SCH4U - Chemistry 12 (2024-25) - A

A. Calculating Changes in Enthalpy

Have you ever stepped out on to the beach on a hot sunny day and felt the bottom of your feet start to burn, only to run into the water to cool them off immediately? Did you ever consider why the sand so much hotter than the water?

The reason the sand feels so much hotter is because it takes much more energy to raise 1 gram of water by 1 °C than it does to raise the temperature of the same mass of sand.  This is due to a characteristic that is known as specific heat capacity, given in units of J/(g*°C) and is represented by the letter: c. The specific heat capacity of a substance is the amount of energy, in units of Joules (J) or kiloJoules (kJ), it takes to raise the temperature of 1 gram of that substance by 1 °C. Water has a c = 4.18 J/g*°C while sand has a c = 0.835, therefore it takes more than 4 times more energy to raise the temperature of water by 1 °C than it does for sand.

The formula for calculating specific heat capacity is: c = Q /(m*ΔT), where Q = energy; m = mass, in grams; and ΔT = the change in temperature.

B. Heat Transfer

We have learned earlier in the unit that chemists are very interested in the heat transfer that takes place between the system and surroundings in chemical processes. We will now begin learning how to calculate these values. Measuring heat is a difficult task for scientists. Remember that heat does not mean temperature, instead it is a measure of energy. Heat affects temperature, causing it to rise or fall. Because it is difficult to measure the change in heat of a system directly, scientists are able to calculate the transfer of heat by rearranging the formula for specific heat capacity to solve for Q. Thus the equation to calculate energy becomes:

Q = m x c x ΔT

In this formula:

Q = the amount of heat absorbed or released by the substance you are measuring in J or kJ

m = mass of the substance in grams (g)

c = specific heat capacity of the substance in J/(g*°C)

ΔT = Final Temperature - Initial Temperature in °C

When the system gains heat, Q is positive; and when the system loses heat, Q is negative. When we are doing these calculations we are really measuring how much heat a system gains or loses, in other words we are calculating the change in heat, or the change in enthalpy (ΔH). Therefore, Q = ΔH.

Sample Problem:

How much heat is transferred when 20.0 g of copper, which has a specific heat capacity of 0.385 J/g*˚C is placed in a sealed, insulated cup of water and cooled from 85.0 ˚C to 25.0 ˚C?

In this question, we are going to calculate the change in heat for the copper, which is the system, while the water acts as the surroundings.

Step 1. Identify the Variables:

Q_copper = m x c x ΔT:

Q_copper = ?

m = 20.0 g

c = 0.385 J/g*˚C

ΔT = (25.0 ˚C - 85.0 ˚C) = - 60 ˚C

Step 2. Solve for the unknown:

Q_copper = (20.0 g) x (0.385 J/g*˚C) x (- 60 ˚C)

Q_copper = - 462 J.

Note, because our value for Q here is negative, this means that the system (copper) lost heat, while the surroundings gained that heat.

Step 3. Solution:

Q_copper = - 462 J. When the piece of copper was cooled from 85.0 ˚C to 25.0 ˚C, 462 J of heat was released. We can also say that the ΔH of the system was - 462 J, therefore this was an exothermic reaction.

C. Calorimetry

In the example above we saw that the piece of copper released 462 J of heat when it cooled down. We also said that the cooling off happened in a sealed, insulated cup of water. Because the cup is insulated and sealed, we can assume that all of the energy that was released by the copper (system) was gained by the surroundings (water). Therefore, we can say that since the value of Q for the copper was - 462 J, the value of Q for the water must be + 462 J. Qsystem = - Qsurroundings ΔHsystem = - ΔHsurroundings It is often very difficult to directly measure the ΔH of a reaction, because we can't necessarily measure the change in temperature of a system and apply that value to our equation Q = m x c x ΔT; however, if the reaction takes place in a surroundings with a known mass and specific heat capacity, that we can accurately measure a change in temperature, than we can simply calculate that value for the surroundings and reverse the sign to find out the ΔH of the system. To measure these ΔH values, scientists use a device known as a calorimeter. In a calorimeter, the heat absorbed or released by the system is measured by a change in the temperature of the surroundings. A calorimeter is made up of a sealed vessel, filled with a known mass of water, where the reaction can take place, a thermometer to measure the change in temperature and a stirring device. For a calorimeter to accurately measure heat transfer, it needs to be sealed and insulated, ensuring that all heat transferred from the system is captured by the surroundings. To calculate a ΔH for a reaction, we measure the initial temperature of the water, allow the reaction to begin and than record the final temperature of the water. We then apply our formula for Q to measure the heat transfer for the surroundings. Once we have the ΔH value for the surroundings, we reverse the sign to determine the ΔH of the system.

Sample Problem:

When a solid dissolves in water, there is a change in enthalpy which we can calculate using a calorimeter. Calculate the ΔH for the dissolution of KBr in water for the following experiment: 125 g of water (the surroundings) is added to a calorimeter, which has an initial temperature of 23.4 ˚C. Next, 10.5 grams of solid KBr (the system) is added to the water in the calorimeter and stirred. Over time, the temperature of the water begins to drop until a final temperature of 20.3 ˚C is reached. Calculate the ΔH, in kJ, for the dissolving of KBr in water and indicate if the reaction is endothermic or exothermic. Note, water has a specific heat capacity of 4.18 J/g*˚C

Step 1. Identify the variables:

Q_surroundings = m x c x ΔT

Q_surroundings = ?

m_water = 125 g

c_water = 4.18 J/g*˚C

ΔT = (20.3 ˚C - 23.4 ˚C) = - 3.1 ˚C

Step 2. Solve for the unknown:

Q_surroundings = m x c x ΔT

Q_surroundings = (125 g) x (4.18 J/g*˚C) x (-3.1 ˚C)

Q_surroundings = -1,620 J or -1.62 kJ

Step 3. Solution

Q_surroundings = -1.62 kJ

Q_system = - Q_{surroundings,}

Q_system = - (-1.62 kJ) = + 1.62 kJ

Q_system = ΔH_system

Therefore, the ΔH for the dissolution of 10.5 g KBr in water is +1.62 kJ and the reaction is endothermic.

D. Molar Enthalpy

In the previous problem we calculated the ΔH for the dissolution of 10.5 g of KBr in water. However, often when calculating ΔH values , we are interested in what is known as the MOLAR ENTHALPY. The molar enthalpy is the ΔH that occurs when 1 mole of a substance reacts. For example, the question above could ask, calculate the molar mass for the dissolution of KBr in water. To determine this value we need to use techniques and equations you should be familiar with from grade 11 chemistry: calculating molar mass, and calculating the number of moles in a sample. To calculate molar mass of a molecule, we simply take the molar mass values from the periodic table of each individual component of the molecule and add them up. Lets use the example from above:

Sample Problem: Calculate the Molar Enthalpy for the dissolution of 10.5 g of KBr in water in terms of kJ/mol.

Step 1: Calculate the Molar mass (M_m) of KBr:

M_mK = 39.1 g/mol

M_mBr = 79.9 g/mol

M_mKBr = (39.1g/mol + 79.9 g/mol) = 119.0 g/mol

Step 2. Calculate the number of moles in your sample.

Recall the formula for calculating the number of moles (n) in a sample:

n = mass of sample (ms) / molar mass (Mm) = ms/Mm

n = 10.5 g / 119.0 g/mol

n = 0.0082 mol of KBr in 10.5 grams

Step 3. Calculate the Molar Enthalpy

To calculate the molar enthalpy, we divide the ΔH by the total number of moles:

ΔH_molar = ΔH / n

ΔH_molar = 1.62 kJ / 0.082

ΔH_molar = 18.4 kJ/mol

Step 4: Solution:

Therefore the molar enthalpy for the dissolution of KBr in water is 18.4 kJ/mol

E. Summary

• Specific heat capacity (c) is the amount of energy (Q) it takes to raise 1 gram of a substance by 1 ˚C
• c = Q /(m*ΔT)
• Q is equivalent to the amount of heat transferred during a reaction
• To calculate the amount of heat transferred (Q) during a reaction, we rearrange the formula for specific heat capacity
• Q = m x c x ΔT
• Values of Q for a given reaction are equivalent to the change in enthalpy (ΔH)

• Q_system = - Q_surroundings

• ΔH_system = - ΔH_surroundings

• Molar enthalpy is the change in enthalpy that occurs when 1 mole of a substance reacts
• n = ms / Mm