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?

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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?

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Answer 1 · 2017-08-18T17:56:16

$1.7 mols ideal gas$ $"1.7 mols ideal gas"$ .

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:

$R = 0.082057 L \cdot atm/mol \cdot K$ $R = "0.082057 L"cdot"atm/mol"cdot"K"$ .

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

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

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

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:

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

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

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

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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?

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