Question

The $pH$ of a centimolar solution of a monobasic acid is $6$. The dissociation constant is approximately equal to:
1.${10^{ - 12}}$
2.${10^{ - 8}}$
3.${10^{ - 10}}$
4.${10^{ - 6}}$

Answer 1

This question gives the knowledge about the $pH$. $pH$ is defined as the negative logarithm of the hydronium ion. The $pH$ of acids is less than seven and for bases it is more than seven. $pH$ helps in describing the potential of hydrogen.

Formula used: The formula used to determine the $pH$ of the solution is as follows:
$pH = - \log \left[ {{H^ + }} \right]$
Where $\left[ {{H^ + }} \right]$ is the concentration of hydronium ion.
The formula used to determine the dissociation constant is as follows:
$\left[ {{H^ + }} \right] = \sqrt {{K_a} \times c}$
Where $\left[ {{H^ + }} \right]$ is the concentration of hydronium ion, ${K_a}$ is the dissociation constant and $c$ is the concentration.

Complete step-by-step answer: $pH$ is defined as the negative logarithm of the hydronium ion. The $pH$ of acids is less than seven and for bases it is more than seven. $pH$ helps in describing the potential of hydrogen. The $pH$ range of acid is from $0$ to $6$, for bases the range of $pH$ is from $8$ to $14$ and for neutral molecules the $pH$ is always $7$.
First we will determine the concentration of hydronium ion using the $pH$ formula as follows:
$\Rightarrow pH = - \log \left[ {{H^ + }} \right]$
Rearrange the above formula as follows:
$\Rightarrow \left[ {{H^ + }} \right] = {10^{ - pH}}$
Substitute the value of $pH$ as $6$.
$\Rightarrow \left[ {{H^ + }} \right] = {10^{ - 6}}$
Consider this as equation $1$.
Now we will determine the dissociation constant as follows:
$\Rightarrow \left[ {{H^ + }} \right] = \sqrt {{K_a} \times c}$
Rearrange the above formula as follows:
$\Rightarrow {K_a} = \dfrac{{{{\left( {\left[ {{H^ + }} \right]} \right)}^2}}}{c}$
Substitute $\left[ {{H^ + }} \right]$ as ${10^{ - 6}}$, $c$ as $0.01M$ in the above formula as follows:
$\Rightarrow {K_a} = \dfrac{{{{\left( {\left[ {{{10}^{ - 6}}} \right]} \right)}^2}}}{{0.01}}$
On simplifying, we get
$\Rightarrow {K_a} = {10^{ - 10}}$
The dissociation constant of monobasic acid is ${10^{ - 10}}$.

Therefore, option $3$ is the correct option.

Note: $pH$ scale generally specifies between the acidic compound and the basic compounds. Acidic compounds contain very high concentrations of hydronium ions and basic compounds contain very high concentrations of hydroxide ions.