Final answer:
To find the mole fraction of gas B in a mixture, divide the partial pressure of gas B by the total pressure of the system.
Step-by-step explanation:
To calculate the mole fraction of gas B, we need to find the total pressure of the system first. Since the vessel is filled with two different gases, we can use Dalton's law of partial pressures. The partial pressure of gas A is 7.00 atm and the partial pressure of gas B is 5.89 atm. Adding these two pressures together, we get a total pressure of 12.89 atm.
To find the mole fraction of gas B, we divide the partial pressure of gas B by the total pressure. So, the mole fraction of gas B is 5.89 atm / 12.89 atm = 0.456.