Question

For the isomerization reaction:
butane ⇌ isobutane
Kp equals 25 at 500°C. If the initial pressures of butane and isobutane are 5.0. atm and 0.0 atm, respectively, what are the pressures of the two gases at equilibrium?

Answer 1

you start out with 5.0atm of butane, and 0.0atm of isobutane. As the reaction proceeeds, some of the butane wil isomerize into isobutane, so the concentration of butane will decrease. Since it's an equilibrium, the isobutane will revert back to butane, and the rates of the reverse reaction will approach, and then equal, the rate of the forward reaction. Once equilibrium has been established, the ratio of K is:\[K_P = \frac{[isobutane]}{[butane]} = 25.0\] The mole ratio of the isomerisation is 1:1, so whatever the butane loses, the isobutane must gain. Some of the 5.00atm of butane will be lost, and the same amount of isobutane will have formed:\[K_P = \frac{[isobutane]}{[butane]} = \frac{[x]}{[5atm - x]} = 25.0\]Solve for x, which is the pressure of isobutane at equilibrium.