×

Hello! Socratic's Terms of Service and Privacy Policy have been updated, which will be automatically effective on October 6, 2018. Please contact hello@socratic.com with any questions.

How do you calculate the ideal gas law constant?

1 Answer
Jan 1, 2014

Answer:

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.

Explanation:

The Ideal Gas Law is

#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#.