Question

How can I calculate the ideal gas law equations?

Answer 1

There are two versions of the ideal gas equation:
Molar version: `pV=nRT` (n is no. of moles & R is molar gas constant).
Molecular version: `pV=NkT` (N is no. of molecules & k is Boltzmann constant – i.e molecular gas constant).

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Where the pressure - P, is in atmospheres (atm)* the volume - V, is in liters (L) the moles -n, are in moles (mol) and Temperature -T is in Kelvin (K) as in all gas law calculations.

*NB SI units for pressure is Pa and for volume is `m^3`.

The value and unit of molar gas constant, `R`, is derived from equation `PV = nRT`.

When we do the algebraic reconfiguration we end up with Pressure and Volume being decided by moles and Temperature, giving us a combined unit of `(atmL) / (molK)`.

The constant value then becomes 0.0821 `(atmL)/(molK)`

If you choose not to have your students work in standard pressure unit factor, you may also use: 8.31 `(kPaL)/(molK)`.

Temperature must always be in Kelvin (K) to avoid using 0 ºC and getting no solution when students divide.

There is a variation of the ideal gas law that uses the density of the gas with the equation `PM = dRT`.

Where M is the Molar Mass in g/mol and d is the Density of the gas in g/L.

Pressure and Temperature must remain in the units atm and K and the Gas Law Constant remains `R = 0.0821 (atm L) / (mol K)`.

In SI `R=8.31 J K^(-1) mol^(-1)`

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Let's take an example of a 2.0 moles of nitrogen at 20 ºC and 3.00 atm and find the volume.

`PV = nRT`

P = 3.00 atm
V = ?
n = 2.0 mol
R = 0.0821 `(atmL)/(molK)`
T = 20 + 273 = 293 K

`V = (nRT)/P`

`V = (2.0 mol(0.0821(atmL)/(molK))293K)/(3.00 atm)`

`V = 16.0L`

I hope this is helpful.
SMARTERTEACHER