Heat of Fusion & Vaporization Solver

Free Heat of Fusion & Vaporization Solver

This calculator solves the molar phase-change equation Q = nΔH for melting (fusion), boiling (vaporization), and sublimation, where the sample skips the liquid stage entirely and turns straight from solid to gas. Pick a process, choose a substance from the built-in preset list, and solve for the heat energy, the amount of substance, or the molar enthalpy itself — all with a full worked solution and a labelled diagram.

A second tool, under Advanced Tools, is a complete multi-stage heating (or cooling) curve solver. Enter a starting and ending temperature and it automatically works out every warming and phase-change stage in between — warm the solid, melt it, warm the liquid, boil it, warm the gas — and adds them all together, exactly the way a full heating-curve problem is solved in a chemistry course.

What Are Heat of Fusion and Heat of Vaporization?

Heat of fusion (ΔHfus) is the energy needed to melt one mole of a solid into a liquid at its melting point, with no change in temperature. Heat of vaporization (ΔHvap) is the energy needed to boil one mole of a liquid into a gas at its boiling point, again at constant temperature. Both are usually reported in kJ/mol.

The same amount of energy is released in reverse: freezing releases the heat of fusion, and condensing releases the heat of vaporization. This is why steam burns are so severe — condensing steam back to liquid water on skin dumps a large amount of energy very quickly, on top of whatever heat the hot water itself carries.

The Formula: Q = nΔH

The governing equation is Q = n × ΔH, where Q is heat energy, n is the amount of substance in moles, and ΔH is the molar enthalpy of the transition — ΔHfus, ΔHvap, or ΔHsub depending on the process. Rearranged, n = Q/ΔH finds the amount of substance, and ΔH = Q/n finds the molar enthalpy itself from experimental data.

If a mass in grams is given instead of moles, convert first using n = mass ÷ molar mass. This calculator does that conversion automatically whenever grams are selected as the input unit.

Sublimation: Skipping the Liquid Phase

Sublimation happens when a solid turns directly into a gas without passing through a liquid stage in between — dry ice (solid carbon dioxide) is the classic everyday example, along with the way ice and snow can slowly disappear on a cold, dry, sunny day even while staying below 0 °C. The energy needed, ΔHsub, is typically close to the sum of ΔHfus and ΔHvap for the same substance, since the particles still have to overcome both the solid's internal structure and the liquid's remaining attraction in one combined step.

Freeze-drying, a common food and pharmaceutical preservation technique, relies entirely on sublimation: a frozen sample is placed under low pressure, and ice sublimates directly out of it without ever passing through a liquid stage that could damage delicate structures.

How to Use This Calculator

On the Standard Solver tab, choose fusion, vaporization, or sublimation, then pick a substance — its molar enthalpy and molar mass fill in automatically, though every field can be overridden. Choose what you're solving for, enter the amount of substance in moles or grams, and the energy in your preferred unit. The result panel shows every variable at once.

On the Advanced Tools tab, pick 'Water (preset values)' or 'Custom substance', enter the mass and the starting and ending temperature, and the calculator automatically figures out which stages apply — warming within a single phase, or a full phase change at the melting or boiling point — and adds up the total energy, with a bar chart breaking down each stage.

Worked Example: Melting Ice

How much energy melts 36 g of ice at 0 °C? First convert to moles: n = 36 ÷ 18.02 ≈ 2.0 mol. Water's heat of fusion is 6.01 kJ/mol, so Q = n × ΔHfus = 2.0 × 6.01 = 12.02 kJ, or 12,020 J.

Notice this is far less energy than boiling the same mass of water would need — melting only has to loosen the solid's rigid crystal structure into a liquid, while boiling has to overcome nearly all of the remaining intermolecular attraction to free the molecules into a gas.

Worked Example: Boiling Ethanol

How much heat is released when 4.6 g of ethanol vapor condenses back to liquid at its boiling point? Ethanol's molar mass is 46.07 g/mol, so n = 4.6 ÷ 46.07 = 0.1 mol. Its heat of vaporization is 38.6 kJ/mol, so Q = n × ΔHvap = 0.1 × 38.6 = 3.86 kJ is released during condensation — the same magnitude that would be absorbed if that ethanol were vaporized instead.

Worked Example: A Full Water Heating Curve

Take 100 g of ice starting at −10 °C and heat it all the way to steam at 120 °C — a classic five-stage heating-curve problem, and exactly what the Advanced Tools tab solves automatically. Stage 1 warms the ice from −10 °C to 0 °C: Q = 100 × 2.09 × 10 = 2,090 J. Stage 2 melts it at 0 °C: Q = 100 × 334 = 33,400 J.

Stage 3 warms the liquid water from 0 °C to 100 °C: Q = 100 × 4.184 × 100 = 41,840 J. Stage 4 boils it at 100 °C: Q = 100 × 2,260 = 226,000 J. Stage 5 warms the resulting steam from 100 °C to 120 °C: Q = 100 × 2.0 × 20 = 4,000 J. Adding every stage together gives a total of about 307,330 J, or roughly 307.3 kJ — and boiling alone accounts for nearly three-quarters of that total.

Why Vaporization Needs So Much More Energy Than Fusion

For almost every substance, ΔHvap is several times larger than ΔHfus. Melting only has to loosen a solid's fixed lattice into a liquid, where particles are still close together and still attracting one another strongly — think of ice cubes shifting into a puddle that still holds together. Vaporization has to pull particles apart almost completely, overcoming nearly all of the intermolecular forces holding the liquid together, which takes far more energy.

Water shows this especially clearly: ΔHvap (40.7 kJ/mol) is about 6.8 times larger than ΔHfus (6.01 kJ/mol), which is exactly why the worked example above spends so much more energy boiling the water than melting the ice.

Common Molar Enthalpy Values

A few reference values in kJ/mol, the same ones used as presets in the calculator above:

• Water: ΔHfus = 6.01, ΔHvap = 40.7
• Ethanol: ΔHfus = 4.9, ΔHvap = 38.6
• Methanol: ΔHfus = 3.16, ΔHvap = 35.21
• Benzene: ΔHfus = 9.87, ΔHvap = 30.72
• Ammonia: ΔHfus = 5.66, ΔHvap = 23.35
• Mercury: ΔHfus = 2.29, ΔHvap = 59.11
• Dry ice (CO2), sublimation: ΔHsub = 25.2
• Iodine (I2), sublimation: ΔHsub = 62.3

Common Mistakes to Avoid

The most common error is applying Q = mcΔT across a phase change instead of Q = nΔH, or the other way around — a heating curve always needs both formulas used in the correct stages, never one formula stretched across the whole path.

• Don't forget to convert grams to moles before using Q = nΔH — molar enthalpy is defined per mole, not per gram.
• Watch for a starting or ending temperature that lands exactly on the melting or boiling point — that boundary case is usually treated as still being in the lower-temperature phase until further heat is added.
• Keep ΔH in kJ/mol and convert to J/mol (× 1000) before mixing it into a calculation that uses joules elsewhere.
• Remember that freezing, condensing, and depositing release energy — the same magnitude as melting, boiling, and sublimation absorb, just in the opposite direction.

Where These Calculations Show Up in Real Life

Heat of fusion and vaporization calculations sit behind refrigeration and air-conditioning cycle design, steam-power-plant engineering, freeze-drying in food and pharmaceutical manufacturing, sizing ice packs and cooling systems, understanding why sweating cools the body, and predicting how much energy a phase-change material can store or release for thermal-management applications.

Limitations to Keep in Mind

This calculator assumes ideal heat transfer with nothing lost to the surroundings, and molar enthalpy and specific heat values that stay constant across the small temperature ranges involved. Real transition enthalpies shift somewhat with pressure — the values used here are standard values at 1 atmosphere.

The heating-curve tool assumes the sample passes cleanly through solid, liquid, and gas phases in order; it isn't designed for substances that sublimate directly under normal pressure, like dry ice, since that path skips the liquid stage the tool assumes exists between Tm and Tb.

Quick Reference: Every Formula on This Page

Q = n × ΔHfus — energy for melting or freezing. Q = n × ΔHvap — energy for boiling or condensing. Q = n × ΔHsub — energy for sublimation or deposition. n = mass ÷ molar mass — converting grams to moles. Q = mcΔT — sensible heat for warming within a single phase, used alongside phase-change energy in a full heating curve.