Question

Equal masses of methane and hydrogen are mixed in an empty container. At 25 degree Celsius. The fraction of total pressure exerted by hydrogen will be?

Answer 1

`8/9`

Explanation:

The idea here is that the partial pressure of hydrogen gas will depend on

• the mole fraction of hydrogen gas in the mixture
• the total pressure of the mixture

Now, let's say that we are mixing `m` `"g"` of hydrogen gas and `m` `"g"` of methane.

Use the molar masses of the two gases to express the number of moles of each component of the mixture in terms of their mass `m`

`m color(red)(cancel(color(black)("g"))) * "1 mole H"_2/(2.0color(red)(cancel(color(black)("g")))) = (m/2)` `"moles H"_2`

`m color(red)(cancel(color(black)("g"))) * "1 mole CH"_4/(16.0color(red)(cancel(color(black)("g")))) = (m/16)` `"moles O"_2`

The total number of moles of gas present in the mixture will be equal to

`(m/2)color(white)(.)"moles" + (m/16)color(white)(.)"moles" = (9/16 * m)color(white)(.)"moles"`

Now, the mole fraction of hydrogen gas is calculated by dividing the number of moles of hydrogen gas by the total number of moles of gas present in the mixture.

`chi_ ("H"_ 2) = ((color(red)(cancel(color(black)(m)))/2)color(red)(cancel(color(black)("moles"))))/((9/16 * color(red)(cancel(color(black)(m))))color(red)(cancel(color(black)("moles")))) = 1/2 * 16/9 = 8/9`

By definition, the partial pressure of hydrogen gas in the mixture is equal to

`P_ ("H"_ 2) = chi_ ("H"_ 2) * P_"total"`

In your case, this will be equal to

`P_ ("H"_ 2) = 8/9 * P_"total"`