Question

A $0.5g$ sample of $K{{H}_{2}}P{{O}_{4}}$ is titrated with $0.1M$$NaOH$. The volume of base required to do this is $25.0ml$. The reaction is represented as:
${{H}_{2}}P{{O}_{4}}^{-}+O{{H}^{-}}\to HPO_{4}^{2-}+{{H}_{2}}O$.
The percentage purity of $K{{H}_{2}}P{{O}_{4}}$ is: ($K=39$, $P=31$)
A. $68%$
B. $34%$
C. $85%$
D. $51%$

Answer 1

Hint: To know the appropriate answer, first find out the number of moles of the base from the information given i.e. molarity and volume. And, then find out the pure mass of the acid and then find out the purity. Purity will be equal to the pure mass of the compound upon total mass of the compound multiplied with hundred.

Complete step by step answer:
Given that,
Mass of the sample given i.e. $K{{H}_{2}}P{{O}_{4}}$ is $0.5g$.
Molarity of the base given i.e. $NaOH$ is $0.1M$.
The volume of the base is $25mL$ which will be equal to $25\times {{10}^{-3}}litres$.
The reaction given is:
 ${{H}_{2}}P{{O}_{4}}^{-}+O{{H}^{-}}\to HPO_{4}^{2-}+{{H}_{2}}O$

Now, we have to find out the number of moles of the base $NaOH$.
As we know, molarity equals the number of moles upon the volume of the solute.
So, the number of moles of the base $NaOH$ will be equal to the product of molarity and volume (in litres) of the base, which are already given.
Then, moles of the base will be equal to $(0.1\times 25\times {{10}^{-3}})=2.5\times {{10}^{-3}}$.
We can see that one mole of $K{{H}_{2}}P{{O}_{4}}$ is reacting with one mole of $NaOH$.
So, the value of one mole of $K{{H}_{2}}P{{O}_{4}}$ will be the same as that of $NaOH$.
So, moles of $K{{H}_{2}}P{{O}_{4}}$will be $2.5\times {{10}^{-3}}$.

We know, the mass of one mole of any element equals the atomic weight of a particular element.
So, mass of $2.5\times {{10}^{-3}}$moles of $K{{H}_{2}}P{{O}_{4}}$ will be $2.5\times {{10}^{-3}}\times \text{Atomic wt}\text{. of }K{{H}_{2}}P{{O}_{4}}$ which will be $2.5\times {{10}^{-3}}\times 136=0.34g$.

Now, we got the pure mass of $K{{H}_{2}}P{{O}_{4}}$and the total mass is $0.5g$.
Using the formula of,
$purity=\dfrac{\text{pure mass}}{\text{total mass}}\times 100$
$purity=\dfrac{0.34}{0.5}\times 100=68%$
So, the correct answer is “Option A”.

Note: Different substances will have different melting and boiling points. And any pure substance will have a specific melting and boiling point. One of the simplest ways to check the purity of a substance is to compare the substance with the certified pure sample. For pure solids, we need to check the melting points of the solids.