Suppose the elements P and Q combine to form two compounds `PQ_(2)` and `P_(3)Q_(2)`. When 0.1 mole of `PQ_(2)` weight 10 g and 0.05 mole of `P_(3)Q_(2)` weight 9 g, the atomic weights of P and Q are

Options

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

Answer

To find the atomic weights of elements P and Q, we can follow these steps:

### Step 1: Define the Variables
Let the atomic weight of element P be \( X \) and the atomic weight of element Q be \( Y \).

### Step 2: Write the Molar Masses of the Compounds
For the compound \( PQ_2 \):
- The molar mass \( M_1 \) is given by:
\[ M_1 = X + 2Y \]

For the compound \( P_3Q_2 \):
- The molar mass \( M_2 \) is given by:
\[ M_2 = 3X + 2Y \]

### Step 3: Set Up the Equations Based on Given Information
From the problem, we know:
- 0.1 mole of \( PQ_2 \) weighs 10 g:
\[ 0.1 \times M_1 = 10 \implies M_1 = \frac{10}{0.1} = 100 \text{ g/mol} \]

- 0.05 mole of \( P_3Q_2 \) weighs 9 g:
\[ 0.05 \times M_2 = 9 \implies M_2 = \frac{9}{0.05} = 180 \text{ g/mol} \]

### Step 4: Write the Equations
Now we have two equations:
1. \( X + 2Y = 100 \) (Equation 1)
2. \( 3X + 2Y = 180 \) (Equation 2)

### Step 5: Solve the Equations
We can solve these equations simultaneously.

Subtract Equation 1 from Equation 2:
\[ (3X + 2Y) - (X + 2Y) = 180 - 100 \]
This simplifies to:
\[ 2X = 80 \implies X = 40 \]

### Step 6: Substitute Back to Find Y
Now substitute \( X = 40 \) back into Equation 1:
\[ 40 + 2Y = 100 \]
This simplifies to:
\[ 2Y = 60 \implies Y = 30 \]

### Conclusion
The atomic weights of elements P and Q are:
- Atomic weight of P \( (X) = 40 \)
- Atomic weight of Q \( (Y) = 30 \)