A scuba diver breathes a mixture of oxygen and helium $($called heliox$)$ at a depth of $100m,$

where the total pressure is $11\mathrm{.}0$atm. The partial pressure of oxygen in the mixture is $0\mathrm{.}21$atm,

which is the same as in air at sea level. Assume that the temperature is constant at $25C.$

$($a$)$ What is the molar volume of the heliox mixture at $100m$ depth, according to the ideal gas

law and the van der Waals equation of state? Use the following values for the van der Waals

constants: $a{O}_2=1\mathrm{.}364L^2$ atm mo${}^{}$l-2,bO2=0.0319Lmol-1, aHe $=0\mathrm{.}0341L^2$ atm $mo{l}^{-2},$ and

bHe $=0\mathrm{.}0238Lmo{l}^{-1}.$ Hint: you can find effective van der Waals constants for the mixture using

$b_{\text{m}\text{i}\text{x}}={\displaystyle \underset{i}{\overset{?}{}}}{x}_i{b}_i$ and $a_{\text{m}\text{i}\text{x}}={\displaystyle \underset{i}{\overset{?}{}}}{\displaystyle \underset{j}{\overset{?}{}}}{x}_i{x}_j\sqrt[\phantom{2}]{a_i{a}_j},$ using the mole fractions $(x_i)$ and the individual

constants $(a_i,b_i)$ of each component.

$($b$)$ What is the molar volume of the mixture at the surface $($where the total pressure is $1$atm $),$

using the ideal gas law and van der Waals equation of state? Explain the differences between

the ideal and real gas molar volumes of the heliox mixture at $100m$ depth and at the surface.