Consider a steel container filled with 40.0 g of helium gas and 40.0 g of argon gas. What is the ratio of pressures that each gas exerts (helium:argon)?
a) 1:1
b) 10:1
c) 1:10
d) 9:1

Question

Wyatt Atkins · Accepted Answer

The response is (10:1), b).

It's crucial to keep in mind that the partial pressures of the individual gases that make up a mixture are determined by how many moles each gas contributes to the total when working with gas mixtures.

In your situation, the partial pressures of the two gases can be expressed using the total pressure inside the container.

#P_("He") = chi_("He") * P_("total")# (1)

#P_("Ar") = chi_("Ar") * P_("total")# (2)

where #chi_("He")# is the mole fraction of the helium gas and #chi_("Ar")# is the mole fraction of the argon gas. The mole fraction of a gas is the ratio between the number of moles of that gas and the total number of moles present in the mixture.

Therefore, calculate the number of moles in the mixture using the molar masses of argon and helium.

#"40.0 g" * "1 mole He"/"4.00 g" = "10.0 moles He"#

#"40.0 g" * "1 mole Ar"/"40.0 g" = "1.00 mole Ar"#

This indicates that you will have a total mole count of

#n_("total") = n_("He") + n_("Ar") = 10.0 + 1.00 = "11.0 moles gas"#

For each of the two gases, the mole fractions will be

#chi_("He") = n_("He")/n_("total") = "10.0"/"11.0"#

#chi_("Ar") = n_("Ar")/n_("total") = "1.00"/"11.0"#

To obtain the desired pressure ratio, divide equation (1) by equation (2) in the end.

#P_("He")/P_("Ar") = chi_("He")/chi_("Ar") = ("10.0"/"11.0")/("1.00"/"11.0") = 10.0/11.0 * 11.0/1.00 = 10/1#

Peyton Adams · Answer

undefined The ratio of pressures that helium to argon gas exerts is:
c) 1:10

Consider a steel container filled with 40.0 g of helium gas and 40.0 g of argon gas. What is the ratio of pressures that each gas exerts (helium:argon)? a) 1:1 b) 10:1 c) 1:10 d) 9:1