How to claculate value of universal gas constant?

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Answer 1 · 2017-01-08T18:56:49

You must do an experiment in which you measure the values of $P, V, n$ , and $T$ .

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

where

$P$ = the pressure
$V$ = the volume
$n$ = the number of moles
$R$ = the Universal Gas Constant
$T$ = the temperature

We can rearrange the Ideal Gas Law to get

$R = (PV)/(nT)$

If you do an experiment in which you measure the values of $P, V, n$ , and $T$ , you can insert these values into the equation and calculate $R$ .

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

You can use this information to evaluate $R$ .

$R = (PV)/(nT) = ("1 bar" × "22.711 L")/("1 mol × 273.15 K") = "0.083 145 L·atm·K"^"-1""mol"^"-1"$

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

$R = (PV)/(nT) = (1.013 25 × 10^5 color(white)(l)"Pa" × 22.414× 10^"-3"color(white)(l) "m"^3)/"1 mol × 273.15 K" = "8.3145 Pa·m"^3"K"^"-1""mol"^"-1"$

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