Enthalpy changes

Every chemical reaction involves an energy transfer between the system (the reacting chemicals) and the surroundings (the solvent, container and environment). At constant pressure this transferred energy is the enthalpy change, $\Delta H$, almost always observed as heat.

The origin of the energy lies in chemical bonds:

• Breaking bonds absorbs energy (endothermic step).
• Forming bonds releases energy (exothermic step).

Whether the overall reaction releases or absorbs heat depends on the balance between energy taken in to break reactant bonds and energy given out when product bonds form.

Energy is conserved (first law of thermodynamics): the energy lost by the system is gained by the surroundings, and vice versa. This is exactly why calorimetry works - we measure the heat picked up (or lost) by the surrounding water and infer the energy change of the reaction.

Key ideas:

• $\Delta H$ is measured per mole of reaction as written, in kJ mol$^{-1}$.
• A negative $\Delta H$ means energy flows out to the surroundings; positive means energy flows in.
• Temperature change of the surroundings is the experimental clue to the sign of $\Delta H$.

Reactions are classified by the direction of heat flow.

Exothermic reactions release heat to the surroundings. The surroundings get warmer, the products have lower enthalpy than the reactants, and

$$\Delta H < 0 \;(\text{negative}).$$

Examples: combustion, neutralisation, most oxidations, respiration.

Endothermic reactions absorb heat from the surroundings. The surroundings get colder, the products have higher enthalpy than the reactants, and

$$\Delta H > 0 \;(\text{positive}).$$

Examples: thermal decomposition, photosynthesis, dissolving ammonium nitrate, the reaction of citric acid with hydrogencarbonate.

A reliable way to decide in the lab: feel the temperature of the surroundings.

• Temperature rises $\Rightarrow$ exothermic $\Rightarrow$ $\Delta H$ negative.
• Temperature falls $\Rightarrow$ endothermic $\Rightarrow$ $\Delta H$ positive.

A common error is to focus on the system rather than the surroundings. The thermometer reads the surroundings' temperature, so an exothermic reaction makes the *water* hotter even though the *chemicals* are losing enthalpy.

An energy profile (reaction pathway diagram) plots potential energy (y-axis) against reaction progress / extent of reaction (x-axis). It shows three key features.

• The reactant energy level (left) and the product energy level (right).
• The activation energy, $E_a$: the height of the hump from the reactants up to the peak (the transition state). Energy must be supplied to reach the top before products can form.
• The enthalpy change, $\Delta H$: the vertical gap between reactants and products, $H_{\text{products}} - H_{\text{reactants}}$.

Reading the sign:

• Exothermic: products lower than reactants, so $\Delta H$ is negative (arrow points down from reactants to products).
• Endothermic: products higher than reactants, so $\Delta H$ is positive (arrow points up).

When sketching, label the reactants, products, $E_a$ (peak height above reactants) and $\Delta H$ (the reactant-to-product gap) clearly, and make sure the products are drawn on the correct side for the sign of $\Delta H$.

Enthalpy changes vary with conditions, so to compare values fairly they are quoted as standard enthalpy changes, $\Delta H^{\ominus}$, measured under standard conditions:

• pressure of 100 kPa,
• a stated temperature, almost always 298 K (25 °C),
• substances in their standard states (most stable form at those conditions),
• any solutions at concentration 1 mol dm$^{-3}$.

The plimsoll symbol $^{\ominus}$ signals standard conditions, and $\Delta H^{\ominus}$ is given per mole of reaction as written, in kJ mol$^{-1}$.

Why it matters:

• It lets data from different experiments and labs be compared directly.
• It fixes the amount (the molar quantities in the balanced equation), so doubling the equation doubles $\Delta H^{\ominus}$.

For example, $\text{H}_2(g) + \tfrac{1}{2}\text{O}_2(g) \rightarrow \text{H}_2\text{O}(l)$ has $\Delta H^{\ominus} = -286$ kJ mol$^{-1}$, where the value refers to forming one mole of liquid water.

Note that standard conditions are not the same as standard temperature and pressure (STP) used for gas volumes - the 298 K reference temperature is a separate convention for thermochemistry.

Calorimetry measures an enthalpy change by tracking the temperature change of the surroundings (usually water or an aqueous solution).

The booklet equation is

$$q = mc\Delta T$$

where $q$ is the heat energy in J, $m$ is the mass of water/solution in g, $c$ is the specific heat capacity (for water $c_w = 4.18$ J g$^{-1}$ K$^{-1}$), and $\Delta T = T_{\text{final}} - T_{\text{initial}}$ is the temperature change in K (a change in °C equals a change in K).

Treat $q$ as the signed heat absorbed by the water: $q$ is positive when the water warms and negative when it cools. With this convention a single rule then covers both cases.

To turn $q$ into a molar enthalpy change:

• find the moles $n$ of the limiting reactant,
• compute $\Delta H = -\dfrac{q}{n}$, then divide by 1000 for kJ mol$^{-1}$.

Because of the minus sign, water that warms ($q>0$) gives a negative $\Delta H$ (exothermic) and water that cools ($q<0$) gives a positive $\Delta H$ (endothermic) automatically - you never adjust the sign by hand.

Useful assumptions made at IB:

• For dilute aqueous solutions, take the density as 1 g cm$^{-3}$, so the volume in cm$^3$ equals the mass in g.
• Use $c = c_w = 4.18$ J g$^{-1}$ K$^{-1}$ for the solution.

Heat loss to the air, the thermometer and the container is the main source of error and is why measured combustion values are usually less exothermic (less negative) than data-book values. Extrapolating a temperature-time graph back to the moment of mixing reduces this error.