# How do you solve Ideal Gas Law problems?

Jun 13, 2014

The Ideal Gas Law is a comparison of the the Pressure, Volume and Temperature of a Gas based upon the amount either by mole value or density.

There are two basic formulas for the Ideal Gas Law

$P V = n R T$ and $P M = \mathrm{dR} T$

P = Pressure in Atmospheres
V = Volume in Liters
n = Moles of the Gas Present
R = The Ideal Gas Law Constant $0.0821 \frac{a t m L}{m o l K}$
T = Temperature in Kelvin
M = Molar Mass of the Gas in $\frac{g r a m s}{m o l}$
d = Density of the Gas in $\frac{g}{L}$

If we were given a 2.5 mole sample of ${H}_{2}$ gas at 30 C in a 5.0 L container, we could use the ideal gas law to find the pressure.

P = ??? atm
V = 5.0 L
n = 2.5 moles
R = $0.0821 \frac{a t m L}{m o l K}$
T = 30 C + 273 = 303 K

$P V = n R T$ can be rearranged algebraically to $P = \frac{n R T}{v}$

$P = \frac{\left(2.5 m o l\right) \left(0.0821 \frac{a t m L}{m o l K}\right) \left(303 K\right)}{5.0 L}$

$P = 12.4 a t m$