Ideal gas law/Tutorials

Example problems
PROBLEM 1) Two liters of gas at 1 atm and 25C is placed under 5 atm of pressure at 25C. What is the final volume of gas?

Using Boyle's law:

Eq. 1.1) $$ \left(p_\mathrm{i}V_\mathrm{i}\right) = \left(\mathrm{constant}\right) = \left(p_\mathrm{f}V_\mathrm{f}\right) $$ or

Eq. 1.2) $$ \left(V_\mathrm{f}\right) = \left(\frac{p_\mathrm{i}V_\mathrm{i}}{p_\mathrm{f}}\right) $$

Eq. 1.3) $$ \left(V_\mathrm{f}\right) = \left(\frac{(1 \mathrm{atm})(2 \mathrm{L})}{(5 \mathrm{atm})}\right) = 0.4 \mathrm{L} $$

Using Ideal gas law:

Eq. 1.4) $$ n = \left(\frac{p_\mathrm{i}V_\mathrm{i}}{RT_\mathrm{i}}\right) = \left(\frac{p_\mathrm{f}V_\mathrm{f}}{RT_\mathrm{f}}\right) $$

Because $$ \left(T_\mathrm{i}\right) = \left(T_\mathrm{f}\right) $$  Eq. 1.4 reduces to Eq. 1.1 shown above.

PROBLEM 2) How many moles of nitrogen are present in a 50L tank at 25C when the pressure is 10 atm? (Note: Kelvin = Celcius + 273.15). Numbers include only 3 significant figures.

Eq 2.1) $$ n = \frac{pV}{RT} = \frac{(10.0 \mathrm{atm})(50 \mathrm{L})} {[(0.0821 \mathrm{L atm} / (\mathrm{K mol})](298\mathrm{K})} = 20.4 mol $$