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Suppose the elements X and Y combine to form two compounds $XY_2$ and $X_3Y_2$. When 0.1 mole of $XY_2$ weighs 10 g and 0.05 mole of $X_3Y_2$ weighs 9 g, the atomic weights of X and Y are
A
20, 30
B
30, 20
C
40, 30
D
60, 40
Explanation
Two molar-mass equations in two unknowns.
Detailed Solution
Let the atomic weights of X and Y be $A_x$ and $A_y$.
$n_{XY_2} = 0.1 = \frac{10}{A_x + 2A_y} \Rightarrow A_x + 2A_y = 100$ ...(1)
$n_{X_3Y_2} = 0.05 = \frac{9}{3A_x + 2A_y} \Rightarrow 3A_x + 2A_y = 180$ ...(2)
Solving (1) and (2): $A_x = 40$, $A_y = 30$
$n_{XY_2} = 0.1 = \frac{10}{A_x + 2A_y} \Rightarrow A_x + 2A_y = 100$ ...(1)
$n_{X_3Y_2} = 0.05 = \frac{9}{3A_x + 2A_y} \Rightarrow 3A_x + 2A_y = 180$ ...(2)
Solving (1) and (2): $A_x = 40$, $A_y = 30$