热化学

Thermochemistry 热化学 tracks energy in reactions. A process is exothermic 放热 if it releases energy to the surroundings 环境 (feels hot, $\Delta H<0$) and endothermic 吸热 if it absorbs energy (feels cold, $\Delta H>0$). Breaking bonds 断键 costs energy; forming bonds 成键 releases it – the net decides the sign.

An energy diagram 能量图 plots energy from reactants 反应物 to products 生成物. Reactants above products means exothermic; below means endothermic. The vertical gap between them is the enthalpy change 焓变 $\Delta H$.

Heat 热量 flows from hot to cold until objects reach thermal equilibrium 热平衡 (equal temperature). Energy is conserved 能量守恒: for an isolated 孤立的 pair, the heat lost by the hot object equals the heat gained by the cold one.

The heat to change a substance's temperature is

where $c$ is the specific heat 比热容 (energy per gram per degree). Calorimetry 量热法 measures a reaction's heat by tracking the temperature change of surrounding water: in a simple insulated 隔热的 model, the heat the water gains equals the heat the reaction releases. Include heat absorbed by the container and any losses when they matter.

Worked example. A reaction in a coffee-cup calorimeter 量热计 warms $100\ \text{g}$ of water by $8.0\,{}^{\circ}\text{C}$ ($c=4.18\ \text{J/(g}\,{}^{\circ}\text{C)}$). The heat absorbed by the water is

By energy conservation the reaction released this $3.3\ \text{kJ}$, so it is exothermic ($q_{\text{rxn}}=-3.3\ \text{kJ}$).

During a phase change 相变 (melting 熔化, boiling 沸腾) the temperature stays constant while heat goes into breaking intermolecular forces 分子间作用力, not raising kinetic energy 动能. The energy needed is $q=n\,\Delta H_{\text{fus}}$ (melting) or $q=n\,\Delta H_{\text{vap}}$ (boiling) – the flat steps on a heating curve 加热曲线.

The enthalpy of reaction 反应焓 $\Delta H_{\text{rxn}}$ is the heat released or absorbed at constant pressure 恒压. Because enthalpy is a state function 状态函数, $\Delta H$ depends only on the initial and final states, not the path taken – the key that makes the next three methods work.

One way to estimate $\Delta H$: sum the energy to break all reactant bonds, then subtract the energy released forming product bonds:

This is an approximation, since bond enthalpies 键焓 are averages.

Worked example. Estimate $\Delta H$ for $\text{H}_2+\text{Cl}_2\rightarrow2\text{HCl}$ using bond enthalpies H–H $=436$, Cl–Cl $=242$, H–Cl $=431\ \text{kJ/mol}$. Break both reactant bonds ($436+242=678$) and form two H–Cl bonds ($2\times431=862$):

exothermic, because the strong H–Cl bonds formed release more than the reactant bonds cost.

The standard enthalpy of formation 生成焓 $\Delta H_f^\circ$ is the enthalpy to make one mole of a compound from its elements 单质 (zero for an element in its standard state 标准状态). Then

Worked example. Find $\Delta H_{\text{rxn}}^\circ$ for burning methane, $\text{CH}_4+2\text{O}_2\rightarrow\text{CO}_2+2\text{H}_2\text{O}$, given $\Delta H_f^\circ$: CH$_4=-75$, CO$_2=-394$, H$_2$O$=-286\ \text{kJ/mol}$ (O$_2=0$). Products minus reactants:

a large release, as expected for a combustion 燃烧.

Hess's law 盖斯定律: if a reaction is the sum of several steps, its $\Delta H$ is the sum of the steps' $\Delta H$ values. Reverse a step and flip the sign; scale a step and scale its $\Delta H$. This lets you find a hard-to-measure $\Delta H$ by combining known reactions – a frequent exam calculation.

Worked example. Find $\Delta H$ for $\text{C}(s)+\tfrac12\text{O}_2(g)\rightarrow\text{CO}(g)$, which cannot be measured directly because some $\text{CO}_2$ always forms. You are given

Keep step 1 as written (it has C on the left). Reverse step 2 so that CO is a product: $\text{CO}_2\rightarrow\text{CO}+\tfrac12\text{O}_2$, $\Delta H=+283\ \text{kJ}$. Add the two: $\text{CO}_2$ cancels, and $\text{O}_2 - \tfrac12\text{O}_2$ leaves $\tfrac12\text{O}_2$ on the left, which is the target. So

Check that every species left over matches the target equation before you add the numbers.

Common mistakes.

• Losing the sign in calorimetry. The water gains heat ($q_{\text{water}}>0$), so the reaction releases it: $q_{\text{rxn}}=-q_{\text{water}}$.
• Using the mass of the solid that dissolved, not of the solution, in $q=mc\,\Delta T$. The temperature change is of the water or solution, so use its mass.
• Turning a bond-enthalpy calculation upside down. It is broken − formed; with products − reactants (the $\Delta H_f^\circ$ order) you get the right size but the wrong sign.
• Counting bonds per molecule, not per equation. In $\text{H}_2+\text{Cl}_2\rightarrow2\text{HCl}$ there are two H–Cl bonds formed.
• Giving $\text{O}_2(g)$ or another element in its standard state a non-zero $\Delta H_f^\circ$. It is zero by definition.
• Forgetting the coefficients with $\Delta H_f^\circ$. Multiply each value by its coefficient: $2(-286)$ for two moles of water.
• Saying bond breaking releases energy. Breaking bonds always costs energy; energy is released only when bonds form.

• An exothermic reaction has $\Delta H<0$ (feels hot); endothermic has $\Delta H>0$ — always give $\Delta H$ a sign and units.
• In calorimetry use $q=mc\,\Delta T$ with the mass of the water/solution; the reaction releases what the water and calorimeter gain in an insulated model.
• Bond enthalpies: $\Delta H\approx\sum(\text{bonds broken})-\sum(\text{bonds made})$ — breaking is endothermic, making is exothermic (the classic sign trap).
• Hess's law: the total $\Delta H$ is the sum of the steps' — reverse a step and flip the sign, scale a step and scale $\Delta H$.
• During a phase change of a pure substance at fixed pressure, temperature stays constant while energy changes the interactions between particles.