\[PV=nRT\]
Boyle's Law: \(P_1V_1 = P_2V_2\) (constant n, T)
Charles' Law: \(\displaystyle{V_1\over T_1} = {V_2\over T_2}\) (constant n, P)
Avogadro's Law: \(\displaystyle{V_1\over n_1} = {V_2\over n_2}\) (constant P, T)
Gay-Lussac's Law: \(\displaystyle{P_1\over T_1} = {P_2\over T_2}\) (constant n, V)
Air Up Your Tires Law: \(\displaystyle{P_1\over n_1} = {P_2\over n_2}\) (constant V, T)
Difficult to Do This Law: \(n_1T_1 = n_2T_2\) (constant P, V)
(note that you will be tested on the actual relationships of the physical properties and not the scientist's names)
and because density (ρ) is m/V and molar mass (M) is m/n, then you also know the molar mass of an ideal gas via:
\[{M={\rho RT\over P}}\]
Dalton's Law of Partial Pressures
\[P_{\rm total}=P_{\rm A} + P_{\rm B} + P_{\rm C} + \cdots\]
mole fraction of gas A: \(x_{\rm A}=P_{\rm A}/P_{\rm total}\)
Van der Waal's Equation of State (Gas Model)
\[\left(P+a{n^2 \over V^2}\right)(V-nb)=nRT\]
The average kinetic energy of an ideal gas
\[E_{\rm k} = U = {3\over 2}RT = {1\over 2}mv^2\]
Root mean squared velocity of a gas
\[{v_{\rm rms}=\sqrt{3RT \over M}}\]
Comparing rms velocities of two different gases at the same temperature
\[{{v_1\over v_2}=\sqrt{M_2 \over M_1}}\]
R = 0.08206 L atm/mol K
R = 62.36 L torr/mol K
R = 0.08314 L bar/mol K
R = 8.314 J/mol K
NA = 6.022 × 1023 mol-1
1 atm = 1.01325 × 105 Pa
1 atm = 760 torr
1 atm = 14.7 psi
1 bar = 105 Pa
1 in = 2.54 cm
1 lb = 453.6 g
1 gal = 3.785 L
\(\rho_{\rm water} = 1.00\) g/mL
\(\rho_{\rm mercury} = 13.6\) g/mL