In a buffer solution containing an equal concentration of ${B^ - }$ and $HB$, the${K_b}$ for ${B^ - }$ is ${10^{ - 10}}$. The pH of the buffer solution is:
A.10
B.7
C.6
D.4

Hint: p${K_b}$ is the negative base-10 logarithm of the base dissociation constant (${K_b}$) of a solution. It is used to determine the strength of a base or alkaline solution. The lower the p${K_b}$ value, the stronger the base. As with the acid dissociation constant, p${K_b}$, the base dissociation constant calculation is an approximation that is only accurate in dilute solutions.

Complete Step by step answer: A buffer solution is one which resists changes in pH when small quantities of an acid or an alkali are added to it. A buffer solution has to contain things which will remove any hydrogen ions or hydroxide ions that you might add to it - otherwise the pH will change. Acidic and alkaline buffer solutions achieve this in different ways.
Notice that we are given here${K_b}$ for ${B^ - }$ is ${10^{ - 10}}$.
$p{K_b} = - {\log _{10}}{K_b} = - \log \left( {{{10}^{ - 10}}} \right) = 10$
We know that $pOH = p{K_b} + \log \dfrac{{\left[ {salt} \right]}}{{acid}}$
Here, the concentration of the salt and the acid is same: $\left[ {salt} \right] = \left[ {acid} \right]$
So we have the second term of the above formula as ${\log _{10}}1 = 0$
Therefore $pOH = p{K_b} = 10$
pH of the buffer solution is given by: $pH = 14 - pOH = 14 - 10 = 4$
$pH = 4$

Hence the correct option is (d).

Note: In chemistry, pH is a scale used to specify the acidity or basicity of an aqueous solution. Acidic solutions (solutions with higher concentrations of hydrogen ions) are measured to have lower pH values than basic or alkaline solutions.
The pH scale is logarithmic and inversely indicates the concentration of hydrogen ions in the solution. This is because the formula used to calculate pH approximates the negative of the base 10 logarithm of the molar concentration of hydrogen ions in the solution. More precisely, pH is the negative of the base 10 logarithm of the activity of the H+ ion.