Question

A gas under a pressure of 74 mmHg and at a temperature of 75°C occupies a 500.0-L container. How many moles of gas are in the container?

Answer 1

`"1.7 mols ideal gas"`.

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Anytime you see a bunch of units in a row, it's probably an ideal gas problem. The first order of business is to convert all these to more usual units. Consider the universal gas constant:

`R = "0.082057 L"cdot"atm/mol"cdot"K"`.

The units of pressure, volume, and temperature are given directly in the units of `R`!

For the units to work out, the pressure `P` could be rewritten in `"atm"`:

`P = 74 cancel"mm Hg" xx "1 atm"/(760 cancel"mm Hg") = "0.0974 atm"`

It is always reasonable to use the temperature `T` in `"K"` for general chemistry, and in this case it makes the units work out...

`75^@ "C" + 273.15 = "348.15 K"`

The volume `V` is in normal units. We do want it in `"L"`, just as we wanted `P` in `"atm"`. Thus, we can now use the ideal gas law:

`bb(PV = nRT)`

where `n` is the mols of ideal gas.

So, to two significant figures, the mols are:

`color(blue)(n) = (PV)/(RT)`

`= ("0.0974 atm" cdot "500.0 L")/("0.082057 L"cdot"atm/mol"cdot"K" cdot "348.15 K")`

`=` `color(blue)ul"1.7 mols ideal gas"`