To determine the hydrogen gas pressure needed to react with 10.1 grams of nitrogen gas, we use the Ideal Gas Law and calculate that the pressure must have been 14.75 ATM in the 2.0-liter cylinder at 350 Kelvin.
To calculate the hydrogen gas pressure required in the cylinder, we must first determine the amount of hydrogen gas that would react with the given amount of nitrogen gas. Nitrogen gas (N₂) reacts with hydrogen gas (H₂) in the Haber process to produce ammonia (NH₃) according to the balanced equation:
N₂ + 3H₂ → 2NH₃
10.1 grams of N₂ is approximately 0.361 moles (molar mass of N₂ = 28 g/mol). From the balanced equation, we know that 1 mole of N₂ reacts with 3 moles of H₂. Therefore, 0.361 moles of N₂ would require 3*0.361 = 1.083 moles of H₂
To find the pressure of the hydrogen gas, we can use the Ideal Gas Law:
PV = nRT
Where: P is the pressure (in atmospheres, ATM), V is the volume (in liters, L), n is the number of moles of gas, R is the ideal gas constant (0.0821 L·atm/K·mol), and T is the temperature (in Kelvin, K).
Reorganizing the formula to solve for P, we get:
P = (nRT)/V
Now, substituting the values we have:
P = (1.083 moles * 0.0821 L·atm/K·mol * 350 K) / 2.0
P = 14.75 ATM (rounded to two decimal places)
Therefore, the hydrogen gas pressure in the cylinder must have been 14.75 ATM to react completely with the nitrogen gas.