Question

The mass of phosphoric acid required to obtain $53.4g$ pyrophosphoric acid is:
A: $58.8g$
B: $60.2g$
C: $65.8g$
D: $68.3g$

Answer 1

Every reaction occurs in a definite proportion of their moles to form particular moles of a substance since we can calculate the gram of substance from the number of moles given. All we need is to find the reaction and observe the number of moles required.
Formula used: ${\text{Given mass = Molar mass }} \times {\text{ No}}{\text{. of moles}}$

Complete step by step answer:
The chemical formula of phosphoric acid is ${H_3}P{O_4}$
The chemical formula of pyrophosphoric acid is ${H_4}{P_2}{O_7}$
And the reaction to for is given below
$2{H_3}P{O_4}\xrightarrow{{}}{H_4}{P_2}{O_7} + {H_2}O$
It can be observed that two mole of phosphoric acid dissociate into one mole of pyrophosphoric acid . For each mole of pyrophosphoric acid we will need two moles of phosphoric acid.
Molar mass of phosphoric acid is $98g$
Molar mass of pyrophosphoric acid is $178g$
Now, according to reaction we need $2 \times 98 = 196g$ of phosphoric acid to make $178g$ grams of pyrophosphoric acid then let we will be need $x$ gram of phosphoric acid to obtain $53.4g$ gram of pyrophosphoric acid as given in question statement.
By unitary method
$x = \dfrac{{196 \times 53.4}}{{178}} = 58.8$
We obtain $x = 58.8g$
Hence our answer is option A that is $58.8g$.

Note:
In this type of question, reaction should be balanced otherwise our answer will not be accurate also law of mass conservation will be violated which states that mass is always conserved (If the reaction is not balanced this means that number of atoms of specific element in reactant is not equal to number of atoms of that particular element in product due to which mass of reactant will come different from mass of product).