Atomic weight of chlorine is 35.5 . It has two isotopes of atomic weight 35 and 37 . What is the percentage of the heavier isotope in the sample ?

Options

A. 5
B. 10
C. 15
D. 20

Answer

To find the percentage of the heavier isotope of chlorine (atomic weight 37) in a sample, we can use the concept of average atomic weight and set up an equation based on the given information.

### Step-by-Step Solution:

1. **Identify the Given Information**:
- Atomic weight of chlorine (average) = 35.5
- Atomic weight of lighter isotope (Cl-35) = 35
- Atomic weight of heavier isotope (Cl-37) = 37

2. **Define Variables**:
- Let the percentage of the heavier isotope (Cl-37) be \( X \).
- Therefore, the percentage of the lighter isotope (Cl-35) will be \( 100 - X \).

3. **Set Up the Equation**:
The average atomic weight can be expressed as:
\[ \text{Average Atomic Weight} = \frac{(\text{Percentage of Cl-37} \times \text{Atomic Weight of Cl-37}) + (\text{Percentage of Cl-35} \times \text{Atomic Weight of Cl-35})}{100} \]
Substituting the known values, we have:
\[ 35.5 = \frac{(X \times 37) + ((100 - X) \times 35)}{100} \]

4. **Multiply Both Sides by 100**:
To eliminate the denominator, multiply both sides by 100:
\[ 3550 = (X \times 37) + ((100 - X) \times 35) \]

5. **Expand the Equation**:
\[ 3550 = 37X + 3500 - 35X \]

6. **Combine Like Terms**:
\[ 3550 = 2X + 3500 \]

7. **Isolate the Variable \( X \)**:
Subtract 3500 from both sides:
\[ 3550 - 3500 = 2X \]
\[ 50 = 2X \]

8. **Solve for \( X \)**:
Divide both sides by 2:
\[ X = \frac{50}{2} = 25 \]

9. **Conclusion**:
The percentage of the heavier isotope (Cl-37) in the sample is \( 25\% \).

### Final Answer:
The percentage of the heavier isotope (Cl-37) in the sample is **25%**.