Question

Ammonium sulfate, an important fertilizer, can be prepared by the reaction of ammonia with sulfuric acid accordingto the following balanced equation: ___ NH3 (g) + ___ H2SO4 → ___ (NH4)2SO4 (aq) a. Calculate the volume of NH3 needed at 24oC and 25 atm to react with 1500 g of H2SO4.

Answer 1

The first step to solve this question is to balance the given equation:

$2NH_3+H_2SO_4\rightarrow(NH_4)_2SO_4$

The next step is to convert the mass of H2SO4 to moles, using the molar mass of H2SO4 (98g/mol).

$1500gH_2SO_4\cdot\frac{molH_2SO_4}{98gH_2SO_4}=15.3molH_2SO_4$

Now, use the stoichiometric ratio given by the reaction to define how many moles of NH3 react with 15.3 moles of H2SO4:

$15.3molH_2SO_4\cdot\frac{2molNH_3}{1molH_2SO_4}=30.6molNH_3$

Finally, use the ideal gas law to determine the volume of the gas at 24°C (297.15K) and 25atm:

$\begin{gathered} PV=nRT \\ V=\frac{nRT}{P} \\ V=\frac{30.6mol\cdot0.082atmL/molK\cdot297.15K}{25atm} \\ V=29.82L \end{gathered}$

The volume of NH3 needed is 29.82L.