Question

A mixture of $N{{H}_{4}}N{{O}_{3}}$ and ${{(N{{H}_{4}})}_{2}}HP{{O}_{4}}$ contains 30.40% mass percent of nitrogen. What is the mass ratio of the two components in the mixture?
(A) 2:1
(B) 1:2
(C) 3:4
(D) 4:1

Answer 1

Hint: The way of expressing a concentration or describing the component in a particular mixture is the mass percentage. The solution composition is described by the mass percentage which shows the mass of solute present in a given mass of solution. The quantity of solute expressed by mass or moles.

Complete step by step solution:
There are many ways to describe the concentration of solution quantitatively,
(1) Mass percentage
(2) Volume percentage
(3) Mass by volume percentage
(4) Mole fraction
(5) Molarity
(6) Normality
(7) Molality
Mass percent formula: The mass percent is expressed as solving for the molar mass also for the mass of each element in 1 mole of the compound. The mass percentage will calculate with the help of these masses.
Mass percentage = $\dfrac{W}{w}X100%$
W = mass of solute
w = mass of solution
Given mass percentage of the mixture $N{{H}_{4}}N{{O}_{3}}$ and ${{(N{{H}_{4}})}_{2}}HP{{O}_{4}}$ = 30.40% --- (1)
Let us consider the weight of $N{{H}_{4}}N{{O}_{3}}$ and ${{(N{{H}_{4}})}_{2}}HP{{O}_{4}}$ are ‘a’ and ‘b’ respectively.
So, mass percentage of nitrogen = $\dfrac{\dfrac{a}{80}X2X14+\dfrac{b}{132}X2X14}{a+b}X100$ -- (2)
From (1) and (2),
$\dfrac{\dfrac{a}{80}X2X14+\dfrac{b}{132}X2X14}{a+b}X100$= 30.40%
Hence, a : b = 2:1
So, the mass ratio of the two components $N{{H}_{4}}N{{O}_{3}}$ and ${{(N{{H}_{4}})}_{2}}HP{{O}_{4}}$in the mixture is 2:1

The correct answer is option A.

Note: The method of expressing the composition of the solution mixture is a mass percentage. This mass percentage will describe the amount of solute (in grams) present in 100 grams of the solution. By knowing the mass percentage of each element in a compound helps to identify the unknown chemicals.