Question 5.6: When an experiment required a source of carbon dioxide, a st......
When an experiment required a source of carbon dioxide, a student combined 1.4 g of sodium bicarbonate (NaHCO_3) with excess hydrochloric acid. If the CO_2 produced is collected at 722 torr and 17°C, what volume will the gas occupy?
Strategy We are asked to find the volume of a gas, and we are given its pressure and temperature. We’ll assume that the gas behaves ideally. So if we knew the number of moles, we could easily use the gas law to get the volume we need. Looking a little closer, we should recognize this as a reaction stoichiometry problem because it asks us how much CO_2 will be produced. The new wrinkle here is that it asks us to express the answer as a volume rather than as a mass or a number of moles. So we will first do a stoichiometric calculation to find the number of moles of CO_2 produced and then use the gas law to find the volume of that amount of gas at the indicated temperature and pressure. As in any stoichiometry problem, we’ll need to start with a balanced equation for the reaction to be sure we use the correct mole ratio.
NaHCO_3 + HCl → NaCl + H_2O + CO_2
1.4\,{\mathrm{g}}\,{\mathrm{NaHCO_{3}}}\times{\frac{1\;{\mathrm{mol~NaHCO_{3}}}}{84.0\;{\mathrm{NaHCO_{3}}}}}\times{\frac{1\;{\mathrm{mol~CO}}_{2}}{1\;{\mathrm{mol~NaHCO_{3}}}}}=0.017\;{\mathrm{mol~CO_{2}}}
Now use the ideal gas law to solve for the volume. As always, we’ll need to remember to convert the temperature from °C to K and to be careful of pressure and volume units.
V=\frac{nRT}{P}={\frac{(0.017\mathrm{~mol})(0.08206\mathrm{~L~atm~mol}^{-1}\mathrm{~K}^{-1})(290\mathrm{~K})}{(0.95\mathrm{~atm})}}=0.42\mathrm{~L}=420\ \mathrm{mL}
Analyze Your Answer Our result of 420 mL is a relatively small volume—does this make sense? In this experiment, the reaction is similar to the one that occurs between baking soda and vinegar. Because 1.4 g of baking soda is not a large amount, it’s not surprising that the amount of gas generated is also small.
Check Your Understanding Suppose that 270 mL of CO_2 at 1.03 atm and 25°C is produced by this reaction. Assuming that an excess of hydrochloric acid was present, how many grams of sodium bicarbonate were used?