Question

Determine the temperature change that occurs when 13.4 g of ammonium chloride dissolve into 2.00x10^2 g of water. The molar enthalpy of solution of ammonium chloride is 15.7 kJ/mol. Write a balanced thermochemical equation for the reaction and sketch an enthalpy diagram for this reaction.

Answer 1

The balanced thermochemical equation is:

NH₄Cl(s) $\rightarrow$ NH₄⁺(aq) + Cl^-(aq), ∆H = 15.7 kJ/mol.

As the enthalpy change is positive, the solution becomes colder upon the dissolution of ammonium chloride.

The number of the moles of NH₄Cl is its mass, 13.4 g divided by its molar mass (53.49 g/mol):

$n = \frac{m}{M}= \frac{13.4}{53.49}= 0.2505$ mol.

Therefore, the quantity of heat absorbed is:

$Q = -\Delta H·n = -15.7·0.2505 = -3.933$ kJ.

Finally, the temperature decrease is related to the heat through the specific heat capacity of water $c = 4.18$ J/ (K g):

$∆T = \frac{Q}{cm} = -\frac{3.933·10^3}{4.18·2.00·10^2} = -4.7$ K, or -4.7 °C (the temperature change in °C and in K has the same absolute value).

An enthalpy diagram for the reaction of dissolution of the NH₄Cl:

In this diagram, $∆H_{LE}$ is the lattice energy of NH₄Cl.