What volume of ammonia, NH3, in liters at STP can be produced from 2.0 kg of hydrogen gas, H2, and an excess of nitrogen gas, N2? (N2 (g) + 3 H2 (g) → 2 NH3 (g))
A
74.6 L
B
22.4 L
C
149.2 L
D
44.8 L
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1
First, convert the mass of hydrogen gas (H2) from kilograms to grams. Since 1 kg = 1000 g, multiply 2.0 kg by 1000 to get 2000 g of H2.
Next, calculate the number of moles of hydrogen gas using its molar mass. The molar mass of H2 is approximately 2.02 g/mol. Use the formula: \( \text{moles of H2} = \frac{\text{mass of H2}}{\text{molar mass of H2}} \).
Using the balanced chemical equation \( \text{N}_2 (g) + 3 \text{H}_2 (g) \rightarrow 2 \text{NH}_3 (g) \), determine the mole ratio between H2 and NH3. From the equation, 3 moles of H2 produce 2 moles of NH3.
Calculate the moles of NH3 produced using the mole ratio. Use the formula: \( \text{moles of NH3} = \frac{2}{3} \times \text{moles of H2} \).
Finally, convert the moles of NH3 to volume at STP (Standard Temperature and Pressure). At STP, 1 mole of any gas occupies 22.4 liters. Use the formula: \( \text{volume of NH3} = \text{moles of NH3} \times 22.4 \text{ L/mol} \).