Suppose elements `X` and `Y` combine to form two compounds `XY_(2)` and `X_(3)Y_(2)` when 0.1 mole of former weigh `10 g` while 0.05 mole of the latter weigh `9g`. What are the atomc weights of `X` and `Y`.

Options

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

Explanation

To find the atomic weights of elements `X` and `Y`, we can follow these steps:

### Step 1: Determine the molecular weight of the first compound, `XY2`.

Given that 0.1 mole of `XY2` weighs 10 g, we can use the formula:

\[ \text{Molecular Weight} = \frac{\text{Weight}}{\text{Moles}} \]

Substituting the values:

\[ \text{Molecular Weight of } XY2 = \frac{10 \text{ g}}{0.1 \text{ moles}} = 100 \text{ g/mol} \]

### Step 2: Write the expression for the molecular weight of `XY2`.

The molecular weight of `XY2` can be expressed in terms of the atomic weights of `X` and `Y`:

\[ \text{Molecular Weight of } XY2 = X + 2Y \]

From Step 1, we have:

\[ X + 2Y = 100 \quad \text{(Equation 1)} \]

### Step 3: Determine the molecular weight of the second compound, `X3Y2`.

Given that 0.05 mole of `X3Y2` weighs 9 g, we can again use the formula for molecular weight:

\[ \text{Molecular Weight of } X3Y2 = \frac{9 \text{ g}}{0.05 \text{ moles}} = 180 \text{ g/mol} \]

### Step 4: Write the expression for the molecular weight of `X3Y2`.

The molecular weight of `X3Y2` can be expressed as:

\[ \text{Molecular Weight of } X3Y2 = 3X + 2Y \]

From Step 3, we have:

\[ 3X + 2Y = 180 \quad \text{(Equation 2)} \]

### Step 5: Solve the equations simultaneously.

Now we have two equations:
1. \( X + 2Y = 100 \)
2. \( 3X + 2Y = 180 \)

We can eliminate `Y` by subtracting Equation 1 from Equation 2:

\[ (3X + 2Y) - (X + 2Y) = 180 - 100 \]

This simplifies to:

\[ 2X = 80 \]

Dividing by 2:

\[ X = 40 \]

### Step 6: Substitute the value of `X` back into Equation 1 to find `Y`.

Substituting \( X = 40 \) into Equation 1:

\[ 40 + 2Y = 100 \]

Subtracting 40 from both sides:

\[ 2Y = 60 \]

Dividing by 2:

\[ Y = 30 \]

### Conclusion

The atomic weights of `X` and `Y` are:

- Atomic weight of `X` = 40
- Atomic weight of `Y` = 30