How To Calculate A Calorific Value

Have you ever wondered where the information about calories on food labels comes from? How is it possible to know how much energy food will provide without actually studying its path from the mouth to whatever cells wind up consuming the glucose molecules generated from the carbohydrates, fats and proteins making up the (non-water) portions of food you eat?

The calorie content, or the calorific value, of a substance is the amount of energy that is liberated when the substance is completely "burned," or undergoes complete combustion. Combustion is one of the five basic types of chemical reactions, and it always occurs in the presence of oxygen gas (O₂), with the other reactant being some kind of (usually carbon-based) fuel.

• The calorific value of a substance is usually given on a per-amount basis, that is, per mole (m) of substance burned.

First, some terminology. A calorie (cal) is the amount of heat (energy) needed to raise the temperature of 1 g (gram) of water 1 degree Celsius (°C). The "calories" on nutrition labels are actually kilocalories, or kcal (1,000 cal). In chemistry, the standard unit of energy is the joule (J), equal to 4.18 cal. Thus, 1 food "calorie" is equal to (1.000)(4.18) J = 4.18 kJ.

The energy content of food is measured by putting a known mass of a specific substance (e.g., ethanol, an amino acid, glucose) into a device called a bomb calorimeter and measuring the amount of heat liberated when the reaction goes to completion. This is accomplished by measuring the temperature change of a known mass of water in the sealed calorimeter.

This sub-science, called calorimetry, allows for a theoretical calculation of calorific value. It depends on knowing how a given energy input changes a known mass of water. In fact, this quantity, called the specific heat of water, has been known for some time and is explained below. (Other substances have their own specific heats for use in different chemistry situations.)

The formula for the heat of combustion (or enthalpy of combustion) is an equation:

H = mCΔT

Here, H is the heat released by combustion, m is the mass in grams of the water used as a heat collector, C is the specific heat of water (4.184 J/g⋅°C) , and ΔT is the temperature change in °C.

The calorific value formula often looks different from this, because H and C are often represented by a different symbols. As long as the units all align so that you are left with units of energy (preferably J), the precise calorific value formula you use does not matter.

A 15.5-gram sample of ethanol, C₂H₆O (the alcohol in "adult beverages") is burned in 2,000 g of H₂O (2 liters at room temperature). This results in a temperature change of 55 °C. What is the molar heat of combustion (heat of combustion per mole) of ethanol? Refer to a periodic table (see the Resources) for molecular weights of elements.

First, use a periodic table to calculate the number of moles of ethanol present. 1 mol contains two C atoms (molecular weight, or MW, of 12.0 g; six H atoms (MW = 1.07 g); and one oxygen atom (MW = 16.0 g). Thus 1 mol = (2)(12) + (6)(1) + 16 = 46.0 g. You have 15.5 g, so you have 15.5/46.0 = 0.336 mol.

Now, refer to the equation above to figure out the energy liberated from the mass m, the known value of C, and the temperature change ΔT of the water:

H = (2,000 g)(4.184 J/g⋅°C)(55 °C) = 460,240 J = 460.24 kJ

Now, divide by the number of moles present to get the molar heat of combustion of ethanol:

(460.24 kJ)/(0.336 mol) = 1,369 kJ/mol.

This is a substantial number, what you would expect of something that can be used to power automobiles.