Finishing Enthalpy and Introduction to Chemical Kinetics: Study Notes

Enthalpy and Calorimetry

Defining Enthalpy

Enthalpy (H) is a thermodynamic quantity that represents the total heat content of a system. It is defined as:

• Enthalpy (H): $H = E + PV$

• At constant pressure, the change in enthalpy ($\Delta H$) is equal to the heat gained or lost by the system: $\Delta H = q$

Key Point: At constant pressure, $\Delta H$ is easily measurable and represents the heat exchanged.

Constant-Pressure Calorimetry

Often called "coffee cup" calorimetry, this method measures the heat change for reactions in aqueous solution at constant pressure.

• Specific heat of water: $4.184\frac{J}{\left(g\cdot K\right)}$

• Equation: $q_{\text{soln}} = C_s \cdot m \cdot \Delta T = q_{\text{rxn}}$

• $C_s$ = specific heat, $m$ = mass, $\Delta T$ = temperature change

Example: Mixing acid and base in a coffee cup calorimeter to measure heat released.

Constant-Volume Calorimetry

"Bomb" calorimetry is used for reactions at constant volume, typically combustion reactions.

• Equation: $q_{\text{rxn}} = -C_{\text{cal}} \cdot \Delta T$

• $C_{\text{cal}}$ = heat capacity of the calorimeter

• Measures change in internal energy ($\Delta E$), not enthalpy ($\Delta H$)

Note: For most reactions, $\Delta E$ and $\Delta H$ are very similar, but not exactly equal.

Hess's Law and Enthalpy of Formation

Hess's Law

Hess's Law states that the total enthalpy change for a reaction is the sum of the enthalpy changes for each step, regardless of the pathway taken.

• Equation: $\Delta H = \sum \Delta H_{\text{products}} - \sum \Delta H_{\text{reactants}}$

• Allows calculation of $\Delta H$ for complex reactions using known values.

Enthalpy of Formation ($\Delta H_f$)

The enthalpy change when one mole of a compound is formed from its elements in their standard states.

• Standard enthalpy of formation: $\Delta H_f^\circ$

• Standard conditions: 25°C and 1.00 atm pressure

• Use fractional coefficients if necessary (e.g., $\frac{1}{2} N_2(g) + \frac{3}{2} H_2(g) \rightarrow NH_3(g)$)

Examples of Standard Enthalpies of Formation

Standard enthalpies of formation for common substances are tabulated for reference.

Substance	Formula	$\Delta H_f^\circ$ (kJ/mol)
Acetylene	C2H2(g)	226.7
Ammonia	NH3(g)	-46.19
Benzene	C6H6(l)	49.0
Calcium carbonate	CaCO3(s)	-1207.1
Carbon dioxide	CO2(g)	-393.5
Water	H2O(l)	-285.8
Water vapor	H2O(g)	-241.8
Glucose	C6H12O6(s)	-1273
Methane	CH4(g)	-74.8
Sodium chloride	NaCl(s)	-411.0

Using Enthalpy of Formation Values

To calculate the enthalpy change for a reaction, break down the reaction into formation and decomposition steps using $\Delta H_f^\circ$ values.

• Decompose reactants to elements

• Form products from elements

• Apply Hess's Law: $\Delta H_{\text{rxn}}^\circ = \sum \Delta H_f^\circ(\text{products}) - \sum \Delta H_f^\circ(\text{reactants})$

Example: For $C_3H_8(g) + 5 O_2(g) \rightarrow 3 CO_2(g) + 4 H_2O(l)$, use tabulated $\Delta H_f^\circ$ values to calculate $\Delta H_{\text{rxn}}^\circ$.

Bond Enthalpy and Reaction Enthalpy

Bond Enthalpy

Bond enthalpy is the energy required to break one mole of a specific bond in a gaseous substance.

• Always positive (energy input required)

• Stronger bonds have higher bond enthalpy

• Energy is released when bonds form

Bond Enthalpy Tables

Average bond enthalpies for common bonds are tabulated for reference.

Bond	Enthalpy (kJ/mol)
C–H	413
C–C	348
C=C	614
C≡C	839
O–H	463
O=O	498
H–H	436
Cl–Cl	243

Calculating Reaction Enthalpies with Bond Enthalpies

Estimate $\Delta H_{\text{rxn}}$ by summing bond enthalpies of bonds broken and subtracting those of bonds formed:

• Equation: $\Delta H_{\text{rxn}} = \sum (\text{bond enthalpies of bonds broken}) - \sum (\text{bond enthalpies of bonds formed})$

• Example: For $CH_4 + Cl_2 \rightarrow CH_3Cl + HCl$, break C–H and Cl–Cl, form C–Cl and H–Cl.

Chemical Kinetics

Introduction to Chemical Kinetics

Chemical kinetics is the study of the rate at which chemical reactions occur. The reaction rate is the change in concentration of reactants or products per unit time.

• Factors affecting rate: physical state, concentration, temperature, catalyst

• Applications: explosions, medications, rusting, erosion

Factors Affecting Reaction Rate

• Physical State: Homogeneous reactions (gases/liquids) are faster; heterogeneous (solids) are slower.

• Reactant Concentration: Higher concentration increases collision frequency and rate.

• Reaction Temperature: Higher temperature increases kinetic energy, collision frequency, and rate.

• Presence of a Catalyst: Catalysts increase rate without being consumed, often by lowering activation energy.

Reaction Rate Expressions

Reaction rate is expressed as:

• $\text{Rate} = \frac{\Delta [A]}{\Delta t}$, where $[A]$ is concentration and $t$ is time

• Rates are reported as positive quantities (amount of product formed per time)

Average and Instantaneous Rate

• Average Rate: Change in concentration over a time interval

• Instantaneous Rate: Slope of concentration vs. time curve at a specific time

Stoichiometry and Rate

• Rates can be measured for reactants or products

• For $C_2H_5Cl(aq) + H_2O(l) \rightarrow C_2H_5OH(aq) + HCl(aq)$:

• $\text{Rate} = -\frac{\Delta [C_2H_5Cl]}{\Delta t} = \frac{\Delta [C_2H_5OH]}{\Delta t}$

• Relative rates depend on stoichiometric coefficients

Rate Laws and Rate Constants

• Rate law: $\text{Rate} = k[A]^x[B]^y$

• $k$ = rate constant, $x$ and $y$ = reaction orders (determined experimentally)

• Overall reaction order = sum of exponents

Order vs. Stoichiometry

• Reaction order is not necessarily related to stoichiometry; must be determined experimentally

• Examples: $2N_2O_5(g) \rightarrow 4NO_2(g) + O_2(g)$, $\text{Rate} = k[N_2O_5]$

Magnitudes and Units of Rate Constant (k)

• Zero order: $\text{M s}^{-1}$ or $\text{M/s}$

• First order: $\text{s}^{-1}$ or $1/\text{s}$

• Second order: $\text{M}^{-1} \text{s}^{-1}$ or $1/(\text{M s})$

Method of Initial Rates

• Determine rate law by comparing rates from experiments with varying reactant concentrations

• Set up ratios: $\frac{\text{conc ratio}^{\text{exponent}}}{\text{rate ratio}}$

• Example: $\text{Rate} = k[NO_2^-][NH_4^+]$