Answer to Question #294686 in General Chemistry for abby

Question

The Haber process is used to synthesize ammonia (NH₃) on a large scale by the reaction of nitrogen gas with hydrogen gas as follows:

N_2 (g)  + 3 H_2 (g)  → 2 NH_3 (g)

 

Consider a reaction between a 6.79 L flask containing nitrogen gas and a 14 L flask of hydrogen gas. Both gases have a temperature of 281 K and the pressures inside both flasks is 0.88 bar.

What mass of ammonia (in g) would you expect to be produced at temperature 281 K and a pressure of 0.88 bar? 

Answer 1

Avogadro's law states: equal volumes of all gases, at the same temperature and pressure, have the same number of molecules.

It means that at the same temperature and pressure 7.89 L of nitrogen needs 7.89*3 = 23.67 L of hydrogen according to the equation. We have less hydrogen, so it is a limiting reagent. Find the volume of ammonia we can obtain from 16.4 L of hydrogen:

$V(NH_3) = 16.4*2/3 = 10.9 L$

The combined gas law states:

$PV =mRT/M$, where R = gas constant (8.314*10^-2 L*bar*K^-1*mol^-1), M -- molar mass (17 g/mol)

Find m:

$m = MPV/RT = 17 * 0.86 * 10.9*100/(8.314*295) = 6.5 (g)$

Answer: 6.5 g of ammonia would be expected to be produced at temperature 295 K and a pressure of 0.86 bar