# Getting Hotter – The Heating Curve

Thermochemistry is a large and active field that relates heat, or specifically change in energy, with the reactions of chemicals. Certain chemicals release heat when combined, becoming exothermic. Some absorb heat, becoming endothermic. Water tends to gain heat as it turns into steam, and loses heat as it turns into ice.

All chemicals, however, do not scale directly in temperature according to their specific heat. Heating ice to water takes far more than the number of calories required to change the temperature. Heat is also required to change the phase of substances. The combination of both the phase changes and temperature changes of an element or compounds is called a heating curve.

The base heating curve for water looks as the following; a small leg of negative temperature to zero, for ice. A short, flat bar as ice converts into water. A large 100 degree slope as the temperature of water reaches one hundred degrees Celsius. A longer phase change bar, approximately seven times longer than the one for ice changing into water, is the change from water to steam. And from there, the temperature of steam steadily increases with the more heat that is applied. Other chemicals will have a heating curve appearing similar, but not at the same melting or boiling points.

It is difficult to calculate the heat required when a substance changes through one or more phase changes. Most of the information can be found online, though the calculations are easier to describe. Again, water will be used, this time a 36 g sample, and it will be heated from -30C to 120C. Ice has a specific heat of 2.1 J/gC. According to the enthalpy formula, the equation is mass multiplied by specific heat multiplied by change in temperature. The change in temperature is the final temperature minus the initial temperature. The first step becomes 36 times 2.1 times (0- -30), or 30. This is 2268 joules, or 2.268 kilojoules. Water has a specific heat of 4.18 J/gC. The equation is 36 times 4.18 times (100 – 0), or simply 100. The q of that reaction is 15,048 J, or 15.048 kJ. Steam has a specific heat of 1.7 J/gC. 36 times 1.7 times (120 – 100) equals 1224 J, or 1.224 kJ.

This is not the whole process; those are just the temperature changes of the individual states. What has to be done next is to convert the mass of the substance into moles. There are have thirty-six grams of water, so the stoichiometry equation 36 x (1 mole water/18 grams water) equals two. This is important, because the energy put into the phase changes is so high that it is typically measured in kilojoules, which is why the above are also converted from joules to kilojoules. The first step is two moles x 6.01 kJ, or the phase change of ice to water, which equals 12.02 kJ. The second step is two moles x 40.7, which is the change of water to steam. This one equals 81.4 kJ.

The final step is to add all the numbers together. Ice to 0C, 2.268 kJ. Ice to water, 12.02 kJ. Water to 100C, 15.048 kJ. Water to steam, 81.4 kJ. Steam to the final temperature of 120C is 1.224 kJ. Adding all of those together results in the total of 111.96 kJ, which is far more than only adding the temperature changes together.

That is how to calculate the temperature of water through its phase changes. Two notes to keep in mind; the heating curve does not always start at ice, or the solid state, nor does it end only after the gaseous form is reached. Perhaps a conversion from solid to liquid is all that is needed; change the final temperatures and take out steps as required. Secondly, some prefer to calculate the heating curve chronologically, meaning that they would calculate ice to 0C, then the heat required to convert ice to water, then water to 100C and so forth.