General Chemistry: Chemical Kinetics and Chemical Equilibrium – Midterm Study Notes

Chemical Kinetics

Rate Laws and Reaction Order

Chemical kinetics studies the speed of chemical reactions and the factors affecting them. The rate law expresses the relationship between the rate of a reaction and the concentrations of reactants.

• General Rate Law: For a reaction $aA + bB \rightarrow cC$, the rate law is $\text{rate} = k[A]^m[B]^n$ where k is the rate constant, and m and n are the reaction orders with respect to A and B.

• Determining Reaction Order: Use experimental data to compare how changes in reactant concentrations affect the rate. If doubling [A] doubles the rate, the reaction is first order in A; if it quadruples, it is second order, etc.

• Example: For the reaction $\mathrm{H_2SeO_4} + 6I^- + 4H^+ \rightarrow \mathrm{SeO_2} + 2I_2 + 3H_2O$, the rate law is determined by comparing initial rates from experiments with varying concentrations.

Calculating the Rate Constant

Once the rate law is known, the rate constant k can be calculated using experimental data.

• Formula: $k = \frac{\text{rate}}{[A]^m[B]^n}$

• Insert values from any experiment to solve for k.

Integrated Rate Laws and Half-Life

Integrated rate laws relate reactant concentration to time. The form depends on the reaction order.

• First Order: $[A]_t = [A]_0 e^{-kt}$ or $\ln\left(\frac{[A]_0}{[A]_t}\right) = kt$

• Half-life (First Order): $t_{1/2} = \frac{0.693}{k}$

• Example: For the decomposition of $\mathrm{N_2O_5}$, use pressure data to determine order and calculate $k$ and $t_{1/2}$.

Arrhenius Equation and Activation Energy

The Arrhenius equation describes how the rate constant varies with temperature:

• $k = A e^{-E_a/(RT)}$

• Taking logarithms: $\ln k = \ln A - \frac{E_a}{R} \frac{1}{T}$

• Activation Energy ($E_a$): The minimum energy required for a reaction to occur.

• Calculating $E_a$: Use two rate constants at different temperatures:

  • $\ln\left(\frac{k_2}{k_1}\right) = -\frac{E_a}{R}\left(\frac{1}{T_2} - \frac{1}{T_1}\right)$

• Effect of Catalysts: Catalysts lower $E_a$, increasing the rate constant.

Reverse Reactions and Rate Laws

• The activation energy for the reverse reaction: $E_{a,\text{reverse}} = E_{a,\text{forward}} - \Delta E$

• Write the rate law for the reverse reaction using the same principles as for the forward reaction.

Chemical Equilibrium

Equilibrium Constant Expressions

At equilibrium, the rates of the forward and reverse reactions are equal. The equilibrium constant ($K$) quantifies the ratio of product and reactant concentrations at equilibrium.

• For Gases (Kp): $K_p = \frac{(P_C)^c (P_D)^d}{(P_A)^a (P_B)^b}$

• For Concentrations (Kc): $K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b}$

• Relationship: $K_p = K_c(RT)^{\Delta n}$, where $\Delta n$ is the change in moles of gas.

• Example: For $S_2(g) \rightleftharpoons 4S(g)$, $K_p = \frac{(P_S)^4}{P_{S_2}}$

ICE Tables (Initial, Change, Equilibrium)

ICE tables help track changes in concentrations or pressures as a system approaches equilibrium.

• Set up initial values, changes (using a variable, often x), and equilibrium values.

• Substitute equilibrium values into the $K$ expression to solve for x.

• Example Table:

	NOCl (g)	NO (g)	Cl2 (g)
Initial (I)	0.5 M	0.5 M	0.5 M
Change (C)	-x	+x	+x
Equilibrium (E)	0.5-x	0.5+x	0.5+x

Le Châtelier’s Principle and Q vs. K

• Reaction Quotient (Q): Calculated like K, but with initial concentrations/pressures.

• If $Q < K$, the reaction proceeds forward; if $Q > K$, it proceeds in reverse.

Temperature Dependence of Equilibrium

The value of $K$ changes with temperature. The van 't Hoff equation relates $K$ at two temperatures:

• $\ln\left(\frac{K_2}{K_1}\right) = -\frac{\Delta H^\circ}{R}\left(\frac{1}{T_2} - \frac{1}{T_1}\right)$

• Exothermic reactions: $K$ decreases as temperature increases.

• Endothermic reactions: $K$ increases as temperature increases.

Sample Equilibrium Calculations

• Given initial amounts and $K$, set up an ICE table, solve for x, and calculate equilibrium concentrations or pressures.

• For gas-phase reactions, use partial pressures in $K_p$ expressions.

Summary Table: Key Equilibrium and Kinetics Equations

Concept	Equation	Description
Rate Law	$\text{rate} = k[A]^m[B]^n$	General form for reaction rate
First Order Integrated	$\ln\left(\frac{[A]_0}{[A]_t}\right) = kt$	Concentration vs. time
Half-life (1st order)	$t_{1/2} = \frac{0.693}{k}$	Time for half to react
Arrhenius Equation	$k = Ae^{-E_a/(RT)}$	Temperature dependence of rate
Equilibrium Constant (Kc)	$K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$	Concentration-based equilibrium
Equilibrium Constant (Kp)	$K_p = \frac{(P_C)^c(P_D)^d}{(P_A)^a(P_B)^b}$	Pressure-based equilibrium
van 't Hoff Equation	$\ln\left(\frac{K_2}{K_1}\right) = -\frac{\Delta H^\circ}{R}\left(\frac{1}{T_2} - \frac{1}{T_1}\right)$	Temperature effect on K

Additional info:

• All problems are based on standard General Chemistry topics: kinetics (rate laws, integrated rate laws, Arrhenius equation), equilibrium (Kc, Kp, ICE tables), and temperature effects on equilibrium.

• Examples and calculations are representative of typical midterm exam questions in a college-level General Chemistry course.