The sum of the mole fractions of all components in a gas mixture equals what value?

• A. 1
• B. The total pressure
• C. The sum of partial pressures
• D. The sum of mole fractions equals 1

Answer: (D)

The key idea is how mole fraction is defined. For each component, the mole fraction xi is the number of moles of that component ni divided by the total moles in the mixture N, where N = sum ni. If you add up all the xi, you get sum xi = (sum ni)/N = N/N = 1. So, the total of all mole fractions must equal 1, regardless of the mixture’s composition.

For example, if a mixture has 2 moles of gas A and 3 moles of gas B, their mole fractions are 2/5 = 0.4 and 3/5 = 0.6, which add up to 1. Mole fractions are dimensionless and always lie between 0 and 1.

This is distinct from the total pressure or partial pressures: the partial pressure of each component is Pi = xi Ptotal, and the sum of all Pi equals the total pressure, not the sum of the mole fractions.