Salts of A (atomic mass 15) B (atomic mass 27) and C (atomic mass 48) were electrolysed using same amount of charge . It was found that when 4.5 g of A was deposited , the masses of B and C deposited were 2.7 g and 9.6 g. The valencies of A, B and C were respectively

Options

A. 1,3 and 2
B. 3,1 and 2
C. 2,6 and 3
D. 2,3 and 2

Answer

To find the valencies of A, B, and C, we can use Faraday's second law of electrolysis, which states that the amount of substance deposited during electrolysis is directly proportional to its equivalent mass. The equivalent mass can be calculated using the formula:

\[ \text{Equivalent mass} = \frac{\text{Atomic mass}}{\text{Valency}} \]

Given:
- Atomic mass of A = 15 g/mol
- Atomic mass of B = 27 g/mol
- Atomic mass of C = 48 g/mol
- Mass of A deposited = 4.5 g
- Mass of B deposited = 2.7 g
- Mass of C deposited = 9.6 g

### Step 1: Set up the ratios using Faraday's law

From Faraday's law, we can write the following ratios:

1. \(\frac{\text{mass of A}}{\text{mass of B}} = \frac{\text{Equivalent mass of A}}{\text{Equivalent mass of B}}\)
2. \(\frac{\text{mass of B}}{\text{mass of C}} = \frac{\text{Equivalent mass of B}}{\text{Equivalent mass of C}}\)
3. \(\frac{\text{mass of A}}{\text{mass of C}} = \frac{\text{Equivalent mass of A}}{\text{Equivalent mass of C}}\)

### Step 2: Substitute the values into the first equation

Using the first equation:

\[ \frac{4.5}{2.7} = \frac{\frac{15}{x_1}}{\frac{27}{x_2}} \]

Cross-multiplying gives:

\[ 4.5 \cdot \frac{27}{x_2} = 2.7 \cdot \frac{15}{x_1} \]

### Step 3: Simplify the equation

Calculating the left side:

\[ \frac{4.5 \cdot 27}{2.7} = 45 \]

So we have:

\[ \frac{45}{x_2} = \frac{15}{x_1} \]

Cross-multiplying gives:

\[ 45x_1 = 15x_2 \implies x_2 = 3x_1 \]

### Step 4: Use the second equation

Now, using the second equation:

\[ \frac{2.7}{9.6} = \frac{\frac{27}{x_2}}{\frac{48}{x_3}} \]

Cross-multiplying gives:

\[ 2.7 \cdot \frac{48}{x_3} = 9.6 \cdot \frac{27}{x_2} \]

### Step 5: Simplify this equation

Calculating the left side:

\[ \frac{2.7 \cdot 48}{9.6} = 13.5 \]

So we have:

\[ \frac{13.5}{x_3} = \frac{27}{x_2} \]

Cross-multiplying gives:

\[ 13.5x_2 = 27x_3 \implies x_3 = 0.5x_2 \]

### Step 6: Substitute \(x_2\) in terms of \(x_1\)

Since \(x_2 = 3x_1\):

\[ x_3 = 0.5(3x_1) = 1.5x_1 \]

### Step 7: Write the ratios of valencies

Now we have:

- \(x_1\) (valency of A)
- \(x_2 = 3x_1\) (valency of B)
- \(x_3 = 1.5x_1\) (valency of C)

### Step 8: Express the ratio of valencies

The ratio of the valencies \(x_1 : x_2 : x_3\) becomes:

\[ x_1 : 3x_1 : 1.5x_1 = 1 : 3 : 1.5 \]

### Step 9: Convert to whole numbers

To express this in whole numbers, multiply each term by 2:

\[ 1 \cdot 2 : 3 \cdot 2 : 1.5 \cdot 2 = 2 : 6 : 3 \]

### Final Answer

Thus, the valencies of A, B, and C are respectively:

\[ \text{Valencies} = 2 : 6 : 3 \]