 0 9 = 0 9 x 760 = 684 (4 16 x moles) 4
_ __ mole K _
P 684 torr
= 1 13 x liters of pure
If = volume of (21 0% by volume) that required, then 0 must provide 1 13 x liters of pure
= 3 99 x of pure
X = = 1 90 x of
PROBLEM:
A 0 2052 g mixture of copper and aluminum analyzed for the percentage of aluminum by adding an excess of and collecting the evolved over water (Copper not react The volume of collected 229 ml at a barometric pressure of 732 torr The temperature 29°C Calculate the percentage of aluminum the original The chemical reaction
2A1 + +
or + +
SOLUTION:
We follow the standard three simple steps ' to find, from the given amount of how much must be present At the end, amount of stated terms of how much sample was used (that the % purity of the sample)
1 From the volume of given (produced), compute the number of moles of that are produced, by using the gas equation The pressure must be corrected for the vapor pressure of water (30 torr at 29°C, from Table
PV (732 torr - 30 2295 liter) 4
mole
= 8 55 x 10 moles H2
Problems A
2. From the moles of produced, calculate the number of moles of that must have been present. The chemical equation shows that 2 moles of Al are required for 3 moles of
moles of Al = )
moles
= 5.70 x moles of Al in original sample 3. From the moles of Al present, calculate the weight of Al present. From
the weight of Al present, then calculate the percentage the original sample.
Weight of Al present = (5.70 x moles Al) 0 mole
= 0.1539 g Al
% Al present = x 100 = 75.0% Al (0.2052 g sample)
All of these illustrative problems have been worked in the three distinct steps, in order to emphasize the reasoning involved. With a little practice, you can combine two or three of these steps into one operation (or set-up), greatly increasing the efficiency in using your calculator.
PROBLEMS A
1. Balance the following equations, which show the starting materials and the reaction products. It is not necessary to supply any additional reactants or products. A A sign indicates that heating is necessary.
(a) +
(b) PbO + +
(c) Na + NaOH +
(d) Fe + +
(e) + +
+ Fe +
(g) + NaOH
(h) + HC1 + +
(i) Zn + +
Cu + + +
(k) + + +
(1) + NaOH + +
180 Stoichlometry II Calculations Based on Chemical Equations
2 Some common gases may be prepared the laboratory using reactions rep-resented by the following balanced equations A A indicates that heating necessary For purity, must be swept out of the apparatus before the gas collected, and some gases must be dried a suitable
FeS + 2HC1 +
(b) How many tons of limestone are needed to prepare 5 00 tons of dry assuming that 30% of the produced wasted converting to the
(c) How many grams of and CaO are needed to make 0 100 mole of (d) How many grams of 95% pure NaCl are needed to produce 2 00 of
(e) What volume commercial by weight, density = 1
and what weight of limestone (90% pure) are needed to produce 2 00 kg of Commercial sulfunc that has a density of 1 84 and 95%
by weight used for the production of HCl What weight of com-mercial needed for the production of 365 g of What volume of needed for the production of 365 g of
(g) Commercial that has a density of 1 45 g/ml and 55 1%
by weight used for the production of What weight and volume of commercial are needed for the production of 50 0 g of (h) A manufacturer supplies 1 cans of calcium carbide whose purity
labeled as 85% How many grams of acetylene can be prepared from 1 00 of product the label
A whipped cream manufacturer wishes to produce 500 of for her chain of soda fountains What the cost of the necessary and
they cost $840 and $1230 per ton,
0) A 0 795 g sample of impure limestone tested for purity by adding (instead of HCl as shown the second equation) After the generated gas
passed over to dry passed over soda (a mixture of sodium and calcium hydroxides), which absorbs the The soda-lime tube increases weight by 0 301 g What the percentage of
the original
(k) The purity of a 0 617 g sample of impure FeS tested by passing the produced by the HCl (as the first equation) a dilute solution of
The precipitate of filtered off, washed, and gently dned
A 181
The weight of the produced is 1.322 g. How pure was the original sample of FeS?
3. How many grams of zinc are needed to prepare 3.00 liters of hydrogen at standard conditions? The reaction is
Zn + +
4. (a) How many grams of zinc are needed to prepare 3.00 liters of collected over water at 750 torr and
(b) How many moles of are used?
5. What volume of at 730 torr and 25°C will react with 3.00 liters of at the same conditions?
6. What volume of steam at and 1 atm is needed to produce 10s of under the same conditions, by the reaction
+ 3Fe +
7. What volume of at 730 torr and is needed to react with 7.00 g of sodium metal by the reaction
2Na + 2NaCl
8. (a) How many grams of are needed to prepare 5.00 liters of at 750 torr and 27°C?
(b) How many moles of HC1 are needed for the reaction? The reaction is
+ 4HC1 + +
9. How much gas at 725 torr and 25°C is needed to react with the copper in 1.5 g of The reaction is
+ CuS +
10. (a) What volume of at 730 torr and is needed to burn 500 g of octane, (b) What volume of air (21% by volume) is needed to provide this amount
of Balance the equation before working the problem.
+ +
Chlorine is prepared by the reaction
+ + + +
(a) What weight of is needed to prepare 2.50 liters of at standard conditions?
(b) How many moles of HC1 are used?
(c) What volume of solution is needed if there are 12.0 moles of HC1 per liter?
(d) What weight of is obtained from the reaction?
12. Nitric oxide is prepared by the reaction
1: 3Cu + +
182 II: Calculations Based on Chemical Equations
(a) What weight of copper and (b) how many moles of are needed to prepare 500 ml NO, measured over water at 730 and
(c) If the nitric acid solution contains 10.0 moles/liter, what volume of the solution is used?
13. Arsenic compounds may be detected easily by the Marsh test. In this test, some metallic zinc is added to an acid solution of the material to be tested, and the mixture is heated. The arsenic is liberated as arsine, which may be decomposed by heat to give an "arsenic mirror." The reaction is
4Zn + + 8HC1 + +
What volume of at 720 torr and is evolved by 7.00 x g of arsenic, the smallest amount of arsenic that can be detected with certainty by this method?
14. gas will cause immediate unconsciousness at a concentration of 1 part per 1000 by volume. What weight of FeS is needed to fill a room 20 ft x 15 ft x 9 ft with at this concentration? Barometric pressure is 740 torr, and the tem-perature is 80°F. The reaction is
FeS + 2HC1 +
15. The Mond process separates nickel from other metals by passing CO over the hot metal mixture. The nickel reacts to form a volatile compound (called nickel carbonyl), which is then swept away by the gas stream. The reaction is
Ni + 4CO
How many cubic feet of CO at atm and needed to react with 1.00 ton of nickel?
16. A cement company produces 100 tons of cement per day. Its product contains 62.0% CaO, which is prepared by calcining limestone by the reaction
CaO +
What volume of at 735 torr and 68°F is sent into the air around the plant each day as a result of this calcination?
17. The Ostwald process of making involves the air oxidation of over a platinum catalyst. The first two steps in this process are
+ + 4NO
+
How many cubic feet of air (21% by volume) at and 1.00 atm are needed for the conversion of 50.0 tons of to by this process?
18. How many cubic feet of air (21% by volume) are needed for the production of at the same conditions as those used to measure the air? (See Problem 17 for the equations involved.)
19. The du Pont company has developed a nitrometer, an apparatus for the rapid routine analysis of nitrates, which measures the volume of NO liberated by
Problems B 183
the reaction of concentrated with nitrates in the presence of metallic mercury, by the reaction
+ + 3Hg + + + 2NO
In a simple form of this apparatus, the NO is collected over water in a grad-uated tube and its volume, temperature, and pressure are measured. A g sample containing a mixture of and is treated in this manner, and 37.50 ml of NO is collected over water at a temperature of 23°C and a pressure of 732.0 torr. Calculate the percentage of in the original sam-ple.
20. A commercial laboratory wished to speed up its routine analysis for in a mixture of acids, using the nitrometer mentioned in Problem 19. To do this, it collects the NO over mercury, uses enough concentrated to make correction for water vapor thermostats its graduated tube at and takes all pressure measurements at 730.0 torr. The tube is grad-uated to 100.0 ml. What weight of original acid sample should always be taken so that the buret reading under these conditions also indicates directly the percentage of in the original sample?
In the Dumas method for measuring the total nitrogen in an organic com-pound, the compound is mixed with CuO and heated in a stream of pure All the gaseous products are passed through a heated tube of Cu turnings, to reduce any oxides of nitrogen to and then through a solution of to remove the and water. The is not absorbed, and its volume is measured by weighing the mercury (density = 13.56 that the dis-places from the apparatus.
(a) A sample of a mixture of glycine, and benzoic acid, yields at 730 torr and This 5.235 g of mercury. Calculate the percentage of glycine in the original mixture.
(b) A 4.71 mg sample of a compound containing C, H, (), and N is subjected to a Dumas nitrogen determination. The at 735 torr and 27°C, dis-places 10.5532 g of mercury. A carbon-hydrogen analysis shows that this compound contains H and C. Determine the empirical formula of this compound.
PROBLEMS B
22. Balance the following equations, which show the starting materials and the reaction products. It is not necessary to supply any additional reactants or products. A A sign indicates that heating is necessary.
(a) +
184 II: Calculations Based on Chemical Equations
23. Some common gases may be prepared in the laboratory by reactions rep-resented by the following equations. A A sign indicates that heating is neces-sary. For purity, air must be swept out of the apparatus before the gas is collected, and some gases must be dried with a suitable desiccant.
+ + +
(b) How many moles of pyrolusite, are needed to prepare 100 g of ( H ) 2.60 moles of
(c) How many pounds of sand, are needed to prepare 10.0 of assuming that 25% of the sand is inert material and does not produce (d) How many grams of sodium formate, HCOONa, are needed to make
0.250 mole of CO?
(e) How many pounds of aluminum hydroxide are produced along with 12.0 moles of
How many moles of are needed to prepare 1.33 moles of by the sixth reaction?
(g) How many grams of 90% pure (sodium peroxide) are needed to prepare 2.50 of
(h) Commercial sulfuric acid that has a density of 1.84 g/ml and is 95%
by weight is used for the production of CO by the fifth reaction. What weight of commercial acid is needed for the production of 560 g of CO? What volume of acid is needed for the production of 560 g of CO?
(i) What volume of commercial HC1 (36% HC1 by weight, density = g/ml) and weight of pyrolusite (85% are needed to produce 5.00 kg of by the second reaction?
(j) Commercial sulfuric acid that has a density of 1.52 g/ml and is 62%
by weight is used for the production of by the first reaction. What
Problems B 185
weight and volume of commercial are needed for the produc-tion of 720 g of
(k) Assume that an excess of metallic aluminum added to a solution contain 100 g NaOH, and that as a result the NaOH used up When the reaction complete, the excess aluminum metal filtered off and the excess water evaporated How many grams of are
24 How many grams of aluminum are needed for the preparation of 5 50 liters of at standard The reaction
2A1 + +
25 What weight of needed for the preparation of 5 00 moles of The reaction
+ + +
26 What volume of at 0 90 and 75°F needed to burn 21 0 liters of propane gas, under the same The reaction
+ +
27 What volume of NO can react 100 liters of 0% by volume) at the same conditions of temperature and pressure The reaction
+
28 An interesting lecture demonstration the Vesuvius ' experiment, which a small mound of heated to commence decomposition It then continues decomposition unaided, gives off heat light and sparks, and
leaves a of The
+ +
What volume of at 730 and produced from 1 60 moles of
29 What volume of at 720 torr and needed for the precipitation of the bismuth 50 0 g of The reaction
+ + 6HC1
30 What volume of at 740 torr and 20°C needed to precipitate the nickel
30 What volume of at 740 torr and 20°C needed to precipitate the nickel