Question

The exact concentration $\left(C_{H^{+}}\right)$ of $H^{+}$ ions in an aqueous HCl solution of arbitrary concentration $\left(C_{HCl}\right)$ can be obtained from the expression.

• A. $C_{H^{+}}=C_{HCl}$
• B. $C_{H^{+}}=C_{HCl}+\frac{K_w}{C_{H^{+}}}$
• C. $C_{H^{+}}=C_{HCl}-\frac{K_w}{C_{H^{+}}}$
• D. $C_{H^{+}}=C_{HCl}+K_w^{-1/2}$

Answer 1

The correct option is B $C_{H^{+}}=C_{HCl}+\frac{K_w}{C_{H^{+}}}$

To specify the concentrations of the HCl in aqueous solution, following rules must follow:

1. The dissociation equilibrium of water must always be satisfied:

$\left[H^{+}\right]\left[O{H}^{–}\right]=K_w$

2. Mass/concentration conservation or mass balance: sum of dissociated and undissociated mass should always be equal to initial mass/concentration.

For HCl solution, $\left[HCl\right]+\left[C{l}^{–}\right]=C_{HCl}$

Since, its a strong acid, therefore it completely dissociates and we get:

$\left[C{l}^{–}\right]=C_{HCl}$

3. Total charge should be balanced i.ie charge neutrality in ionic solution:

$\left[H^{+}\right]=\left[O{H}^{–}\right]+\left[C{l}^{–}\right]$

Using all three relations we get:

$\left[H^{+}\right]=\left[O{H}^{–}\right]+C_{HCl}$

or $\left[H^{+}\right]=\frac{K_w}{H^{+}}+C_{HCl}$

Since $\frac{K_w}{H^{+}}={10}^{-7}$, therefore for concentrations less than ${10}^{-6}M$of $HCl$, this term is considered and for concentrated $HCl$ solutions it is negligible.

option B is correct