To solve the problem, we can use the ideal gas law and the mole ratio of the balanced chemical equation to determine the partial pressures of the gases at equilibrium, and then add them to obtain the total pressure.
First, we need to calculate the number of moles of each reactant:
n(H2) = 5.966 g / (2.016 g/mol) = 2.965 mol
n(C) = 22.44 g / (12.01 g/mol) = 1.869 mol
According to the balanced equation, the mole ratio of H2 to CH4 is 2:1. Therefore, the number of moles of CH4 produced at equilibrium is:
n(CH4) = n(H2) / 2 = 1.483 mol
Next, we can use the ideal gas law to calculate the partial pressures of the gases at equilibrium:
PV = nRT
For H2:
n = 2.965 mol
R = 0.0821 L·atm/(mol·K)
T = 1000 K
V = 9.75 L
P(H2) = nRT/V = 7.74 atm
For CH4:
n = 1.483 mol
R = 0.0821 L·atm/(mol·K)
T = 1000 K
V = 9.75 L
P(CH4) = nRT/V = 3.85 atm
Therefore, the total pressure at equilibrium is:
total = P(H2) + P(CH4) = 7.74 atm + 3.85 atm = 11.59 atm
For the second part of the question, we repeat the same process, but with a different amount of carbon:
n(H2) = 5.966 g / (2.016 g/mol) = 2.965 mol
n(C) = 8.006 g / (12.01 g/mol) = 0.666 mol
The mole ratio of H2 to CH4 is still 2:1, so the number of moles of CH4 produced at equilibrium is:
n(CH4) = n(H2) / 2 = 1.483 mol
Using the ideal gas law, we can calculate the partial pressures of the gases at equilibrium:
For H2:
n = 2.965 mol
R = 0.0821 L·atm/(mol·K)
T = 1000 K
V = 9.75 L
P(H2) = nRT/V = 7.74 atm
For CH4:
n = 1.483 mol
R = 0.0821 L·atm/(mol·K)
T = 1000 K
V = 9.75 L
P(CH4) = nRT/V = 3.85 atm
Therefore, the total pressure at equilibrium is:
total = P(H2) + P(CH4) = 7.74 atm + 3.85 atm = 11.59 atm
Note that the total pressure is the same as in the first part of the question, despite the different amount of carbon used. This is because the mole ratio of H2 to CH4 and the temperature are the same in both cases.