Energy Relations in Chemistry: Thermochemistry

Calorimetry

Experimentally, we can determine the heat flow (DH_rxn) associated with a chemical reaction by measuring the temperature change it produces.

• The measurement of heat flow is called calorimetry
• An apparatus that measures heat flow is called a calorimeter

The temperature change experienced by an object when it absorbs a certain amount of energy is determined by its heat capacity.

• The heat capacity of an object is defined as the amount of heat energy required to raise its temperature by 1 K (or °C)
• The greater the heat capacity of an object, the more heat energy is required to raise the temperature of the object

For pure substances the heat capacity is usually given for a specified amount of the substance

• The heat capacity of 1 mol of a substance is called its molar heat capacity
• The heat capacity of 1 gram of a substance is called its specific heat

The specific heat of a substance can be determined experimentally by measuring the temperature change (DT) that a known mass (m) of the substance undergoes when it gains or loses a specific quantity of heat (q):

209 J of energy are required to increase the temperature of 50.0 g of water by 1.00 K. What is the specific heat of water?

Specific heat values of some substances (J g^-1K^-1)

We can calculate the quantity of heat that a substance has gained or lost by using its specific heat together with its measured mass and temperature change:

rearrange:

How much heat is required to raise the temperature of 250g of water from 22 °C to 98 °C? (specific heat of water is 4.18 J g^-1 K^-1).

q = (4.18 J g^-1 K^-1)*(250g)*(371-295 K)

q = 79,420 J (79.420 kJ, or 7.942 x 10⁴ J)

What is the molar heat capacity of water?

Molar heat capacity = 4.18 J g^-1 K^-1 * (18 grams/1.0 mole)

= 75.2 J mole^-1 K^-1

Recall that DH is defined as the quantity of heat transferred under constant pressure (DH = q_p).

A calorimeter for such measurements would have the following general construction:

Note that the pressure regulator could be just a vent to allow the pressure to be maintained at atmospheric pressure

• For reactions which involve dilute aqueous solutions, the specific heat of the solution will be approximately that of water (4.18 J g^-1 K^-1)
• The heat absorbed by an aqueous solvent is equal to the heat given off by the reaction of the solutes:

Remember: If a reaction gives off heat, it is exothermic and DH is negative. The enthalpy of the products is less than the enthalpy of the reactants

DH = H_products-H_reactants

In our calorimeter with an aqueous solution, if the reaction of the solutes is exothermic, the solution will absorb this heat and increase in temperature.

Thus, for an exothermic reaction:

• The solutes have a lower final enthalpy after the reaction (DH negative)
• The solution has a higher final enthalpy after the reaction (DH positive)

So, to determine the actual DH_rxn we would invert the sign of the DH_soln (the actual value we will measure)

50 ml of 1.0 M HCl and 50 ml of NaOH are combined in a constant pressure calorimeter. The temperature of the solution is observed to rise from 21.0 °C to 27.5 °C. Calculate the enthalpy change for the reaction (assume density is 1.0 gram/ml, and that the specific heat of the solution is that of water).

DT_solution = 27.5 - 21.0 °C = 6.5 °C (K)

specific heat = 4.18 J g^-1 K^-1

mass = (100 ml)*(1 gram/ml) = 100 grams

DH_solution = q_p = (4.18 J g^-1 K^-1)*(100 g)*(6.5 K) = 2,717 J

We know that DH_rxn = -DH_solution therefore,

DH_rxn = - 2,717 J

Note: exothermic reactions have negative values for DH_rxn thus, if the reaction gave off heat (i.e. raised the temperature of the solution) you know that the sign for DH_rxn must be negative.

What is the enthalpy change on a molar basis?

HCl + NaOH -> NaCl + H₂O

This is the balanced equation, and we combined:

(0.05 liters HCl)*(1.0 mol/liter) = 0.05 moles HCl

and

(0.050 liters NaOH)*(1.0 mol/liter) = 0.05 moles NaOH

The stoichiometry for HCl and NaOH in this reaction is 1:1, so they are combining in stoichiometrically equivalent amounts and will produce 0.05 moles of NaCl (and H₂O).

So, the enthalpy change for the production of 0.05 moles of NaCl in the above reaction would be:

-2717 J for each 0.05 moles NaCl, or

-2717 J/.05 moles = 54,340 J/mole = 54.34 kJ/mole

Since combustion reactions involve dramatic increases in pressure, they are typically studied under conditions of constant volume in a device known as a bomb calorimeter.

The bomb calorimeter is essentially a sealed insulated instrument with no pressure regulation.

The sealed reaction chamber is surrounded by water, and the energy released, or absorbed, by the sample is measured indirectly by monitoring the temperature change of the water.

Analyses under constant volume allow determination of DE (energy change at constant volume), not DH (energy change at constant pressure).

1996 Michael Blaber