The pressure in a vessel containing methane and water at 70^∘ C is 10 atm. At the given temperat

step 1 So methane is typically in the gas form, and so there should be very little liquid phase with th

The pressure in a vessel containing methane and water at...

The pressure in a vessel containing methane and water at $70^{\circ} \mathrm{C}$ is 10 atm. At the given temperature, the Henry's law constant for methane is $6.66 \times 10^{4}$ atm/mole fraction. Estimate the mole fraction of methane in the liquid.

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Key Concepts

Mole Fraction

Mole fraction is a way of expressing the concentration of a component in a mixture, defined as the ratio of the number of moles of the component to the total number of moles of all components. It is a dimensionless quantity and is particularly useful in problems involving gas-liquid equilibrium where proportional relationships like Henry's Law apply.

Henry's Law

Henry's Law states that, at a constant temperature, the amount of a gas dissolved in a liquid is directly proportional to the partial pressure of that gas in equilibrium with the liquid. This relationship is often expressed by the equation p = K_H * x, where p is the gas's partial pressure, K_H is the Henry's law constant, and x is the mole fraction of the gas in the liquid.

Henry's Law Constant

The Henry's law constant is a proportionality factor that relates the partial pressure of a gas to its mole fraction in a solution. Its value depends on the nature of both the gas and the solvent as well as the temperature. A larger constant indicates that a higher pressure is needed to dissolve a given amount of gas.

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