Question

The degree of dissociation of a 0.01 M weak acid is ${10^{ - 3}}$. Its pOH is:
A. 5
B. 3
C. 9
D. 11

Answer 1

Weak acids are those which completely do not dissociate in the water when dissolved in it, therefore weak acids are considered as a weak electrolyte.

Complete step by step answer:
The pH is the measurement of acidity and basicity of the solution. The pH scale ranges from 0 to 14. The solutions which give a value less than 7 are said to be acidic and the solutions which give a value more than 7 are said to be basic.
The pH of the solution is defined as the negative logarithm of hydrogen ion.
The equation is given as shown below.
$pH = - \log [{H^ + }]$
The pOH is defined as the negative logarithm of hydroxide ion.
The equation is given as shown below.
$pOH = - \log [O{H^ - }]$
The dissociation of a weak acid is shown below.
Weak acid $(HA) \rightleftharpoons {H^ + } + {A^ - }$
At initial state concentration of weak acid and its dissociated ion will be
$C\;\;\;\;\;\;\;\;0\;\;\;\;\;\;\;\;\;0$
At equilibrium concentration of weak acid and its dissociated ion will be
$C - C\alpha \;\;\;\;\;\;\;\;C\alpha \;\;\;\;\;\;\;C\alpha$
The equilibrium constant of the reaction is given as shown below.
${K_a} = \dfrac{{[C\alpha ][C\alpha ]}}{{C - C\alpha }}$
$\Rightarrow {K_a} = C{\alpha ^2}$(as concentration of $\alpha$ of weak acid (HA) is very small)
The value of $\alpha$ is $\sqrt {\dfrac{{{K_a}}}{C}}$
${H^ + } = C\alpha (Eq i)$
Substitute the value of $\alpha$ in the above equation, we get
${H^ + } = \sqrt {{K_a}.} C$
Given,
Concentration (C) is 0.01 M.
Degree of dissociation $(\alpha )$is ${10^{ - 3}}$
Substitute the value in equation (i).
${H^ + } = 0.01 \times {10^{ - 3}}$
$\Rightarrow {H^ + } = {10^{ - 5}}$
$\Rightarrow {H^ + } = 5$
Depending on the equilibrium concentration of hydrogen ion and hydroxide ion in water, the relation between them is shown below.
$pH + pOH = 14$
To calculate the value of pOH, substitute the of pH in the above equation
$pOH = 14 - 5$
$\Rightarrow pOH = 9$

Therefore, the correct option is C. .

Note: As we can see that in pH there is a negative sign in front of logarithmic. This means that pH is a negative logarithmic scale where a negative sign shows that the pH is in inverse relation with the hydrogen ion.