With an understanding of the ideal gas laws, it is now possible to apply these principles to chemical stoichiometry problems. For example, zinc metal and hydrochloric acid (hydrogen chloride dissolved in water) react to form zinc (II) chloride and hydrogen gas according to the equation shown below: 2 HCl (aq) + Zn (s) → ZnCl2 (aq) + H2 (g) A sample of pure zinc with a mass of 5.98 g is reacted with excess hydrochloric acid and the (dry) hydrogen gas is collected at 25.0 ˚C and 742 mm Hg. What volume of hydrogen gas would be produced? This is a “single state” problem, so we can solve it using the ideal gas law, PV = nRT. In order to find the volume of hydrogen gas (V), we need to know the number of moles of hydrogen that will be produced by the reaction. Our stoichiometry is simply one mole of hydrogen per mole of zinc, so we need to know the number of moles of zinc that are present in 5.98 grams of zinc metal. The temperature is given in centigrade, so we need to convert into Kelvin, and we also need to convert mm Hg into atm. Conversions: \[25.0\; C+273=298\; K \nonumber \] \[(742\; mm\; Hg)\times \left ( \frac{1\; atm}{760\; mm\; Hg} \right )=0.976\; atm \nonumber \] \[(5.98\; g\; Zn)\times \left ( \frac{1.00\; mol}{65.39\; g\; Zn} \right )=0.0915\; mol \nonumber \] Substituting: \[PV=nRT \nonumber \] \[(0.976\; atm)\times V=(0.0915\; mol)(0.0821\; L\; atm\; mol^{-1}K^{-1})(298\; K) \nonumber \] \[V=\frac{(0.0915\; mol)(0.0821\; L\; atm\; mol^{-1}K^{-1})(298\; K)}{(0.976\; atm)}=2.29\; L \nonumber \] We can also use the fact that one mole of a gas occupies 22.414 L at STP in order to calculate the number of moles of a gas that is produced in a reaction. For example, the organic molecule ethane (CH3CH3) reacts with oxygen to give carbon dioxide and water according to the equation shown below: 2 CH3CH3 (g) + 7 O2 (g) → 4 CO2 (g) + 6 H2O (g)
An unknown mass of ethane is allowed to react with excess oxygen and the carbon dioxide produced is separated and collected. The carbon dioxide collected is found to occupy 11.23 L at STP; what mass of ethane was in the original sample?
Because the volume of carbon dioxide is measured at STP, the observed value can be converted directly into moles of carbon dioxide by dividing by 22.414 L mol–1. Once moles of carbon dioxide are known, the stoichiometry of the problem can be used to directly give moles of ethane (molar mass 30.07 g mol-1), which leads directly to the mass of ethane in the sample. \[(11.23\; L\; CO_{2})\times \left ( \frac{1\; mol}{22.414\; L} \right )=0.501\; mol\; CO_{2} \nonumber \] Reaction stoichiometry: \[(0.501\; mol\; CO_{2})\times \left ( \frac{2\; mol\; CH_{3}CH_{3}}{4\; mol\; CO_{2}} \right )=0.250\; mol\; CH_{3}CH_{3} \nonumber \] The ideal gas laws allow a quantitative analysis of whole spectrum of chemical reactions. When you are approaching these problems, remember to first decide on the class of the problem:
Once you have isolated your approach ideal gas law problems are no more complex that the stoichiometry problems we have addressed in earlier chapters.
2 NaN3 (s) → 2 Na (s) + 3 N2 (g) What mass of sodium azide is necessary to produce the required volume of nitrogen at 25 ˚C and 1 atm?
2 Fe2O3(s) + 3 C (s) → 4 Fe (s) + 3 CO2 (g)
Zn (s) + 2 HCl (aq) → ZnCl2 (aq) + H2 (g) Recommended textbooks for you Introductory Chemistry For Today Chemistry: Matter and Change Author:Dinah Zike, Laurel Dingrando, Nicholas Hainen, Cheryl Wistrom Publisher:Glencoe/McGraw-Hill School Pub Co Introductory Chemistry: A Foundation Author:Steven S. Zumdahl, Donald J. DeCoste Publisher:Cengage Learning Chemistry: The Molecular Science Author:John W. Moore, Conrad L. Stanitski Publisher:Cengage Learning Chemistry for Engineering Students Author:Lawrence S. Brown, Tom Holme Publisher:Cengage Learning World of Chemistry, 3rd edition Author:Steven S. Zumdahl, Susan L. Zumdahl, Donald J. DeCoste Publisher:Brooks / Cole / Cengage Learning Introductory Chemistry For Today ISBN:9781285644561 Author:Seager Publisher:Cengage Chemistry: Matter and Change ISBN:9780078746376 Author:Dinah Zike, Laurel Dingrando, Nicholas Hainen, Cheryl Wistrom Publisher:Glencoe/McGraw-Hill School Pub Co Introductory Chemistry: A Foundation ISBN:9781337399425 Author:Steven S. Zumdahl, Donald J. DeCoste Publisher:Cengage Learning Chemistry: The Molecular Science ISBN:9781285199047 Author:John W. Moore, Conrad L. Stanitski Publisher:Cengage Learning Chemistry for Engineering Students ISBN:9781337398909 Author:Lawrence S. Brown, Tom Holme Publisher:Cengage Learning World of Chemistry, 3rd edition ISBN:9781133109655 Author:Steven S. Zumdahl, Susan L. Zumdahl, Donald J. DeCoste Publisher:Brooks / Cole / Cengage Learning |