Question

A mixture of `2.00` moles of `"H"_2`, `3.00` moles of `"NH"_3`, `4.00` moles of `"CO"_2`, and `5.00` moles of `"N"_2` exerts a total pressure of `"800. mmHg"`. What is the partial pressure of each gas?

Answer 1

Here's what I got.

Explanation:

The idea here is that the partial pressure of each gas will be proportional to the mole fraction each gas has in the mixture `->` think Dalton's Law of Partial Pressures.

`P_ "gas i" = chi_ "gas i" * P_"total"`

Here

• `P_"gas i"` is the partial pressure of gas `i`
• `chi_"gas i"` is the mole fraction of gas `i`
• `P_"total"` is the total pressure of the mixture

In other words, the partial pressure of a given gas will be equal to the pressure that gas would have if it were to occupy the same volume alone.

Consequently, the sum of these partial pressures must be equal to the total pressure exerted by the mixture.

`P_"total" = P_( "H"_ 2) + P_ ("NH"_ 3) + P_ ("CO"_ 2) + P_ ("N"_ 2)`

Now, the mole fraction of a component of this mixture is calculated by dividing the number of moles of said component by the total number of moles of gas present in the mixture.

For hydrogen gas, you will have

`chi_ ("H"_ 2) = (2.00 color(red)(cancel(color(black)("moles"))))/((2.00 + 3.00 + 4.00 + 5.00)color(red)(cancel(color(black)("moles")))) = 0.1429`

Similarly, for ammonia, you will have

`chi_ ("NH"_ 3) = (3.00 color(red)(cancel(color(black)("moles"))))/((2.00 + 3.00 + 4.00 + 5.00)color(red)(cancel(color(black)("moles")))) = 0.2143`

For carbon dioxide, you will have

`chi_ ("CO"_ 2) = (4.00 color(red)(cancel(color(black)("moles"))))/((2.00 + 3.00 + 4.00 + 5.00)color(red)(cancel(color(black)("moles")))) = 0.2857`

Finally, for nitrogen gas, you will have

`chi_ ("N"_ 2) = (5.00 color(red)(cancel(color(black)("moles"))))/((2.00 + 3.00 + 4.00 + 5.00)color(red)(cancel(color(black)("moles")))) = 0.3571`

To find the partial pressure of hydrogen gas, simply multiply the mole fraction of hydrogen gas by the total pressure of the mixture.

`P_ ("H"_ 2) = 0.1429 * "800m mmHg" = color(darkgreen)(ul(color(black)("114 mmHg")))`

Similarly, the partial pressure of ammonia will be

`P_ ("NH"_ 3) = 0.2143 * "800. mmHg" = color(darkgreen)(ul(color(black)("171 mmHg")))`

Use the same approach to find the partial pressures of carbon dioxide and nitrogen gas.

Don't forget to round the answers to three sig figs and make sure to double-check your calculations by using the fact that all the partial pressures must add up to give the total pressure of the mixture.