Question

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. 40, 30
• B. 60, 40
• C. 20, 30
• D. 30 , 20

Answer 1

The Correct Option is A

To determine the atomic weights of elements \( X \) and \( Y \), we must analyze the given information about the compounds \( XY_2 \) and \( X_3Y_2 \).

1. Information for Compound \( XY_2 \):
   • The molar mass of \( XY_2 \) is calculated from the data given: \( 0.1 \) mole of \( XY_2 \) weighs \( 10 \, g \).
   • Molar mass = \(\frac{10 \, \text{g}}{0.1 \, \text{mol}} = 100 \, \text{g/mol}\).
2. Information for Compound \( X_3Y_2 \):
   • The molar mass of \( X_3Y_2 \) is calculated from the data given: \( 0.05 \) mole of \( X_3Y_2 \) weighs \( 9 \, g \).
   • Molar mass = \(\frac{9 \, \text{g}}{0.05 \, \text{mol}} = 180 \, \text{g/mol}\).
3. Setting up equations:
   • Let the atomic weight of \( X \) be \( A \) and of \( Y \) be \( B \).
   • For \( XY_2 \), we have the equation: \( A + 2B = 100 \).
   • For \( X_3Y_2 \), we have the equation: \( 3A + 2B = 180 \).
4. Solving the equations:
   • Subtract the first equation from the second: \((3A + 2B) - (A + 2B) = 180 - 100\)
   • \(2A = 80 \Rightarrow A = 40\).
   • Substitute \( A = 40 \) back into the first equation: \( 40 + 2B = 100\).
   • \(2B = 60 \Rightarrow B = 30\).
5. Conclusion:
   • The atomic weights are determined as \( A = 40 \) for \( X \) and \( B = 30 \) for \( Y \).

Therefore, the correct answer is: 40, 30.