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?

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"#