The balanced chemical equation for the reaction is:
$$N_2 + 3H_2 \rightarrow 2NH_3$$
According to the equation, 1 mole of nitrogen reacts with 3 moles of hydrogen. Therefore, 0.1 mol hydrogen requires 1/3 moles of nitrogen to achieve complete reaction.
Using the ideal gas law, $$PV = nRT$$ where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature.
We can rearrange the equation to calculate the volume of nitrogen: $$V = \frac{nRT}{P}$$
Given:
- Temperature, $$T = 215 °C + 273 = 488 K$$ (Converting Celsius to Kelvin)
- Pressure, $$P = 715 mmHg = 715/760 = 0.941 atm (Converting mmHg to atm)$$
- Number of moles of nitrogen, $$n = \frac{1}{3} \times 0.1 = 0.033 mol$$
- Gas constant, $$R = 0.08206 L * atm / mol * K$$
Plugging in the values: $$V = \frac{(0.033 mol) \times (0.08206 L * atm / mol * K) \times (488 K)}{0.941 atm}$$ $$V \approx 1.14 L$$
Therefore, approximately 1.14 liters of nitrogen at 215 °C and 715mmHg would be required to react with 0.1 mol of hydrogen and produce ammonia.
