Question

A mixture of gases contains `"H"_2` and `"O"_2` gases in the ratio of `"1:4 w/w"`. What is the molar ratio of two gases in the mixture?

Answer 1

`"H"_2:"O"_2 = 4:1`

Explanation:

All you have to do here is to convert the mass ratio to a mole ratio by using the conversion factor that takes you from grams to moles or vice versa, i.e. the molar mass.

You know that you have

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

`M_ ("M O"_ 2) ~~ "32 g mol"^(-1)`

Now, if you take `x` `"g"` to be the mass of hydrogen gas present in the mixture, you can say that the mass of oxygen gas will be equal to `(4 * x)` `"g"` `->` the `1:4` mass ratio comes into play here.

The molar ratio of the two gases will be equal to

`(x color(white)(.)"g H"_2)/(4xcolor(white)(.)"g O"_2) = (x color(white)(.)color(red)(cancel(color(black)("g H"_2))) * "1 mole H"_2/(2color(red)(cancel(color(black)("g H"_2)))))/(4xcolor(red)(cancel(color(black)("g O"_2))) * "1 mole O"_2/(32color(red)(cancel(color(black)("g O"_2))))) = ((x/2) color(white)(.)"moles H"_2)/( ((4x)/32)color(white)(.)"moles O"_2)`

This can be simplified to

`((color(red)(cancel(color(black)(x)))/2) color(white)(.)"moles H"_2)/( ((4color(red)(cancel(color(black)(x))))/32)color(white)(.)"moles O"_2) = (1/2 * 32/4)"moles H"_2/"moles O"_2 = "4 moles H"_2/"1 mole O"_2`

Therefore, the mixture contains hydrogen gas and oxygen gas in a `4:1` mole ratio.