Exercise 2 solution

Weighted average = (mass of isotope 1 x its fraction) + (mass of isotope 2 x its fraction).

Fractions: 75.8% = 0.758 and 24.2% = 0.242 (they add to 1.000).

  35 x 0.758 = 26.530
  37 x 0.242 =  8.954
  total      = 35.484

So the weighted average is 35.484, which rounds to 35.5. That matches the 35.5 daltons quoted from the Isotope article.

Why it is not 36: a plain average of 35 and 37 would be 36, but chlorine-35 is about three times as common as chlorine-37, so the answer is pulled towards 35.

Note: using whole mass numbers (35 and 37) as the isotope masses is an approximation; real isotope masses are not exact whole numbers (silicon-28 is 27.97693 Da in the chapter, for example). It works here because the result still rounds to the quoted value.

The arithmetic was checked with Python (35 x 0.758 + 37 x 0.242 = 35.484).