# Question Video: Calculating the Standard Enthalpy of Reaction for the Decomposition of Ammonium Chloride Chemistry

Using the standard enthalpies of formation in the given table, what is the standard enthalpy of reaction for the decomposition of ammonium chloride? NH₄Cl(s) ⟶ NH₃(g) + HCl(g)

03:50

### Video Transcript

Using the standard enthalpies of formation in the given table, what is the standard enthalpy of reaction for the decomposition of ammonium chloride? NH4Cl solid reacts to form NH3 gas plus HCl gas.

Because it can be difficult to measure the enthalpy of certain types of reactions, chemists calculate enthalpy changes by using enthalpy data from other reactions. In this question, we need to calculate the enthalpy change for the decomposition of ammonium chloride. We can calculate this enthalpy change indirectly by using the standard enthalpies of formation and creating a Hess cycle.

The standard enthalpy of formation is the enthalpy change when one mole of substance is formed from its constituent elements in their standard states and under standard conditions. To create our Hess cycle, we can start by writing the balanced equation that was provided in the problem and labeling it reaction one. Below the cycle, we should write the constituent elements of the reactants and products, which are nitrogen, hydrogen, and chlorine. We need to use a subscript of two for all of these elements, because they exist as diatomic molecules in their standard state.

Now, let’s draw an arrow from the elements to the reactant ammonium chloride. This reaction represents the formation of one mole of ammonium chloride from its constituent elements. To balance this equation, we need a coefficient of one-half in front of N2, a coefficient of two in front of H2, and a coefficient of one-half in front of Cl2. Let’s label this reaction as reaction two.

Now, let’s draw an arrow from the elements to the products and label this reaction as reaction three. This equation is already balanced and represents the formation of one mole of ammonia gas and one mole of hydrogen chloride gas from their constituent elements. Using the Hess cycle we created, we can state that the enthalpy change of reaction one is equal to the enthalpy change of reaction two plus the enthalpy change of reaction three.

However, it’s important to note that when moving through the cycle, we complete reaction two in the opposite direction of the arrow. Because of this, we will need to change the sign of the enthalpy change of reaction two in our equation.

Now, to calculate the enthalpy change of reaction one, we will need to substitute the correct values from the given table. We should substitute negative 314 kilojoules per mole, which is the standard enthalpy of formation of ammonium chloride, as the enthalpy change of reaction two. We should add together the standard enthalpies of formation for ammonia gas and hydrogen chloride gas to calculate the enthalpy change of reaction three. After simplification, we get Δ𝐻 one equals 314 kilojoules per mole minus 138 kilojoules per mole. After subtraction, the result is positive 176 kilojoules per mole.

Therefore, the standard enthalpy of reaction for the decomposition of ammonium chloride is positive 176 kilojoules per mole.