Average atomic mass of chlorine is 35.5 then the correct naturally occuring molar ratio of `"^(35)Cl & ^(37)Cl` is

Options

A. 4:1
B. 2:1
C. 3:1
D. 1:1

Answer

To find the naturally occurring molar ratio of \(^{35}\text{Cl}\) and \(^{37}\text{Cl}\) given that the average atomic mass of chlorine is 35.5, we can follow these steps:

### Step-by-Step Solution:

1. **Define Variables**:
Let \(x\) be the molar ratio of \(^{35}\text{Cl}\) and \(1 - x\) be the molar ratio of \(^{37}\text{Cl}\).

2. **Set Up the Average Atomic Mass Equation**:
The average atomic mass can be expressed as:
\[ \text{Average Atomic Mass} = (35 \times x) + (37 \times (1 - x)) \]
Given that the average atomic mass of chlorine is 35.5, we can set up the equation:
\[ 35.5 = 35x + 37(1 - x) \]

3. **Expand and Simplify the Equation**:
Expanding the equation gives:
\[ 35.5 = 35x + 37 - 37x \]
Simplifying this, we get:
\[ 35.5 = -2x + 37 \]

4. **Isolate the Variable \(x\)**:
Rearranging the equation to isolate \(x\):
\[ -2x = 35.5 - 37 \]
\[ -2x = -1.5 \]
Dividing both sides by -2:
\[ x = \frac{1.5}{2} = 0.75 \]

5. **Determine the Molar Ratio**:
Now that we have \(x\), we can find \(1 - x\):
\[ 1 - x = 1 - 0.75 = 0.25 \]
Therefore, the molar ratio of \(^{35}\text{Cl}\) to \(^{37}\text{Cl}\) is:
\[ \frac{x}{1 - x} = \frac{0.75}{0.25} = 3 \]

6. **Final Molar Ratio**:
Thus, the naturally occurring molar ratio of \(^{35}\text{Cl}\) to \(^{37}\text{Cl}\) is:
\[ 3 : 1 \]

### Final Answer:
The correct naturally occurring molar ratio of \(^{35}\text{Cl}\) to \(^{37}\text{Cl}\) is \(3 : 1\).