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 it down step by step.

### Step 1: Calculate the Molecular Mass of B₂A₃
We know that:
- 0.05 moles of B₂A₃ weigh 9 g.

Using the formula for molecular mass:
\[ \text{Molecular Mass} = \frac{\text{Mass in grams}}{\text{Number of moles}} \]
Substituting the values:
\[ \text{Molecular Mass of B₂A₃} = \frac{9 \text{ g}}{0.05 \text{ moles}} = 180 \text{ g/mol} \]

### Step 2: Set Up the Equation for B₂A₃
Let the atomic weight of A be \( x \) and the atomic weight of B be \( y \). The molecular formula B₂A₃ indicates:
\[ \text{Molecular Mass of B₂A₃} = 2y + 3x \]
From Step 1, we know this equals 180 g/mol:
\[ 2y + 3x = 180 \quad \text{(Equation 1)} \]

### Step 3: Calculate the Molecular Mass of B₂A
We know that:
- 0.1 moles of B₂A weigh 10 g.

Using the same formula:
\[ \text{Molecular Mass of B₂A} = \frac{10 \text{ g}}{0.1 \text{ moles}} = 100 \text{ g/mol} \]

### Step 4: Set Up the Equation for B₂A
The molecular formula B₂A indicates:
\[ \text{Molecular Mass of B₂A} = 2y + x \]
From Step 3, we know this equals 100 g/mol:
\[ 2y + x = 100 \quad \text{(Equation 2)} \]

### Step 5: Solve the Equations Simultaneously
Now we have two equations:
1. \( 2y + 3x = 180 \)
2. \( 2y + x = 100 \)

We can solve for \( x \) from Equation 2:
\[ x = 100 - 2y \quad \text{(Substituting into Equation 1)} \]

### Step 6: Substitute \( x \) into Equation 1
Substituting \( x \) in Equation 1:
\[ 2y + 3(100 - 2y) = 180 \]
Expanding this:
\[ 2y + 300 - 6y = 180 \]
Combining like terms:
\[ -4y + 300 = 180 \]
Rearranging gives:
\[ -4y = 180 - 300 \]
\[ -4y = -120 \]
Dividing by -4:
\[ y = 30 \]

### Step 7: Find \( x \)
Now substituting \( y \) back into Equation 2:
\[ 2(30) + x = 100 \]
\[ 60 + x = 100 \]
\[ x = 100 - 60 \]
\[ x = 40 \]

### Conclusion
The atomic weights of A and B are:
- Atomic weight of A = 40
- Atomic weight of B = 30

### Final Answer
The atomic weights of A and B are 40 and 30, respectively.

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