Question

X and Y are two elements which can form $X_{2}Y$ and $X_2$ $Y_3$. 0.2 mole $X_2{Y}_3$ weighs 15.2 g and 0.5 mole $X_{2}Y$ weighs 22 g. Atomic weights of $X$ and $Y$ are:

• A. 20, 15
• B. 31, 16
• C. 14, 16
• D. 16, 27

Answer 1

The correct option is C 14, 16

$X$ and $Y$ are two elements which can form $X_{2}Y$ and $X_2{Y}_3$.
0.2 mole $X_2{Y}_3$ weighs 15.2 g and 0.5 mole $X_{2}Y$ weighs 22 g. Atomic weights of $X$ and $Y$ are $14,16$
Let $x$ g/mol and $y$ g/mol be the atomic weights of $X$ and $Y$ respectively.
The molecular weight of $X_{2}Y=2x+y$ g/mol.
The molecular weight of $X_2{Y}_3=2x+3y$ g/mol.
0.2 mole $X_2{Y}_3$ weighs 15.2 g
1 mole $X_2{Y}_3$ weighs
$15.2\times \frac{1}{0.2}=78$ g
$76=2x+3y$......(1)
0.5 mole $X_{2}Y$ weighs 22 g.
1 mole $X_{2}Y$ will weigh
$22\times \frac{1}{0.5}=44$ g
$2x+y=44$
$y=44-2x$.......(2)
Substitute (2) in (1)
$76=2x+3(44-2x)$
$76=2x+132-6x$
$4x=56$
$x=14$