Question

A canister contains the following gases at the following pressures: oxygen gas at 760 mmHg, carbon dioxide gas at 0.24 atm, and nitrogen at 63 kPa. What is the total pressure inside this canister?

Answer 1

`P_"total" = 1410` `"mm Hg" = 1.86` `"atm" = 188` `"kPa"`

Explanation:

According to Dalton's law of partial pressures, the total pressure of a system is the sum of the individual pressures of the gases if they were present alone.

To keep things clear, we need to convert the pressure units to a single unit, and I'll choose `"mm Hg"`.

Converting them:

`P_"O" = 760` `"mm Hg"` (given, no conversion necessary)

`P_ ("CO"_2) = 0.24cancel("atm")((760"mm Hg")/(1cancel("atm"))) = 180` `"mm Hg"` (`2` sig figs)

`P_ ("N"_2) = 63"kPa"((760"mm Hg")/(101.325"kPa")) = 470` `"mm Hg"` (`2` sig figs)

Now that our units are consistent, let's add them up:

`760"mm Hg" + 180"mm Hg" + 470"mm Hg" = color(red)(1410` `color(red)("mm Hg"`

If you chose other units, you may have gotten answers something like

`color(red)(1.86` `color(red)("atm"`

or

`color(red)(188` `color(red)("kPa"`

(This may differ slightly from the other calculated pressures due to arbitrary rounding here and there, but these answers are correct, if you choose to follow all the rules for significant figures.)