Question

Which of the following is a true statement:

• A. The ionisation constant and ionic product of water are same.
• B. Water is a strong electrolyte.
• C. The value of ionic product of water is less than that of its ionisation constant
• D. At $298K$, the number of $H^{+}$ ions in a litre of water is $6.023\times {10}^{16}$.

Answer 1

The correct option is D At $298K$, the number of $H^{+}$ ions in a litre of water is $6.023\times {10}^{16}$.

Let's check the options one by one:
(1) False. They are not the same.
Ionisation constant of water is
$K_{a\left(H_{2}O\right)}=\frac{\left[H^{+}\right]\left[{OH}^{-}\right]}{\left[H_{2}O\right]}$
Ionic product of water is
$K_w=K_{a\left(H_{2}O\right)}\times \left[H_{2}O\right]K_w=\left[H^{+}\right]\left[{OH}^{-}\right]$
(2) False. Water is a weak electrolyte. In fact, pure water is a non-electrolyte.
(3) False. $K_w=K_{a\left(H_{2}O\right)}\times \left[H_{2}O\right]$
Clearly, $K_w>K_{a\left(H_{2}O\right)}$
value of ionic product is more than value of ionisation constant.
(4) At 298K, pH of water is 7
$\therefore concof\left[H^{+}\right]={10}^{-7}$moles per litre
1 mole contains $6.023\times {10}^{23}$ ions
$\therefore conc\left[H^{+}\right]={10}^{-7}\times 6.023\times {10}^{23}=6.023\times {10}^{16}$