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 1: Understand the Average Atomic Mass Formula
The average atomic mass (\(A\)) can be calculated using the formula:
\[ A = \frac{\text{Total Mass}}{\text{Total Moles}} \]
In this case, we have two isotopes of chlorine: \(^{35}\text{Cl}\) and \(^{37}\text{Cl}\).

### Step 2: Define Variables for Moles
Let:
- \(x\) = moles of \(^{35}\text{Cl}\)
- \(y\) = moles of \(^{37}\text{Cl}\)

### Step 3: Set Up the Equation for Average Atomic Mass
The average atomic mass of chlorine can be expressed as:
\[ 35.5 = \frac{35x + 37y}{x + y} \]

### Step 4: Cross Multiply to Eliminate the Denominator
Cross multiplying gives:
\[ 35.5(x + y) = 35x + 37y \]

### Step 5: Expand the Equation
Expanding the left side:
\[ 35.5x + 35.5y = 35x + 37y \]

### Step 6: Rearrange the Equation
Rearranging the equation to isolate terms involving \(x\) and \(y\):
\[ 35.5x + 35.5y - 35x - 37y = 0 \]
This simplifies to:
\[ 0.5x - 1.5y = 0 \]

### Step 7: Solve for the Ratio of \(x\) to \(y\)
Rearranging gives:
\[ 0.5x = 1.5y \]
Dividing both sides by \(0.5\):
\[ x = 3y \]

### Step 8: Write the Molar Ratio
Thus, the ratio of \(x\) to \(y\) is:
\[ \frac{x}{y} = \frac{3y}{y} = 3 \]
This means the 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 \(3:1\).