Enthalpy Calculator (Hess's Law)
Enter known reaction steps with their ΔH values, flip or scale any step, and sum them to find the overall enthalpy change using Hess's Law — with an energy-level diagram and full step-by-step arithmetic.
Background
Hess's Law says enthalpy is a state function: the overall ΔH depends only on the initial and final states, not the path taken to get there. That means known reactions can be reversed (flip the sign of ΔH) or scaled (multiply ΔH by the same factor) and added together to build a target reaction — and the sum of their ΔH values gives the ΔH of that target, regardless of how many intermediate steps it took.
How to use this calculator
- Choose Simple (quick 1–3 steps) or Advanced (add as many steps as you need).
- For each step: enter ΔH in kJ or kcal. If you reverse a reaction, check Flip — this changes the sign of ΔH. If you multiply a reaction by n, set the Multiplier (e.g., 2 or 1/2) — this scales ΔH by that same factor.
- Calculate: get the total ΔH, an energy-level diagram, a full breakdown table, and the exact arithmetic for every step.
How Hess's Law works
The core idea. Enthalpy is a state function — it depends only on where you start and where you end up, not the road you took. So if you can build your target reaction by combining known reactions (reversing or scaling them as needed), the ΔH values of those known reactions add up to the ΔH of the target.
Flipping a reaction. Reversing a reaction's direction reverses the sign of ΔH — an exothermic step (releases energy, ΔH < 0) becomes endothermic (absorbs energy, ΔH > 0) when flipped, and vice versa.
Scaling a reaction. Multiplying every coefficient in a reaction by n multiplies its ΔH by that same n — doubling the reaction doubles the enthalpy change.
Units. This calculator converts kcal to kJ internally (1 kcal = 4.184 kJ) so steps in different units can be summed directly, then shows the total in both.
Formulas Used
Overall enthalpy change: ΔH = Σ (sᵢ · mᵢ · ΔHᵢ) for steps i = 1…N
sᵢ = +1 as written, or −1 if the step is flipped
mᵢ = the multiplier applied to that step (e.g., 2, 1/2)
ΔHᵢ = that step's enthalpy in consistent units (kJ)
Fully Worked Example Problems
Example 1 — Reversing a step
Given: H₂ + ½ O₂ → H₂O(l), ΔH = −285.8 kJ.
Reverse it to form H₂O(l) → H₂ + ½ O₂. Flipping changes the sign: +285.8 kJ.
Example 2 — Scaling a step
Given: CO(g) + ½ O₂ → CO₂(g), ΔH = −282.7 kJ.
Doubling the reaction (2 CO + O₂ → 2 CO₂) multiplies ΔH by 2: −565.4 kJ.
Example 3 — Summing two steps
Step 1: C(s) + O₂ → CO₂(g), ΔH = −393.5 kJ
Step 2: H₂(g) + ½ O₂(g) → H₂O(l), ΔH = −285.8 kJ
Sum (no flips, multiplier = 1): ΔHtotal = −679.3 kJ.
Example 4 — Flip and scale together
Given: N₂ + 3H₂ → 2NH₃, ΔH = −92.2 kJ. Find ΔH for ⅔NH₃ → ⅓N₂ + H₂.
This is the reverse (flip: sign changes to +92.2 kJ) scaled by ⅓ (multiplier = 1/3): +92.2 × ⅓ = +30.7 kJ.
Example 5 — A 4-step chain (methane combustion)
Find ΔH for CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l) using formation reactions:
CH₄(g) → C(s) + 2H₂(g), flipped: +74.8 kJ
C(s) + O₂(g) → CO₂(g): −393.5 kJ
H₂(g) + ½O₂(g) → H₂O(l) (×2, entered as two rows): −285.8 kJ + −285.8 kJ
Sum: 74.8 − 393.5 − 285.8 − 285.8 = −890.3 kJ — the standard enthalpy of combustion of methane.
Frequently Asked Questions
What does "Flip (reverse)" do?
It reverses the reaction's direction and changes the sign of its ΔH — exothermic becomes endothermic, and vice versa.
How do multipliers work?
Multiplying all coefficients in a reaction by n scales its ΔH by that same n. Doubling a reaction doubles ΔH; halving it halves ΔH.
Can I mix kJ and kcal across steps?
Yes. Every step is converted to kJ internally (1 kcal = 4.184 kJ) before summing, and the total is shown in both units.
What does a negative total ΔH mean?
A negative ΔH means the overall reaction is exothermic — it releases energy to the surroundings. A positive ΔH means it's endothermic and absorbs energy.
Does the order I enter steps in matter?
No — addition is commutative, so the total ΔH is the same regardless of step order. The order only affects how the energy-level diagram is drawn.
Why enter a reaction equation if it's optional?
It's just for your own reference and to label the diagram/table clearly — the calculation only uses the ΔH, flip, and multiplier values, not the equation text itself.
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