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