# A gas cylinder contains 2.0 mol of gas X and 6.0 mol of gas Y at a total pressure of 2.1 atm. What is is partial pressure of gas Y?

Jul 6, 2017

${P}_{\text{Y" = "1.58 atm}}$

#### Explanation:

Okay, so here is what is going on.

You have some gas cylinder which contains a mixture of 2 different gases: $\text{Gas X" and "gas Y}$. Each gas is exerting its own pressure which is contributing to the total pressure. You are asked to figure out the partial pressure of gas Y. Here is how you go about doing that.

$- - - - - - - - - - - - - - - - - - - - -$

Write out our givens.

Given

• $\text{2.0 moles of gas X}$
• $\text{6.0 moles of gas Y}$
• $\text{Total pressure = 2.1 atm}$

To find the partial pressure of $\text{gas Y}$, you need to use the following formula:

color(white)(aaaaaaaaaaaaaa)color(blue)[P_"Y" = P_"T" * x_"Y"

Where

• $\text{P"_"Y" = "partial pressure of gas Y}$

• $\text{P"_"T" = "total pressure}$

• $\text{x"_"Y" = "mole fraction of gas Y}$

We were given the total pressure of the system, but we need to figure out the mole fraction of gas Y. To calculate it, we use the following equation:

$\textcolor{w h i t e}{a a a a a a a a a a} \textcolor{b l u e}{{x}_{\text{Y" = ("moles of gas Y")/("total moles of gas}}}$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a}$

Plugin and solve for the mole fraction of gas Y

• $\textcolor{b l u e}{{x}_{\text{Y" = ("moles of gas Y")/("total moles of gas}}}$
$\textcolor{w h i t e}{-}$

• $\rightarrow \left(\text{6.0 moles of gas Y")/("2.0 moles of gas X + 6.0 moles of gas Y}\right)$

• $\rightarrow \left(\text{6" cancel"moles")/("8" cancel"moles}\right)$

• $\rightarrow \textcolor{red}{\text{ 0.75}}$

Note: moles over moles cancel out so the mole fraction is unitless
$\textcolor{w h i t e}{a a a a a a a a a a a a a a}$

You now can use the mole fraction to solve for the partial pressure of gas Y by using the first equation which was given out.

• color(blue)[P_"Y" = P_"T" * x_"Y"
• ${P}_{\text{Y" = "(2.1 atm)" * "(0.75)}}$
• ${P}_{\text{Y" = color(magenta)"1.58 atm}}$

Answer: ${P}_{\text{Y" = color(magenta)"1.58 atm}}$