Question

Two containers, one with a volume of 3.0 L and the other with a volume of 2.0 L contain, respectively, argon gas at 1.1 atm and helium at 0.75 atm. The containers are initially separated by a valve, and then the valve is opened to connect the two containers. Assume perfect gases and determine the followings.
a. The total pressure of the mixed gases
b. The partial pressure of each gas
c. The mole fraction of each gas

Answer 1

Answer:

a. $p_T=0.93atm$.

b.

$p_{Ar}=0.66atm\\\\p_{He}=0.3atm$

c.

$x_{Ar}=0.6875\\\\x_{He}=0.3125$

Explanation:

Hello,

In this case, considering that the valve is opened, we can use the Boyle's law in order to compute the final pressure of argon by considering its initial pressure and volume and a final volume of 5.0 L:

$p_{Ar}=\frac{1.1atm*3.0L}{5.0L}=0.66atm$

And the final pressure of helium:

$p_{He}=\frac{0.75atm*2.0L}{5.0L}=0.3atm$

Which actually are the partial pressure of both of them, it means that the total pressure is:

Finally, the mole fraction of each gas is computed by considering the Dalton's law:

$x_i=\frac{p_i}{p_T}$

$x_{Ar}=\frac{0.66atm}{0.93atm} =0.6875\\\\x_{He}=\frac{0.3atm}{0.93atm} =0.3125$

Best regards.