Enthalpy and enthalpy change
The part of a substance’s energy that shows up as heat effects is described by its enthalpy (H)焓. We can’t measure how much enthalpy a substance has, but we can measure the difference before and after a change:
At constant pressure (an open beaker or a coffee cup), ΔH equals the heat the system absorbs or releases. ΔH < 0 means exothermic; ΔH > 0 means endothermic.
Energy diagrams
The vertical axis of an energy diagram能量图 is enthalpy (energy), not temperature. Draw the reactants and the products each as a horizontal line:
- Exothermic: the products are below the reactants, and the ΔH arrow points down. The extra energy is released to the surroundings as heat.
- Endothermic: the products are above the reactants, and the ΔH arrow points up. The missing energy must be absorbed from the surroundings.
The energy profiles in U5.6 also showed the transition-state “hill.” The height of the hill is the activation energy, which sets how fast the reaction goes; the difference between the two ends is ΔH, which says whether it is endothermic or exothermic. This unit focuses on the two ends.
Reversing and doubling
Energy diagrams also show two rules:
- When a process runs in reverse, the start and end swap, so ΔH changes sign. CaO(s) + H₂O(l) → Ca(OH)₂(s) has ΔH = −65.2 kJ/mol, so Ca(OH)₂(s) → CaO(s) + H₂O(l) has ΔH = +65.2 kJ/mol.
- When the amounts double, twice as much heat is released (or absorbed), so ΔH doubles. An enthalpy change is proportional to how much reacts.
Explaining dissolving with a stepwise diagram
When an ionic compound dissolves in water, we can imagine it happening in three steps (the real process happens all at once; the steps are just for accounting):
- Separate the solute particles: overcoming the attractions between ions in the crystal is endothermic.
- Separate the solvent molecules: making room for the ions means overcoming attractions between water molecules, which is endothermic.
- Let the particles and solvent interact: ions and water molecules attract each other (ion–dipole attractions), which is exothermic.
The sum of the three enthalpy changes is ΔH for dissolving. If step 3 releases more energy than steps 1 and 2 absorb, dissolving is exothermic (as for NaOH); if less, dissolving is endothermic (as for NH₄NO₃).
Draw energy diagrams for several processes, and try reversing and doubling them; then use “Dissolving in three steps” to adjust the energy of each step:
Example 1: Drawing an energy diagram
Draw the energy diagram for CaO(s) + H₂O(l) → Ca(OH)₂(s) (ΔH = −65.2 kJ/mol, calculated from NBS enthalpies of formation), and give ΔH for the reverse reaction and for 2 mol of CaO reacting.
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Which end is higher? ΔH = −65.2 kJ/mol < 0, exothermic: the product Ca(OH)₂(s) has 65.2 kJ less enthalpy than the reactants CaO(s) + H₂O(l).
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Draw it.
- A high line on the left: CaO(s) + H₂O(l)
- A line 65.2 kJ lower on the right: Ca(OH)₂(s)
- A downward arrow labeled ΔH = −65.2 kJ
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Reverse reaction. Reversing the direction flips the sign of ΔH, and the arrow points up:
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2 mol of CaO. ΔH is proportional to the amount reacting, so doubling the coefficients doubles ΔH (in kJ):
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Check. Reversing or doubling only changes the arrow’s direction or length; which line is lower (products below reactants) is set by the forward reaction.
Example 2: Why do some salts absorb heat as they dissolve?
When NH₄NO₃ dissolves in water, the solution gets colder. Explain using a stepwise energy diagram.
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Break dissolving into three steps. Start the diagram from solid + water:
- Step 1: separate the ions in the crystal (overcome ion–ion attractions)
- Step 2: push water molecules apart to make room
- Step 3: ions and water molecules attract (ion–dipole interactions)
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Direction of each step. Steps 1 and 2 overcome attractions and absorb energy, so the diagram rises; step 3 forms attractions and releases energy, so it falls.
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Compare the rises and the drop. The drop in step 3 is smaller than the total rise in steps 1 and 2, so the end is higher than the start:
The CRC Handbook gives +25.69 kJ/mol for .
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Connect to what you see. The heat absorbed by dissolving (the system) comes from the water (the surroundings), which loses heat, so the solution gets colder.
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Conclusion. Separating the ions and the water molecules takes more energy than forming ion–water attractions releases, so dissolving is endothermic.
- A reaction with ΔH = −92 kJ/mol
Exothermic, so the products are below.
- A reaction with ΔH = +178 kJ/mol
Endothermic, so the products are above.
- Methane burning
Combustion is exothermic.
- Ice melting (H₂O(s) → H₂O(l))
Melting is endothermic.
- Steam condensing (H₂O(g) → H₂O(l))
Condensation is exothermic.
- Calcium carbonate decomposing
It needs continuous heating: endothermic.
- NaOH dissolving as the solution warms
Exothermic.
- KNO₃ dissolving as the solution cools
Endothermic.
- The reverse of an exothermic reaction
Reversing changes the sign of ΔH.
- Photosynthesis: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
Light energy is absorbed and stored as chemical energy.
Common mistakes
Mistake 1: “The vertical axis of an energy diagram is temperature.” It is enthalpy (energy). In an exothermic reaction the products have less enthalpy, yet the surroundings get warmer.
Mistake 2: “An exothermic reaction needs no energy to get started.” ΔH compares only the two ends. Many exothermic reactions still have an activation energy (U5.6); methane, for example, has to be lit before it burns.
Mistake 3: “Separating the solute particles releases energy when a solid dissolves.” Pulling apart particles that attract each other always absorbs energy; energy is released only when new attractions form between particles (step 3).
Quick check
On a process’s energy diagram, the products are 40 kJ above the reactants. Which statement is correct?
The products have more enthalpy, so ΔH is positive and the system absorbs heat from the surroundings.
The reaction A → B has ΔH = −120 kJ/mol. What is ΔH for 2B → 2A?
Reversing gives +120 kJ, and doubling gives +240 kJ.
Dissolving an ionic compound is split into three steps: separating the solute, separating the solvent, and letting the particles interact with the solvent. Which step releases energy?
The first two steps overcome attractions and are endothermic; only the third, which forms ion–dipole attractions, is exothermic.
A salt dissolves endothermically in water. Which explanation is best?
ΔH for dissolving is the sum of the three steps; endothermic means steps 1 and 2 absorb more than step 3 releases. A describes the exothermic case.
An energy diagram shows the reactants, a transition-state hill, and the products. What represents ΔH?
B is the forward activation energy and C the reverse activation energy; ΔH compares only the two ends.
CaO(s) + H₂O(l) → Ca(OH)₂(s) has ΔH = −65.2 kJ/mol. To decompose Ca(OH)₂(s) into CaO(s) and H₂O(l), what is needed per mole?
The reverse process has ΔH = +65.2 kJ/mol, so it is endothermic.
AP-style free response
The CRC Handbook gives ΔH = −44.51 kJ/mol for NaOH(s) dissolving in water and ΔH = +25.69 kJ/mol for NH₄NO₃(s) dissolving in water.
(a) Each solid is dissolved in the same amount of water. Which solution warms up? Justify your answer.
(b) Draw (or describe) the energy diagram for NaOH dissolving, and label ΔH.
(c) Use the three steps of dissolving to explain why NaOH dissolves exothermically.
(d) How much heat is released when 0.100 mol of NaOH dissolves completely?
(e) What is ΔH when 1 mol of NaOH(s) crystallizes out of an NaOH solution (the reverse of dissolving)?
Model answer and scoring
(a) The NaOH solution. Dissolving NaOH has ΔH < 0, so it releases heat to the water in the solution; NH₄NO₃ dissolves endothermically, so its solution cools.
(b) A line on the left for NaOH(s) + water and a line 44.51 kJ lower on the right for Na⁺(aq) + OH⁻(aq), with a downward arrow: ΔH = −44.51 kJ/mol.
(c) Separating the ions in the NaOH crystal and pushing water molecules apart both absorb energy; the ions and water molecules attracting each other releases energy. Step 3 releases more than steps 1 and 2 absorb together, so overall ΔH < 0.
(d) 0.100 mol × 44.51 kJ/mol = 4.45 kJ.
(e) ΔH = +44.51 kJ/mol (reversing changes the sign).
Scoring: (a) correct choice linked to the sign of ΔH; (b) products below, arrow down; (c) which steps absorb and release energy, and the comparison; (d) the calculation; (e) the sign change.
Summary
- ΔH = H(products) − H(reactants); at constant pressure it equals the heat absorbed or released.
- An energy diagram’s vertical axis is enthalpy: for an exothermic process the products are below, and for an endothermic one above. The hill’s height is the activation energy, and the difference between the ends is ΔH.
- Reversing a process changes the sign of ΔH; doubling the amounts doubles ΔH.
- Dissolving can be imagined as three steps: separating the solute (endothermic), separating the solvent (endothermic), and the particles interacting with the solvent (exothermic). Their sum decides whether dissolving is endothermic or exothermic.
AP tip: When reading an energy diagram, first check that the vertical axis is energy, then compare the two ends to get the sign of ΔH. To explain the heat effect of dissolving, say which steps absorb energy, which releases it, and which is larger.