Question

5 moles of $NH_4OH$ and one mole of $HCl$ are mixed and diluted to ${\text{1L}}$.${\text{p}}{{\text{K}}_{\text{b}}}$ of ${\text{N}}{{\text{H}}_{\text{4}}}{\text{OH}}$ is $4.8$. The ${\text{pH}}$ of the solution is.
A)$4.8$
B)$4.1979$
C)$9.8021$
D)$9.2$

Answer 1

We can define pH as the power of hydrogen ion in a given solution. We can calculate pH of the solution using a formula,
$pH = - \log 10\left[ {{H^ + }} \right]$
If the pH of the solution is 0 then the solution is highly acidic, $14$ means the solution is highly basic. The pH value of 7 shows as neutral as water.

Complete step by step answer:
When we add 1 mole of HCl responds with 1 mole of ammonium hydroxide to shape 1 mole of ammonium chloride, 4 moles of ammonium hydroxide remain unreacted.
Accordingly the arrangement is a fundamental cushion arrangement.
$\left[ {salt} \right] = 1M$ and $\left[ {base} \right] = 4M$
We can calculate the ${\text{pOH}}$ of the basic buffer solution as below.
$pOH = p{K_b} + \log \dfrac{{\left[ {salt} \right]}}{{\left[ {base} \right]}}$
It is give than $p{K_b} = 4.8$
Substituting the value in the equation,
$pOH = 4.8 + \log \,\left( {\dfrac{1}{4}} \right) = 4.1979$
We can calculate the $pH$ of the solution as follows,
$pH = 14 - pOH$
$\Rightarrow pH = 14 - 4.1979$
$\Rightarrow pH = 9.8021$
Therefore, the option C is correct.

Additional Information:
We know that dissociation constant is an equilibrium constant which measures the tendency of a bigger object to separate reversibly into smaller components; the equilibrium constant also can be called ionization constant.
For a general reaction:
${A_x}{B_y} \rightleftharpoons xA + yB$
The dissociation constant of the reaction is,
${K_d} = \dfrac{{{{\left[ A \right]}^x}{{\left[ B \right]}^y}}}{{\left[ {{A_x}{B_y}} \right]}}$
The equilibrium concentrations of A, B are $\left[ A \right]$,$\left[ B \right]$, and $\left[ {{A_x}{B_y}} \right]$.
A weak base may be a base that ionizes only slightly in a solution. Recall that a base is often defined as a substance, which accepts a proton from another substance. When a weak base like ammonia is dissolved in water, it accepts a Hydrogen ion from water, forming the hydroxyl ion and therefore the conjugate acid of the bottom, the ammonium .The numerical value of Kb may be a reflection of the strength of the bottom. Weak bases with comparatively high ${K_b}$ values are stronger than bases with comparatively lower ${K_b}$ values.

Note: We can calculate the ${\text{pH}}$ of the solution is from the value of ${\text{pOH}}$ by using the given formula,
${\text{pOH + pH = 14}}$
${\text{pH = 14 - pOH}}$
We characterize indicators as weak acids that exist as characteristic colors and demonstrate the centralization of particles during an answer through shading change. The estimation is resolved from the negative logarithm of this focus and is locked in to point to the acidic, essential, or nonpartisan nature of the substance you're trying.