Chemistry - Physical Chemistry Lecture Notes PDF

# Chemistry - Physical Chemistry ## Lecture 1 **Mon 7.10.2014** ### Matter - Anything has mass and occupies space. - Consists of molecules that tend to fly apart because of kinetic energy. - There are attraction forces among them called "Van der Waal's force". ### Some Notes - Liquids are more d...

# Chemistry - Physical Chemistry ## Lecture 1 **Mon 7.10.2014** ### Matter - Anything has mass and occupies space. - Consists of molecules that tend to fly apart because of kinetic energy. - There are attraction forces among them called "Van der Waal's force". ### Some Notes - Liquids are more dense than gases. - Gases have more volume than liquids. - Gases are compressible. - All gases have the same behavior. - They don't have specific volume, it depends on the mole number, not the nature of the gas. - The volume of gas is equal to the volume of the container. - Elastic collisions result in no loss of energy. - No attraction or repulsion between molecules of gas. ## Gaseous State ### Ideal Gas - Obeys the gas laws at all conditions. - Volume of gas is very small and can be neglected. - No attraction or repulsion forces, so no intermolecular space. ### Real Gas - Obeys the gas laws at low pressure and high temperature. - Volume cannot be neglected. - Molecules of real gas exert some attraction and repulsion forces on each other. ## 4 Quantities of Gas Needed: 1. **Volume:** Gas expands uniformly to fill any container placed in it. - Volume of gas = Volume of container 2. **Temperature:** - $T_K = [°C] + 273.15$ - $[°C] = ([°F] - 32) \times \frac{ 5}{9}$ - $[°F] = [°C] \times \frac{ 9}{5} - 32$ 3. **Amount:** Number of moles ($n$) and mass in grams ($m$) - $m = M \times n$ where $M$ is molar mass 4. **Pressure:** - $1 \ atm = 76 \ cmHg = 760 \ mmHg = 1.013 \times 10^{5} \ N/m^2$ or Pascal - $ = 1.013 \times 10^{6}dyne/cm^2 $ ## The Laws Governing the Ideal Gas Behavior: 1. **Boyle's Law:** at constant temperature (T) and volume of a fixed amount, pressure on gas is inversely as volume. - $V \propto \frac{1}{P}$ (at constant T) - $P_1V_1 = P_2V_2 = K_1$ or $V = \frac{K_1}{P}$ 2. **Charles's or Gay-Lussac's Law:** at constant pressure, volume of a fixed amount of gas is directly proportional to the absolute temperature (T). - $V \propto T$ (at constant P & n) - $\frac{V_1}{T_1} = \frac{V_2}{T_2}$ ## The Mole: - It's a number equal to the number of Carbon atoms in 12 grams of pure $^{12}C$. - This number ($6.022 \times 10^{23}$) is called Avogadro's number. - $mass = no. of moles (n) \times molar mass (M)$ - $n = \frac {m}{M}$ - $no. of moles = \frac{no. of molecules}{6.022 \times 10^{23}}$ ## Lecture 3 ### Avogadro's law - 1 mole of every gas under STP occupies the same volume (22.4 L). - $Vol. \propto n$ (no. of moles). - $Vol. = n \times 22.4 L$ ### The combined gas law and the ideal gas equation: - Boyle: $V \propto \frac{ 1}{P}$ - Charles: $V \propto T$ - Avogadro: $V \propto n$ - **Ideal gas equation:** $PV=nRT$ - $P$ : pressure (atm) - $V$ : volume (L) - $n$ : number of moles - $T$ : temperature (Kelvin) - $R$ : general gas constant - $R = 0.082 \ atm.L.mol^{-1}.K^{-1} = 8.3 \ J.K.mol^{-1} = 1.98 \ Cal.K.mol^{-1} $ ### Dalton's law of partial pressures: - A mixture of gases in a container, the total pressure is the sum of the partial pressures. - $P_T = P_1+P_2+P_3+...$ - Each partial pressure can be calculated by: - $P_i = \frac{n_i}{n_{total}} \times (RT) \times \frac{1}{V}$ - The partial pressure of each gas depends on the number of moles of that gas. - $P_T = (n_1 + n_2 + ...) \times (RT) \times \frac{1}{V}$ : sum of the number of moles in all gases. ### Mole Fraction: - Ratio of the number of moles of a given component in a mixture to the total number of moles in the mixture. - $X_i = \frac{n_i}{n_{total}}$ ## Lecture 4 - **Diffusion and Effusion of Gases, Graham's Law** - **Diffusion**: flow of gas through the space available to it. - **Effusion**: flow of gas through tiny pores. - **Graham's Law:** The rate of diffusion or effusion is inversely proportional to the square root of its density at constant temperature and pressure. - $ \frac{rate \ of \ eff. \ A}{rate\ of\ eff. B} = (\frac{density \ A}{density\ B})^{\frac{1}{2}} = (\frac{M_b}{M_a})^{\frac{1}{2}}$ where $M_b$ and $M_a$ are the molecular weights of gases A and B respectively. - **Kinetic Molecular Theory of Ideal Gases** 1. The particles of the gas are so small compared with the distances between them. 2. The gas molecules are in constant, rapid, and random motion. 3. The pressure of the gas causes collisions of molecules by the walls of the container. 4. Molecules are elastic. There is no net loss of energy due to collisions. 5. No forces are between gas molecules. 6. $⟨KE⟩ \propto T(K)$ - **Fundamental Equation of Kinetic Theory:** $P\times V = \frac{1}{3} \times m \times n \times ⟨c^2⟩$ - $P$ : pressure - $V$ : volume - $m$ : mass of single molecule - $n$ : number of molecules - $⟨c^2⟩$ : average square of molecular velocity.