Question 70147

May 14, 2015

The mole fraction will be 0.78 and the mole percent will be 78%.

So, you have a mixture of various different gasses, all located inside the same container and under the same conditions for pressure and temperature.

This tells you that you can use the ideal gas law equation, $P V = n R T$, to determine the total number of moles present in the container.

$P V = n R T \implies n = \frac{P V}{R T}$

${n}_{\text{total" = (786/760cancel("atm") * 1cancel("L"))/(0.082(cancel("atm") * cancel("L"))/("mol" * cancel("K")) * (273.15 + 25)cancel("K")) = "0.0423 moles}}$

SIDE NOTE Do not forget to convert pressure to atm and temperature to K!

Since you know the mass of nitrogen gas you're dealing with, you can use its molar mass to determine how many moles of nitrogen can be found in the container

M_M = m/n = (0.925cancel("g"))/(28.0134cancel("g")/"mol") = "0.0330 moles" ${N}_{2}$

The mole fraction of a gas is defined s the ratio between the number of moles of that gas and the total number of moles present in the container. This means that you have

chi_(N_2) = n_(N_2)/n_"total" = (0.0330cancel("moles"))/(0.0423cancel("moles")) = color(green)(0.78)

The mole percent is simply the mole ratio multiplied by 100

"%"N_2 = chi_(N_2) * 100 = 0.78 * 100 = color(green)(78%)#

SIDE NOTE I left the answers with two sig figs, despite the fact that you only gave one sig fig for the volume of the container.