Final answer:
To find the equilibrium pressure of hydrogen gas, we set up an ICE table based on the reaction between H2O and C. Using the equilibrium constant Kp, we solve for the change in pressure, x, to determine the equilibrium pressures of H2 and CO at 315 K.
Step-by-step explanation:
To calculate the pressure of hydrogen gas (H2) at equilibrium, we can utilize the given equilibrium constant (Kp) and initial conditions. The initial pressures of the reactants are given, and we can assume that the carbon solid (C) does not affect the pressure directly because it's not a gas. We start by writing down the balanced chemical equation:
H2O(g) + C(s) ⇌ H2(g) + CO(g)
The equilibrium constant expression is:
Kp = (P_H2 * P_CO) / (P_H2O)
Where P_H2O, P_H2, and P_CO are the partial pressures of water, hydrogen, and carbon monoxide at equilibrium, respectively. We can use an ICE table to visualize the changes in pressure that occur as the reaction proceeds towards equilibrium:
- Initial: P_H2O = 2.00 atm, P_H2 = 0 atm, P_CO = 0 atm
- Change: P_H2O decreases by x atm, P_H2 increases by x atm, P_CO increases by x atm
- Equilibrium: P_H2O = 2.00 atm - x, P_H2 = x atm, P_CO = x atm
According to the Kp expression:
95.8 = (x * x) / (2.00 - x)
Now we can solve this quadratic equation for x, which represents the equilibrium pressure of H2 and CO (since they are produced in a 1:1 ratio). Many high school students are familiar with the general method for solving quadratic equations and can carry out the algebraic steps to find the value of x. Remember that the quadratic equation has the general form ax^2 + bx + c = 0, and you can use the quadratic formula to solve for x. However, since the value of Kp is much greater than the initial pressure of H2O, we can approximate that x is much smaller than 2.00 atm and thus ignore x in the denominator. This simplification makes the math easier and is a common approach when dealing with large equilibrium constants.
By simplifying and solving for x, we find the approximate equilibrium pressures of H2 and CO. Please note that 20.0 g of carbon is in excess, ensuring the reaction can proceed to produce H2 gas until equilibrium is reached.