# Question cc3ae

Aug 26, 2017

#### Answer:

$\text{0.8 bar}$

#### Explanation:

The first thing that you need to do here is to figure out the mole ratio that exists between the two gases in the mixture.

To do that, use the molar masses of hydrogen gas and of oxygen gas.

M_ ("M O"_ 2) = "32.0 g mol"^(-1)

M_ ("M H"_ 2) ~~ "2.0 g mol"^(-1)

Now, you know that this mixture contains 20% hydrogen gas by mass. This means that if you take $m$ $\text{g}$ to be the total mass of the mixture, you will have

m_ ("H"_ 2) = 20/100 * mcolor(white)(.)"g" = (1/5 * m)color(white)(.)"g"

m_ ("O"_ 2) = mcolor(white)(.)"g" - (1/5 * m) color(white)(.)"m" = (4/5 * m)color(white)(.)"g"

The number of moles of each gas present in the mixture will be

(1/5 * m) color(red)(cancel(color(black)("g"))) * "1 mole H"_2/(2.0color(red)(cancel(color(black)("g")))) = (1/10 * m)color(white)(.)"moles H"_2

(4/5 * m) color(red)(cancel(color(black)("g"))) * "1 mole O"_2/(32.0color(red)(cancel(color(black)("g")))) = (1/40 * m)color(white)(.)"moles O"_2

Now, you know that the partial pressure of a gas that's part of a gaseous mixture depends on its mole fraction in the mixture and on the total pressure of the mixture.

The mole fraction of hydrogen gas will be equal to the number of moles of hydrogen gas divided by the total number of moles present in the mixture.

chi_ ("H"_ 2) = ((1/10 * color(red)(cancel(color(black)(m)))) color(red)(cancel(color(black)("moles"))))/((1/10 * color(red)(cancel(color(black)(m)))+ 1/40 * color(red)(cancel(color(black)(m)))) color(red)(cancel(color(black)("moles")))) = 1/10 * 40/5 = 4/5

If you take ${P}_{\text{total}}$ to be the total pressure of the mixture, you can say that the partial pressure of hydrogen gas will be

color(blue)(ul(color(black)(P_ ("H"_ 2) = chi_ ("H"_ 2) * P_"total")))

P_ ("H"_ 2) = 4/5 * P_"total"

In your case, you have

${P}_{\text{total" = "1 bar}}$

which means that the partial pressure of hydrogen gas will be

P_ ("H"_ 2) = 4/5 * "1 bar" = color(darkgreen)(ul(color(black)("0.8 bar")))#

The answer is rounded to one significant figure.