Why is chlorine 35.5? — answer key

1. IQ8 · Practice

Model answer. Multiply each mass number by its abundance: 10 × 20 = 200 and 11 × 80 = 880. Add them: 1080. Divide by 100: Ar = 10.8. Check: 10.8 is between 10 and 11 and nearer 11, because 80 % of the atoms are boron-11.

Checked automatically

• Relative atomic mass, Ar: 10.8 (within ±0.05)
  • Common wrong answer 10.5 : That is the simple mean. Multiply each mass number by its abundance first.
  • Common wrong answer 1080 : You have the total for 100 atoms. Divide by 100.
  • Common wrong answer 11 : That is the most common isotope. The boron-10 atoms pull the average down a little.

A full answer includes

• 10 × 20 + 11 × 80 = 200 + 880 = 1080.
• 1080 ÷ 100 = 10.8.
• I checked that 10.8 lies between 10 and 11, nearer 11, the more abundant isotope.

Also accept

• 10.8

Watch for

• “Ar is 10.5, halfway between 10 and 11.” — That would be true only if both isotopes had the same abundance. Four atoms in five are boron-11, so the average is nearer 11.

2. IQ9 · Practice

Model answer. 6 × 7.5 = 45 and 7 × 92.5 = 647.5. The total is 692.5, and 692.5 ÷ 100 = 6.925, so Ar = 6.9 to one decimal place. Check: it is between 6 and 7 and very close to 7, because 92.5 % of the atoms are lithium-7.

Checked automatically

• Relative atomic mass, Ar: 6.9 (within ±0.05)
  • Common wrong answer 6.5 : That is the simple mean. Multiply each mass number by its abundance.
  • Common wrong answer 692.5 : That is the total for 100 atoms. Divide by 100.

A full answer includes

• 6 × 7.5 + 7 × 92.5 = 45 + 647.5 = 692.5.
• 692.5 ÷ 100 = 6.925, so 6.9 to one decimal place.

Also accept

• 6.9

Watch for

• “Ar is 6.5, halfway between 6 and 7.” — Only 7.5 % of the atoms are lithium-6, so the average is much nearer 7.

3. IQ10 · Practice

Model answer. Ar must lie between 63 and 65, which rules out 63.0, only possible if every atom were X-63. Most of the atoms (69 %) are X-63, so Ar is below the halfway value of 64: that leaves 63.6. The full calculation agrees: (63 × 69 + 65 × 31) ÷ 100 = 63.62.

A full answer includes

• 63.6.
• I explained that Ar is between 63 and 65 and nearer 63, because more than two thirds of the atoms are X-63.

Also accept

• 63.6

Watch for

• “Ar is 64.0, the mean of 63 and 65.” — The isotopes are not equally common. With 69 % X-63, the average is pulled below 64.
• “Ar is 64.4, because X-65 is heavier.” — The heavier isotope is the rarer one here, so the average sits nearer the lighter, common isotope.

4. IQ11 · Practice

Model answer. (a) An atom has a whole number of protons and neutrons, so its mass number is 35 or 37. 35.5 is the average mass of all the atoms in a sample. (b) The average counts each isotope by its abundance. 75 % of the atoms are chlorine-35, three times as many as chlorine-37, so the average is pulled towards 35: (35 × 75 + 37 × 25) ÷ 100 = 35.5. The simple mean, 36, would apply only if the two isotopes were equally common.

A full answer includes

• (a) Every chlorine atom is either chlorine-35 or chlorine-37; 35.5 is the average mass of the mixture.
• (b) There are three times as many chlorine-35 atoms, so the average is nearer 35: (35 × 75 + 37 × 25) ÷ 100 = 35.5. 36 would be right only for equal abundances.

Also accept

• (a) It is an average of 35s and 37s. (b) Weighted by abundance: 75 % are chlorine-35.

Watch for

• “Some chlorine atoms have half a neutron.” — Neutrons are whole particles. 35.5 is not the mass of any one atom but the average of many.

5. IT2 · Apply

Model answer. From the chart: neon-20 is 90.5 %, neon-21 is 0.3 % and neon-22 is 9.2 %. 20 × 90.5 = 1810, 21 × 0.3 = 6.3 and 22 × 9.2 = 202.4. The total is 2018.7, and 2018.7 ÷ 100 = 20.187, so Ar = 20.2. Check: between 20 and 22, very close to 20.

Checked automatically

• Relative atomic mass, Ar: 20.2 (within ±0.05)
  • Common wrong answer 21 : That is the simple mean of 20, 21 and 22. Weight each by its abundance.
  • Common wrong answer 2018.7 : That is the total for 100 atoms. Divide by 100.
  • Common wrong answer 20 : The neon-22 atoms add a little: give one decimal place.

A full answer includes

• 20 × 90.5 + 21 × 0.3 + 22 × 9.2 = 1810 + 6.3 + 202.4 = 2018.7.
• 2018.7 ÷ 100 = 20.187, so 20.2.

Also accept

• 20.2

Watch for

• “Ar is 21, the middle isotope.” — Neon-21 is the rarest isotope. Most atoms are neon-20, so the average is close to 20.