Percentage by weight of 'M' in `MCl_(3)` is 20%. Atomic weight of that element M is

Options

A. 26.6
B. 13
C. 40
D. 10.4

Explanation

To find the atomic weight of the element 'M' in the compound \( MCl_3 \) given that the percentage by weight of 'M' is 20%, we can follow these steps:

### Step 1: Understand the formula for percentage by weight
The percentage by weight of an element in a compound is given by the formula:

\[ \text{Percentage by weight} = \left( \frac{\text{Atomic weight of the element}}{\text{Molecular weight of the compound}} \right) \times 100 \]

### Step 2: Write down the molecular weight of \( MCl_3 \)
The molecular weight of \( MCl_3 \) can be expressed as:

\[ \text{Molecular weight of } MCl_3 = \text{Atomic weight of } M + 3 \times \text{Atomic weight of Cl \]

Given that the atomic weight of chlorine (Cl) is approximately 35.5 g/mol, we can write:

\[ \text{Molecular weight of } MCl_3 = M + 3 \times 35.5 = M + 106.5 \]

### Step 3: Set up the equation using the given percentage
We know that the percentage by weight of 'M' is 20%. Therefore, we can set up the equation:

\[ 20 = \left( \frac{M}{M + 106.5} \right) \times 100 \]

### Step 4: Simplify the equation
To simplify, we divide both sides by 100:

\[ 0.2 = \frac{M}{M + 106.5} \]

### Step 5: Cross-multiply to eliminate the fraction
Cross-multiplying gives us:

\[ 0.2(M + 106.5) = M \]

### Step 6: Distribute and rearrange the equation
Distributing the 0.2:

\[ 0.2M + 21.3 = M \]

Now, rearranging the equation gives:

\[ M - 0.2M = 21.3 \]

\[ 0.8M = 21.3 \]

### Step 7: Solve for M
Now, divide both sides by 0.8:

\[ M = \frac{21.3}{0.8} = 26.625 \]

### Step 8: Round to the nearest whole number
Since atomic weights are typically expressed as whole numbers, we can round 26.625 to 27.

Thus, the atomic weight of element 'M' is approximately **27 g/mol**.

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