Question

How to claculate value of universal gas constant?

Answer 1

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

Explanation:

The Ideal Gas Law is

`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`.