Suppose that A and B form the compounds `B_(2)A_(3)` and `B_(2)A` if 0.05 mole of `B_(2)A_(3)` weighs 9 g and 0.1 mole of `B_(2)A` weighs 10 g, the atomic weight of A and B respectively are

Options

A. 30 and 40
B. 40 and 30
C. 20 and 5
D. 15 and 20

Answer

To solve the problem, we need to determine the atomic weights of elements A and B based on the given compounds and their weights. Let's break down the solution step by step.

### Step 1: Calculate the molar mass of B2A3
We know that:
- The mass of 0.05 moles of B2A3 = 9 g

Using the formula for molar mass:
\[ \text{Molar Mass of } B_2A_3 = \frac{\text{Mass}}{\text{Moles}} = \frac{9 \, \text{g}}{0.05 \, \text{moles}} = 180 \, \text{g/mol} \]

### Step 2: Write the molar mass equation for B2A3
The molar mass of B2A3 can be expressed in terms of the atomic weights of A and B:
\[ \text{Molar Mass of } B_2A_3 = 2M_B + 3M_A \]
Where \(M_A\) is the atomic weight of A and \(M_B\) is the atomic weight of B.

From Step 1, we have:
\[ 2M_B + 3M_A = 180 \quad \text{(1)} \]

### Step 3: Calculate the molar mass of B2A
We know that:
- The mass of 0.1 moles of B2A = 10 g

Using the formula for molar mass:
\[ \text{Molar Mass of } B_2A = \frac{\text{Mass}}{\text{Moles}} = \frac{10 \, \text{g}}{0.1 \, \text{moles}} = 100 \, \text{g/mol} \]

### Step 4: Write the molar mass equation for B2A
The molar mass of B2A can be expressed in terms of the atomic weights of A and B:
\[ \text{Molar Mass of } B_2A = 2M_B + M_A \]
From Step 3, we have:
\[ 2M_B + M_A = 100 \quad \text{(2)} \]

### Step 5: Solve the system of equations
Now we have two equations:
1. \(2M_B + 3M_A = 180\) (Equation 1)
2. \(2M_B + M_A = 100\) (Equation 2)

We can subtract Equation (2) from Equation (1):
\[ (2M_B + 3M_A) - (2M_B + M_A) = 180 - 100 \]
This simplifies to:
\[ 2M_A = 80 \]
\[ M_A = 40 \quad \text{(3)} \]

### Step 6: Substitute M_A back into one of the equations
Now we can substitute \(M_A = 40\) into Equation (2):
\[ 2M_B + 40 = 100 \]
\[ 2M_B = 60 \]
\[ M_B = 30 \quad \text{(4)} \]

### Final Result
The atomic weights of A and B are:
- \(M_A = 40\)
- \(M_B = 30\)

### Summary
Thus, the atomic weights of A and B are 40 and 30, respectively.