Enthalpy

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The following is the text and related diagrams of a worksheet that I use with A-level students during the study of enthalpy. It includes practice calculations for both exothermic and endothermic reactions. Some of the formatting has changed as I copied it to the website so it will need a bit of tweaking before use.

In most chemical reactions there is an associated energy change. These energy changes are usually observed as heat changes and it is therefore generally possible to measure the value of this change. The chemicals involved in a reaction can be referred to as the ‘system’. When a system evolves (loses or more generally, gives out) energy to the surroundings, the reaction is said to be exothermic. When a system absorbs (gains) energy from the surroundings, the reaction is said to be endothermic. From now on, this sheet will refer mainly to heat changes rather than to energy changes.

The quantity of heat evolved or absorbed depends on the following factors:

The amounts of substances involved in the reaction. Is usual to quote heat changes for specific molar amounts.

Physical states of the reactants since any change in state will involve an energy change.

The temperature at which the reaction is carried out.

The pressure at which the reaction is carried out.

Any pressure changes during the experiment.

The long and the short of this lot is that the conditions need to be stated along with the figures.

During an exothermic reaction, heat is lost from the system to the surroundings. The products must therefore be in a lower energy state. The enthalpy for such a reaction is said to be negative. The following is an enthalpy change diagram that represents any exothermic reaction.

The opposite is true for any endothermic reaction.

It is really important that you learn and undersatand the following paragraph. The highlighted words have a great significance to your ability to do the calculations.

There are two important standard enthalpy changes in terms of this module. The standard enthalpy of combustion is the enthalpy change when 1 mole of an element or compound is completely burned in oxygen under standard conditions. The standard enthalpy of formation is the enthalpy change when 1 mole of a compound is formed from its elements, in their normal states, under standard conditions.

In 1840, the German chemist Hess, stated a law:

"the enthalpy change in a reaction is the same whether the reaction is brought about in one stage or through intermediate stages".

In other words the total energy change resulting from a chemical reaction is dependent only on the initial and final states of the reactants and is independent of the route. Consider the following illustration:

B can be formed from A either via intermediates C and D or via intermediate E. Using Hess's Law, (a + b) = (x + y + z).

If you think about this using common sense, you will soon realise that Hess's Law is simply a case of the Law of Conservation of Energy (try imagining (a + b) is greater than (x + y + z)).

To see Hess's Law in action,  work through the following example. In each case the enthalpy changes have been measured by experiment.

Method 1 - convert CaO into Ca(OH)2 by reaction with water (-75.5 kJ) then neutralise using HCl to form CaCl2 (-117 kJ). Adding the individual enthalpy changes together gives the total enthalpy change as -192.5 kJ.

Method 2 - Add CaO directly to HCl (-192.5 kJ).

As you can see, the total enthalpy change in each case is identical. This can be represented using an enthalpy diagram:

Enthalpy changes for some reactions can not be determined directly. Hess's Law can be used to calculate these from other experimental results. For example, methane (CH4) cannot be made directly from C and H2. However, all can be burnt and the enthalpies of combustion can then be used to calculate the enthalpy of formation of CH4.

Assignment 1 - comprehension.

What are the most common energy changes observed in chemical reactions?

Define the "system" in terms of a chemical reaction.

What factors can affect the amount of energy exchanged with the surroundings?

State the conditions for standard molar enthalpy changes.

State Hess's Law and explain what it means in terms of chemical reactions.

Use language appropriate to A-level to explain exothermic and endothermic.

Assignment 2 - application and knowledge,

    Give some other (than heat) forms of energy that could be evolved during a chemical reaction. For each one, give an example of a possible reaction (chemical detail not needed e.g. kinetic energy. Example, in a reaction in which a gas is evolved, the gas can be made to move something. Moving objects have kinetic energy.)

    Draw an enthalpy diagram for an endothermic reaction.

    The enthalpy changes in going from R to S, S to T, T to U and R to U are +v, +w, -x and -y respectively. Represent that information on an enthalpy diagram and say how v, w, x and y are related to each other.

    Given that the enthalpy of combustion of benzene (C6H6) is -3278 kJmol-1 and that the enthalpies of formation of CO2 and H2O are -393.4 and -285.8 kJmol-1 respectively, calculate the enthalpy of formation of benzene.

    The molar enthalpies of combustion of hydrogen (H2), carbon and methane (CH4) are -285.8, -393.5,  and -890.4 kJmol-1 . Calculate the molar enthalpy of formation of methane.

    The molar enthalpies of combustion of C and CO are -393.3 and -284.5 kJmol-1. Calculate the molar enthalpy of formation of CO.

    The molar enthalpies of formation of water and carbon dioxide are -285.8 and - 405.4 kJmol-1 respectively at 15ºC. The molar enthalpy of combustion of ethane (C2H6) is -1423 kJmol-1. Use Hess's Law to calculate the enthalpy of formation of ethane at 15ºC.

    State Hess's Law in your own words. The molar enthalpy of combustion of ethanol (C2H5OH) is -1430 kJmol-1 and the molar enthalpies of formation of water and carbon dioxide are -285.8 and -393.4 kJmol-1. What is the molar enthalpy of formation of ethanol under the same conditions?

    Given that:

CO(g) + H2(g)          H2O(g) + C(s)

DeltaHm º (298K) = -131.3 kJmol-1

    Calculate the enthalpy change at 25ºC when 1g of C reacts completely with water vapour to form carbon monoxide and hydrogen.

Calculate the enthalpy of formation of carbon disulphide given that its enthalpy of combustion is exothermic and has a value of 1108 kJmol-1 and that the enthalpies of formation of CO2 and SO2 are -405 and -293 kJmol-1 respectively.