Question

What is the percent X by mass for compound $X{{Y}_{2}}$ if compound XY is 74% X by mass?
A. 25%
B. 40%
C. 60%
D. 75%

Answer 1

Hint: percentage by mass of any substance in a compound is calculated as the mass of that substance upon total mass of the compound multiplied by 100. Mass by mass percentage is denoted as m/m %.
Formula used: m/m % = $\dfrac{mass}{total\,mass}\times 100$

Complete answer:
We have been given a compound XY in which mass % of X is 74 %. We have to find the mass percent of X in the compound $X{{Y}_{2}}$
Since, we have percentage of X as 74%, then percentage of Y = 100 – X,
Y = 100 - 74 = 26 %, so, Y is 26 % in XY.
So, to have a value for mass of X and Y, we will keep this in the formula for mass percent, as,
$\dfrac{mass\,of\,X}{mass\,of\,X+mass\,of\,Y}=\dfrac{74}{100}$ (Assuming the total mass X+Y=100)
Therefore, 100 mass of X = 74 (mass X) + 74 (mass Y)
26 mass X = 74 mass Y,
On simplifying we get, 13 mass X = 37 mass Y.
So it can be inferred that mass of X is = $\dfrac{37}{13}$ mass of Y. Now keeping this for calculating the mass % of X in $X{{Y}_{2}}$, we have,
Mass % of X in $X{{Y}_{2}}$= $\dfrac{mass\,of\,X}{mass\,of\,X+2(mass\,of\,Y)}\times 100$
Mass % of X in $X{{Y}_{2}}$= $\dfrac{\dfrac{37}{13}mass\,of\,Y}{\dfrac{63}{13}(mass\,of\,Y)}\times 100$
Mass % of X in $X{{Y}_{2}}$= 60 %
Hence, mass percent of X in $X{{Y}_{2}}$is 60 %.

So option C is correct.

Note:
Mass by mass (m/m %) percent of any substance is calculated when mass is given, while volume by volume (v/v %) percent is calculated when volume is given. Also mass by volume (m/v %) percent is calculated when mass is divided by volume and multiplied to 100. It gives the percent of mass in a particular volume.