When a substance changes its state of matter, it takes a specific amount of energy to complete the change. When the phase change is between liquid and gas, the amount of energy per unit mass is called the heat of vaporization. These two heat of vaporization example problems will show how to apply heat of vaporization to heat equations.

The equation to find this energy is rather simple.

Q = m · ΔH_{v}

where

Q = Energy (heat)

m = mass

ΔH_{v} = heat of vaporization

### Heat of Vaporization Example Problem 1

**Question:** The heat of vaporization of water is 2257 Joules/gram or 540 calories/gram. What energy in Joules is required to convert 50 grams of water into steam? How much energy in calories?

**Solution:** Plug what we know into the heat formula from above.

m = 50 grams

ΔH_{v} = 2257 J/gram

Q = m · ΔH_{v}

Q = (50 g) · (2257 J/g)

Q = 112850 J = 112.85 kJ

In calories:

ΔH_{v} = 540 cal/g

Q = m · ΔH_{v}

Q = (50 g) · (540 cal/g)

Q = 27000 cal = 27 kcal

**Answer:** It takes 112850 Joules or 27000 calories of heat to convert 50 grams of liquid water into gaseous water or steam.

### Heat of Vaporization Example Problem 2

**Question:** Liquid sulfur vaporizes at 445 °C. If it takes 28125 J to convert 20 grams of 445 °C liquid sulfur to 445 °C gaseous sulfur, what is the heat of vaporization of sulfur?

**Solution:** List what we know:

m = 20 g

Q = 28125 J

Plug these values into the heat of vaporization equation.

Q = m · ΔH_{v}

28125 J = (20 g) · ΔH_{v}

Solve for ΔH_{v}.

ΔH_{v} = (28125 J) / (20 g)

ΔH_{v}= 1406.25 J/g

**Answer:** The heat of vaporization of sulfur is 1406.25 J/g.

### Heat of Vaporization Homework Tips

These problems are not particularly difficult to perform but they can yield incorrect answers if you don’t watch your units.

Energy and mass have several different types of units. Energy has Joules, calories, kilocalories, electronvolts, ergs….just to name a few. Mass is usually some multiples of grams (kilograms, milligrams, micrograms, etc) but could also be ounces or pounds. Make sure you check which units you need for the problem at hand.

Another point of error can occur when looking up heats of vaporization from tables. Chemists are often the scientists who work with heats of vaporization of elements and compounds, and their unit of “mass” is the mole. Their tables typically have heat of vaporization units of Joules/mole or the amount of energy to vaporize one mole of the substance.

### Heat and Energy Example Problems

Heat of Fusion Example Problem – Example Problems showing how to use or find the heat of fusion of a substance.