Question 18.p.6: Write a balanced equation for the dissociation of NH4^+ in w......
Write a balanced equation for the dissociation of \text{NH}_4^+ in water. Using the given information, construct a table that describes the initial and equilibrium concentrations. Construct an equilibrium expression and make assumptions where possible to simplify the calculations.
The initial concentration of \text{NH}_4^+ = 0.2 \ M because each mole of \text{NH}_4\text{Cl} completely dissociates to form one mole of \text{NH}_4^+ .
\text{x} = [\text{H}_3\text{O}^+] = [\text{NH}_3] = 10^{-\text{pH}} = 10^{-5.0} = 1.0 \times 10^{-5} \ M \\ K_\text{a}=\frac{[\text{NH}_3][\text{H}_3\text{O}^+]}{[\text{NH}_4^+]} =\frac{\text{x}^2}{(0.2-\text{x})} =\frac{(1.0\times 10^{-5})(1.0\times 10^{-5})}{(0.2-1.0\times 10^{-5})} \\ =5\times 10^{-10}
Check: The small value of K_\text{a} is consistent with the value expected for a weak acid.