Question 3.10: Urea [(NH2)2CO] is a by-product of protein metabolism. This ...
Urea [(NH2)2CO] is a by-product of protein metabolism. This waste product is formed in the liver and then filtered from the blood and excreted in the urine by the kidneys. Urea can be synthesized in the laboratory by the combination of ammonia and carbon dioxide according to the equation
2NH3(g) + CO2(g) → (NH2)2CO(aq) + H2O(l)
(a) Calculate the amount of urea that will be produced by the complete reaction of 5.25 moles of ammonia. (b) Determine the stoichiometric amount of carbon dioxide required to react with 5.25 moles of ammonia.
Strategy Use the balanced chemical equation to determine the correct stoichiometric conversion factors, and then multiply by the number of moles of ammonia given.
Setup According to the balanced chemical equation, the conversion factor for ammonia and urea is either
\frac{2 mol NH_{3}}{1 mol (NH_{2})_{2} CO} or \frac{1 mol (NH_{2})_{2} CO}{2 mol NH_{3}}
To multiply by moles of NH3 and have the units cancel properly, we use the conversion factor with moles of NH3 in the denominator.
Similarly, the conversion factor for ammonia and carbon dioxide can be written as
\frac{2 mol NH_{3}}{1 mol CO_{2}} or \frac{1 mol CO_{2}}{2 mol NH_{3}}
Again, we select the conversion factor with ammonia in the denominator so that moles of NH3 will cancel in the calculation.
(a) moles (NH2)2CO produced = 5.25 \cancel{mol NH_{3}} × \frac{1 mol (NH_{2})_{2} CO}{2 \cancel{mol NH_{3}}} = 2.63 mol (NH_{2})_{2}CO
(b) moles CO2 required = 5.25 \cancel{mol NH_{3}} × \frac{1 mol CO_{2}}{2 \cancel{mol NH_{3}}} = 2.63 mol CO_{2}