Question 3.11: Nitrous oxide (N2O), also known as “laughing gas,” is common...
Nitrous oxide (N2O), also known as “laughing gas,” is commonly used as an anesthetic in dentistry. It is manufactured by heating ammonium nitrate. The balanced equation is
NH_{4}NO_{3}(s) \xrightarrow{\Delta} N_{2}O(g) + 2H_{2}O(g)
(a) Calculate the mass of ammonium nitrate that must be heated in order to produce 10.0 g of nitrous oxide. (b) Determine the corresponding mass of water produced in the reaction.
Strategy For part (a), use the molar mass of nitrous oxide to convert the given mass of nitrous oxide to moles, use the appropriate stoichiometric conversion factor to convert to moles of ammonium nitrate, and then use the molar mass of ammonium nitrate to convert to grams of ammonium nitrate. For part (b), use the molar mass of nitrous oxide to convert the given mass of nitrous oxide to moles, use the stoichiometric conversion factor to convert from moles of nitrous oxide to moles of water, and then use the molar mass of water to convert to grams of water.
Setup The molar masses are as follows: 80.05 g/mol for NH4NO3, 44.02 g/mol for N2O, and 18.02 g/mol for H2O. The conversion factors from nitrous oxide to ammonium nitrate and from nitrous oxide to water are, respectively:
\frac{1 mol NH_{4}NO_{3}}{1 mol N_{2}O} and \frac{2 mol H_{2}O}{1 mol N_{2}O}
(a) 10.0 \cancel{g N_{2}O} × \frac{1 mol N_{2}O}{44.02 \cancel{g N_{2}O}} = 0.227 mol N_{2}O
0.227 \cancel{mol N_{2}O} × \frac{1 mol NH_{4}NO_{3}}{1 \cancel{mol N_{2}O}} = 0.227 mol NH_{4}NO_{3}
0.227 \cancel{mol NH_{4}NO_{3}} × \frac{80.05 g NH_{4}NO_{3}}{1 \cancel{mol NH_{4}NO_{3}}} = 18.2 g NH_{4}NO_{3}
Thus, 18.2 g of ammonium nitrate must be heated in order to produce 10.0 g of nitrous oxide. (b) Starting with the number of moles of nitrous oxide determined in the first step of part (a),
0.227 \cancel{mol N_{2}O} × \frac{2 mol H_{2}O}{1 \cancel{ mol N_{2}O}} = 0.454 mol H_{2}O
0.454 \cancel{mol H_{2}O} × \frac{18.02 g H_{2}O}{1 \cancel{mol H_{2}O}} = 8.18 g H_{2}O
Therefore, 8.18 g of water will also be produced in the reaction.