Question

Which of the following statement(s) is/are correct?
(Given, $\log \left(1.1\right)=0.04$)

• A. The $pH$ of $1.0\times {10}^{-8}M$ solution of $HCl$ is $8$
• B. The conjugate base of $HP{O}_4^{2-}$ is $H_{2}P{O}_4^{-}$
• C. Autoprotolysis constant of water increases with temperature
• D. $P{O}_4^{3-}$ is an amphiprotic ion

Answer 1

The correct option is C Autoprotolysis constant of water increases with temperature

(a) $HCl$ is a strong acid hence $pH$ of the solution can't be more than $7$.
${10}^{-8}\text{M}$ solution of $HCl$ means the solution is very very dilute. Hence, concentration of $H^{+}$ will be taken from both $H_{2}O$ and $HCl$.
$\left[H^{+}\right]={10}^{-7}\left(H_{2}O\right)+{10}^{-8}\left(HCl\right)$
$\left[H^{+}\right]={10}^{-7}[1+{10}^{-1}]$
$={10}^{-7}\left[1.1\right]$
$pH$ $=-\log \left[H^{+}\right]=-\log {10}^{-7}+(-\log [1.1\left]\right)=7-0.04$
$\Rightarrow pH=6.96$
$pH$ of ${10}^{-8}MHCl$ solution will be $6.96$.

(b) Conjugate base of $HP{O}_4^{2-}$ is $P{O}_4^{3-}$.

(c) $H_{2}O\left(l\right)+H_{2}O\left(l\right)\rightleftharpoons H_3{O}^{+}\left(aq\right)+O{H}^{-}\left(aq\right)$
$k_w=\left[H_3{O}^{+}\right]\left[O{H}^{-}\right]$
The value of $k_w$ is temperature dependent.

(d) An amphiprotic ion is one which can donate proton as well as accept proton. $P{O}_4^{3-}$ ion can accept proton(s) but cannot donate any proton. Hence, $P{O}_4^{3-}$ is not an amphiprotic ion.