How do you calculate the ideal gas law constant?

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Answer 1 · 2014-01-01T22:23:12

You do an experiment in which you measure the values of $P, V, n$ , and $T$ , and then you insert these values into the Ideal Gas Law.

$color(blue)(bar(ul(|color(white)(a/a)PV=nRTcolor(white)(a/a)|)))" "$

where $R$ is the Universal Gas Constant.

We can rearrange this to get

$R = (PV)/(nT)$

The units of $R$ depend on the units you use for $P$ and $V$ .

For example, repeated experiments show that at standard temperature and pressure (STP) — 273.15 K and 1 bar — 1 mol of gas occupies 22.711 L.

You can use this information to evaluate $R$ .

$R = (PV)/(nT) = ("1 bar ×22.711 L")/("1 mol × 273.15 K") = "0.083 14 bar·L·K"^"-1""mol"^"-1"$

If the pressure is measured in kilopascals (1 bar = 100 kPa), you calculate

$R = (PV)/(nT) = ("100 kPa × 22.711 L")/("1 mol × 273.15 K") = "8.314 kPa·L·K"^"-1""mol"^"-1"$

If you use strictly SI units, then pressure is measured in pascals and volume is measured in cubic metres.

$R = (PV)/(nT) = (100 × 10^3 color(white)(l)"Pa" × 22.711 × 10^"-3" color(white)(l)"m"^3)/("1 mol × 273.15 K") = "8.314 Pa·m"^3"K"^"-1""mol"^"-1"$

Always use the value of $R$ that corresponds to the units that you are using for $P$ and $V$ .