A mixture of helium, neon, and xenon gases is made with the same mass of each gas. Which (if any) gas will have the highest partial pressure?

a. They will all have the same partial pressure

b. Xe

c. He

d. Ne

Xe will have the highest partial pressure

Explanation:

Using Dalton's law of partial pressures for ideal gases

p=P*x

where

p = partial pressure, P = total pressure and x = mole fraction = n / ∑n

since the number of moles is related with mass through

n = m/M

where

m = mass and M = molecular weight

then if m is the same for all the gases

x = m*M / ∑ (m*M) = m*M / m∑ M = M/∑ M

thus

p=P*x = P*M / ∑ M

for the 3 gases

p₁=P*x₁ = P*M₁ / (M₁+M₂+M₃)

p₂=P*x₃ = P*M₂ / (M₁+M₂+M₃)

p₂=P*x₃ = P*M₃ / (M₁+M₂+M₃)

then for gasses under the same pressure (P=constant) and same mass (m=constant), p is higher when the molecular weight is higher. Therefore Xe will have the highest partial pressure

He

Explanation:

The partial pressure of a gas is given by mole fraction of the gas multiplied by the total pressure of the gas. The mole fraction of each gas is the number of moles of that gas divided by the total number of moles present. The number of moles of each gas depends on its relative atomic mass since they are all of the same mass. The smaller the relative atomic mass, the greater number of moles of a gas and the greater mole fraction of that gas and the greater its partial pressure. Hence, helium is the lightest gas in the list hence it will have the highest partial pressure.