Calorimetry

How do you measure the energy change of a reaction? It's not possible to do this directly. However, we can do it indirectly. One way of doing this is by measuring the reaction's enthalpy change using a process called calorimetry.

• This article is about calorimetry in physical chemistry.
• We'll start by looking at the different types of calorimetry.
• We'll then explore the equation you use in calorimetry to calculate enthalpy change.
• After that, we'll look at how you use calorimetry to calculate enthalpies of reaction, neutralisation, and combustion.
• Finally, we'll go over some of the limitations of calorimetry.

What is Calorimetry?

As we explored above, calorimetry is a method used to measure the enthalpy change of the reaction. In other words, it measures the heat change of a reaction. However, it is impossible to measure heat change directly. Instead, we have to measure the temperature change caused by heat.

Types of Calorimetry

There are a few different types of calorimetry:

• Direct calorimetry
• Indirect calorimetry
• Differential scanning calorimetry

Direct calorimetry

Direct calorimetry, as the name suggests, measures the heat change of a chemical reaction by directly measuring the temperature change it causes. It does this using a calorimeter.

A simple calorimeter can be made with a polystyrene drinking cup, water, and a thermometer. The reaction we're interested in releases heat energy which warms the water up. The idea is that we minimise heat loss and measure the temperature change of the water, and then use this to calculate the enthalpy change of the reaction.

Indirect calorimetry

Indirect calorimetry is a term used in biology. It is a way of measuring the heat change of an organism by measuring either their intake of oxygen or their output of carbon dioxide or nitrogen.

Differential scanning calorimetry

Different substances all need different amounts of heat energy to raise their temperature. Differential scanning calorimetry is a technique used to measure the difference in the amount of energy needed to raise the temperatures of a sample and a reference substance by the same amount. It is often used in biology to find out the specific heat capacity of various proteins and other biological molecules, and investigate their response to heating.

Calorimetry Equation

As we explored above, the aim of calorimetry is to measure the enthalpy change of a reaction. We do this by measuring the temperature change of another substance that a reaction causes. Let's call this substance X. Temperature and enthalpy are related by the following equation:

$\mathrm{q}=\mathrm{mc\Delta T}$

In this equation:

• q is the enthalpy change of the reaction, measured in J.
• m is the mass of X, measured in g.
• c is the specific heat capacity of X, measured in J g^-1 K^-1.
• ΔT is the temperature change of X, measured in K.

Don't worry - we'll practice using this equation in just a second. But for now, let's get on to the main focus of this article: carrying out calorimetry.

Calorimetry Experiment

We've already explored one type of calorimeter. It consists of a polystyrene cup filled with water or another solution. The heat energy released by a reaction is used to heat the water and the water's temperature change is measured. We're now going to look in more detail at how you can use calorimetry to work out enthalpies of reaction, neutralisation, and combustion.

Remember:

Finding enthalpy of reaction

For reactions involving mixing two solutions or adding a solid to a solution, you can work out the enthalpy of reaction using calorimetry. You do this by either mixing the two solutions or adding the solid to the solution, and measuring the solution's temperature change. In this example, we'll add a solid to an aqueous solution. Here's the method:

• Rinse a polystyrene cup and a measuring cylinder in the solution you are going to use, then dry thoroughly.
• Measure out 50 cm³ of the solution and pour into the polystyrene cup. Place the cup in a beaker and add a lid on top.
• Weigh out approximately 2.00g of your solid reactant into a weighing boat.
• Poke a thermometer through a hole in the lid. Measure the temperature of the solution every 30 seconds for three minutes.
• At the third minute, don't measure the temperature, but instead, add your solid reactant to your solution. Reweigh the weighing boat to see if any solid is left behind, and subtract this from the starting weight.
• Measure the temperature of the solution every 30 seconds for five minutes, or until the temperature remains constant.

Finding the enthalpy change

We now need to find the temperature change of the reaction, as we can use this to calculate the reaction's enthalpy change. However, we haven't got a temperature value for the exact moment when we added the solid and started the reaction. The point of addition is 3 minutes, whereas our first data point is at the 3 minute 30 second mark. To find the exact temperature rise of the reaction, we first need to plot a graph of the temperature of the solution against time and extrapolate the temperature back to the point of addition. Sound confusing? Here is how you do it.

To calculate the enthalpy change of the reaction, we need to use the equation we discussed earlier: $\mathrm{q}=\mathrm{mc\Delta T}$. What values do we know?

Well, m refers to the mass of the solution being heated, in this case, copper sulphate solution. Copper sulphate has a density of $1\mathrm{g}{\mathrm{cm}}^{-3}$ and so our solution weighs 50g. c refers to the specific heat capacity of the copper sulphate solution, which is given in the question: $4.18\mathrm{J}{\mathrm{g}}^{-1}{\mathrm{K}}^{-1}$. We just need to find ΔT, the total temperature change of the reaction. To do this, let's plot our points on a graph. Put temperature on the y-axis and time on the x-axis. You should end up with something like this:

Data points for a calorimetry experiment plotted on a graph. Anna Brewer, StudySmarter Originals

We now need to draw two lines of best fit – one before we added the zinc at the 3-minute mark, and one after. Notice how there isn't a data point at the 3-minute mark itself. instead, we extrapolate our lines back to that point. You can see this below:

To find the temperature change of the reaction, we measure the difference between the two lines at the point of addition, which is the 3-minute mark.

We can now substitute all of these values into the equation:

$$\begin{gathered} \mathrm{q}=\mathrm{mc}∆\mathrm{T} \\ \mathrm{q}=50\mathrm{x}4.18\mathrm{x}27=5643\mathrm{J} \end{gathered}$$

However, this isn't quite the final answer. We need to do two more things.

Firstly, we've simply calculated enthalpy change. The question has asked for the enthalpy of reaction, which is given in kJ per mole. We need to work out how many moles of zinc reacted and divide the enthalpy change we worked out by this number. Zinc has an atomic number of 65.4, and we have 2.00 grams of it in the question. We therefore have $2÷65.4=0.0306\mathrm{mol}$. $5643÷0.0306=184.4\mathrm{kJ}{\mathrm{mol}}^{-1}$ .

Finally, this was an exothermic reaction. Overall, energy was released. Therefore, the final answer needs a negative sign in front of it: $-184.4\mathrm{kJ}{\mathrm{mol}}^{-1}$.

Finding enthalpy of neutralisation

Finding the enthalpy of neutralisation works in exactly the same way as finding the enthalpy of reaction. You combine your two reactants, whether they be solutions or a solid and a solution, and record the temperature change over several minutes. You then plot a graph and extrapolate back to the point of addition in order to find a maximum temperature. You then work out the temperature change and calculate enthalpy change, as described above.

Finding enthalpy of combustion

For reactions involving combustion, we can calculate the enthalpy of combustion using calorimetry. We do this by burning a fuel below a beaker of water and measuring the temperature change of the water. Here's how you go about it:

1. Measure a known mass of cold water into a copper can.
2. Suspend the copper can above a fuel burner using a stand and clamp or a tripod.
3. Measure the temperature of the water and the mass of the fuel burner.
4. Light the fuel burner and let it burn until the temperature of the water has risen by approximately 25 ° C. Keep measuring the temperature as it could still increase after the fuel has been extinguished.
5. Measure the mass of the fuel burner again and subtract this from its starting mass to find the fuel burner's change in mass.

Finding the enthalpy change

First, we need to calculate the enthalpy change of the reaction. Here, m = 150 and c = 4.18. To find ΔT, the change in temperature, we subtract the starting temperature from the end temperature. Here, ΔT = 50 - 21 = 29 ℃ . Putting all of these values into the equation for enthalpy gives us the following:

$$\begin{gathered} \mathrm{q}=\mathrm{mc}∆\mathrm{T} \\ \mathrm{q}=150\mathrm{x}4.18\mathrm{x}29=18183\mathrm{J} \end{gathered}$$

However, the enthalpy of combustion is measured in kilojoules per mole. We now need to divide the enthalpy change by the number of moles of ethanol burnt. Ethanol has a relative formula mass of 46. We therefore have $0.5÷46=0.0109$moles of ethanol. Ethanol's enthalpy of combustion is therefore $18183÷0.0109=1668.2\mathrm{kJ}{\mathrm{mol}}^{-1}$. But we're not quite finished - once again, this is an example of an exothermic reaction and so we need a negative sign in front of the answer. Our final answer is $-1668.2\mathrm{kJ}{\mathrm{mol}}^{-1}$.

Limitations of Calorimetry

Calorimetry can be extremely frustrating. You may follow an identical method to your partner but obtain extremely different results. This is because there are many variables that come into play during calorimetry and it is impossible to accurately control all of them. For example:

• There could be energy transfer to or from the environment, usually in the form of heat loss.
• We always assume the solution used has the specific heat capacity and density of pure water, but this might not be the case.
• The reaction could be incomplete.
• Some of the heat energy released could heat up the apparatus instead of the solution itself.
• Some of the fuel might evaporate.

However, there are ways to minimise variation in results. These mostly involve minimising heat loss to the environment. Examples include:

• When measuring the enthalpy of reaction, you put the reacting solution inside of a polystyrene cup, which is in turn placed inside a beaker. This insulates the solution.
• When measuring the enthalpy of combustion, you might use a wind shield to protect the fuel burner from any drafts. You should also keep the beaker of water a fixed distance above the burner, to make your results more reproducible.
• In both cases, you could put a lid on top of the beaker or polystyrene cup, again to improve insulation and minimise any heat loss.