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# Chemical Principles ## The Properties of Gases ### 5.1 Gas Properties * Gases uniformly fill any container. * Gases are easily compressible. * Gases mix completely with any other gas. * Gases exert pressure on the walls of the container. ### 5. 2 Pressure #### Pressure = $\frac{Force...

# Chemical Principles ## The Properties of Gases ### 5.1 Gas Properties * Gases uniformly fill any container. * Gases are easily compressible. * Gases mix completely with any other gas. * Gases exert pressure on the walls of the container. ### 5. 2 Pressure #### Pressure = $\frac{Force}{Area}$ * SI units = Newton/meter$^{2}$ = 1 Pascal * 1 standard atmosphere = 101,325 Pa = 1 atm * 1 atm = 760 mm Hg = 760 torr ##### Barometer Used to measure atmospheric pressure. ##### Manometer Device used for measuring the pressure of gases other than the atmosphere. ### 5.3 The Gas Laws of Boyle, Charles, and Avogadro #### Boyle's Law $PV = k$ $P_1V_1 = P_2V_2$ (constant $n, T$) A plot of $V$ versus $P$ shows an inverse relationship #### Charles's Law $V = bT$ $\frac{V_1}{T_1} = \frac{V_2}{T_2}$ (constant $n, P$) A plot of $V$ versus $T$ shows a direct relationship ##### Absolute Zero $-273^\circ C$ = 0 K #### Avogadro's Law $V = an$ $\frac{V_1}{n_1} = \frac{V_2}{n_2}$ (constant $P, T$) ### 5.4 The Ideal Gas Law $PV = nRT$ $R = 0.08206 \frac{L \cdot atm}{mol \cdot K}$ $R = 8.3145 \frac{J}{K \cdot mol}$ #### Molar Density (mol/L) $\frac{n}{V} = \frac{P}{RT}$ #### Density (g/L) $d = \frac{m}{V} = \frac{PM}{RT}$ (M = molar mass) ### 5. 5 Gas Stoichiometry 1. The balanced equation provides the mole ratios. 2. Use the Ideal Gas Law to convert between moles and $P, V,$ and $T$. ### 5. 6 Dalton's Law of Partial Pressures $P_{total} = P_1 + P_2 + P_3 +...$ $P_1 = n_1\frac{RT}{V}, P_2 = n_2\frac{RT}{V},...$ #### Mole Fraction $\chi_1 = \frac{n_1}{n_{total}} = \frac{P_1}{P_{total}}$ ### 5.7 The Kinetic Molecular Theory of Gases 1. Gases consist of tiny particles. 2. These particles are so small compared with the distances between them that the volume of the individual particles can be assumed to be negligible (zero). 3. The particles are in constant random motion, colliding with the walls of the container. These collisions with the walls cause the pressure exerted by the gas. 4. The particles are assumed not to attract or to repel each other. 5. The average kinetic energy of the gas particles is directly proportional to the Kelvin temperature of the gas. #### Average Kinetic Energy $\overline{KE} = \frac{3}{2}RT$ ##### Root Mean Square Velocity $u_{rms} = \sqrt{\frac{3RT}{M}}$ (M = mass in kg/mol)