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?

1 Answer
Jun 9, 2017

Answer:

#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"#