# Enthalpy and Thermochemistry

Chemistry I · Energy, Equilibrium and Electrochemistry · https://tryals.app/learn/chemistry-i/enthalpy-and-thermochemistry

## Heat at Constant Pressure

Most reactions run in open vessels, where pressure is fixed and volume is free to change. **Enthalpy** is defined to make that case simple:

$$H = U + PV$$

so that at constant pressure $\Delta H = q_p$, the enthalpy change *is* the heat exchanged. A reaction with $\Delta H < 0$ is **exothermic** and warms its surroundings; $\Delta H > 0$ is **endothermic** and cools them.

Enthalpy is a state function, which gives **Hess's law**: the enthalpy change of a reaction is the sum of the enthalpy changes of any sequence of steps that connects the same reactants to the same products. Two rules follow, reversing a reaction flips the sign of $\Delta H$, and multiplying a reaction by $n$ multiplies $\Delta H$ by $n$.

The most useful version uses **standard enthalpies of formation** $\Delta H_f^\circ$, the enthalpy change forming one mole of a compound from its elements in their standard states:

$$\Delta H_{rxn}^\circ = \sum n \Delta H_f^\circ (\text{products}) - \sum n \Delta H_f^\circ (\text{reactants})$$

An element in its standard state has $\Delta H_f^\circ = 0$ by definition, that is a choice of reference point, not a measurement.

**Calorimetry** measures these quantities. A known mass absorbs the heat and its temperature rise gives $q = mc\Delta T$. A coffee-cup calorimeter runs at constant pressure and therefore measures $\Delta H$ directly; a bomb calorimeter runs at constant volume and measures $\Delta U$ instead.

Finally, reaction enthalpies drift with temperature. **Kirchhoff's equation** says the drift rate is the difference in heat capacities:

$$\Delta H(T_2) = \Delta H(T_1) + \Delta C_p (T_2 - T_1)$$

> **Common pitfall:** forgetting to scale $\Delta H$ when you scale the equation. Enthalpy is extensive, burning two moles releases twice the heat of one. A Hess cycle that doubles a step must double its enthalpy too, and reversing a step must flip its sign.

## Practice questions

6 of this lesson's 12 practice questions, with answers. The full set is in the app.

### 1. Why does a coffee-cup calorimeter measure $\Delta H$ while a bomb calorimeter measures $\Delta U$?

A. The coffee cup allows work to be done; the bomb prevents all heat transfer entirely
B. The coffee cup measures aqueous enthalpy; the bomb calorimeter only measures heat capacity
C. The coffee cup operates at constant volume; the rigid bomb operates at constant pressure
D. The coffee cup is open at constant pressure; the bomb is sealed at constant volume

**Answer:** D. The coffee cup is open at constant pressure; the bomb is sealed at constant volume

**Why:** At constant pressure $q_p = \Delta H$; at constant volume no expansion work is possible, so $q_v = \Delta U$. The apparatus decides which quantity you measure, which is why combustion data often needs converting between the two.

Page: https://tryals.app/practice/chemistry-i/enthalpy-and-thermochemistry/why-does-a-coffee-cup-calorimeter-measure-h-while-a-bomb

### 2. For a reaction, the sum of the standard formation enthalpies of the products is $-820$ kJ/mol and that of the reactants is $-560$ kJ/mol. Compute the standard reaction enthalpy in kJ/mol.

**Answer:** -260 (within ±1)

**Why:** $\Delta H^\circ_{rxn} = -820 - (-560) = -260$ kJ/mol. Subtracting a negative is where sign errors creep in, and it is exothermic because the products sit lower than the reactants.

Page: https://tryals.app/practice/chemistry-i/enthalpy-and-thermochemistry/for-a-reaction-the-sum-of-the-standard-formation-enthalpies-of-the

### 3. Enthalpy is an extensive state function, rather than an intensive property or a path-dependent quantity. What follows from this distinction when constructing a Hess cycle to calculate an unknown reaction enthalpy?

A. Step values remain constant regardless of the molar quantities in each step
B. Step values depend directly upon the experimental route chosen by the chemist
C. Step values scale with stoichiometric multipliers but ignore the route taken
D. Step values must be converted to intensive heat capacities before summation

**Answer:** C. Step values scale with stoichiometric multipliers but ignore the route taken

**Why:** Confusing extensive properties with intensive ones leads to omitting stoichiometric multipliers, whilst treating enthalpy as path-dependent denies Hess's law entirely. Enthalpy behaves like altitude: independent of the route, but strictly proportional to quantity.

Page: https://tryals.app/practice/chemistry-i/enthalpy-and-thermochemistry/enthalpy-is-an-extensive-state-function-rather-than-an-intensive

### 4. Match each thermochemical quantity to its definition.

**Answer:**

- Standard enthalpy of formation → Forming one mole of a compound from its elements
- Standard enthalpy of combustion → Burning one mole completely in excess oxygen
- Bond dissociation enthalpy → Breaking one mole of a bond in the gas phase
- Lattice enthalpy → Separating one mole of an ionic solid into gaseous ions

**Why:** Each standard enthalpy fixes both the amount (one mole) and the exact process, so that values from different laboratories can be added in a Hess cycle without ambiguity.

Page: https://tryals.app/practice/chemistry-i/enthalpy-and-thermochemistry/match-each-thermochemical-quantity-to-its-definition

### 5. An element in its standard state is assigned a formation enthalpy of exactly zero.

**Answer:** True

**Why:** True, it is a definition, not a measurement. Enthalpy has no absolute zero, so elements in their standard states are chosen as the reference point, exactly as sea level is chosen for altitude.

Page: https://tryals.app/practice/chemistry-i/enthalpy-and-thermochemistry/an-element-in-its-standard-state-is-assigned-a-formation-enthalpy-of

### 6. Arrange the steps of a Hess-cycle calculation in the order you would carry them out.

**Answer:**

1. Write the target equation with its correct coefficients
2. Reverse or scale each known equation to match the target
3. Adjust the sign and magnitude of each enthalpy change accordingly
4. Add the adjusted enthalpy changes to obtain the target value

**Why:** Define the target first, then manipulate the known equations to build it, then apply exactly the same manipulations to their enthalpies, and only then add. Adjusting the equations without adjusting the enthalpies is the classic failure.

Page: https://tryals.app/practice/chemistry-i/enthalpy-and-thermochemistry/arrange-the-steps-of-a-hess-cycle-calculation-in-the-order-you-would