Elements X and Y combine to form two compounds XY and X₂Y. Find the atomic weight of X and Y, if the weight of 0.1 moles of XY is 10g and 0.05 moles of X₂Y is 9g

The correct option is 80, 20.

Let us find the atomic weights of elements $X$ and $Y$ step-by-step.

Let the atomic weight of element $X$ be $x$ g/mol and the atomic weight of element $Y$ be $y$ g/mol.

Step 1: Analyze the first compound, $XY$
The molar mass of $XY$ is the sum of the atomic weights of $X$ and $Y$:
Molar mass of $XY$ = $x+y$
We are given that the weight of 0.1 moles of $XY$ is 10 g.
Using the formula:
$\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}$
We can write:
$0.1=\frac{10}{x+y}$
Rearranging the terms:
$x+y=\frac{10}{0.1}$
$x+y=100$    — (Equation 1)

Step 2: Analyze the second compound, $X_{2}Y$
The molar mass of $X_{2}Y$ is:
Molar mass of $X_{2}Y$ = $2x+y$
We are given that the weight of 0.05 moles of $X_{2}Y$ is 9 g.
Using the same relation:
$0.05=\frac{9}{2x+y}$
Rearranging the terms:
$2x+y=\frac{9}{0.05}$
$2x+y=180$    — (Equation 2)

Step 3: Solve the system of equations
Subtract Equation 1 from Equation 2:
$(2x+y)-(x+y)=180-100$
$x=80$
Now, substitute the value of $x$ back into Equation 1:
$80+y=100$
$y=100-80$
$y=20$

Thus, the atomic weight of $X$ is 80 and the atomic weight of $Y$ is 20.