The average molar mass of chlorine is 35.5 g mol –1 . The ratio of ³⁵Cl to ³⁷Cl in naturally occuring chlorine is close to :

Solution

Chemistry ma’am · 3 steps

Let the fraction of chlorine-35 be x and make the weighted average of 35 and 37 come out to 35.5.

1. Set up the average. Natural chlorine is a mixture of two isotopes. Take the fraction of ³⁵Cl as x, so the fraction of ³⁷Cl is 1 - x. Each mass counts in proportion to how much of that isotope is present.

   35x + 37(1 - x) = 35.5

2. Solve for x. This gives 37 - 2x = 35.5, so 2x = 1.5 and x = 0.75. That leaves 1 - x = 0.25 for ³⁷Cl.
3. So. The ratio ³⁵Cl : ³⁷Cl = 0.75 : 0.25 = 3 : 1, which is option (c).

The idea to keep. Average atomic mass is a weighted mean. It always sits closer to the more abundant isotope, and the distances to the two masses give the ratio in reverse: here 1.5 and 0.5, so 3 : 1.

Answer from the NTA final answer key. Solution by PrepWiser.