Answers · Relative masses

How heavy is a water molecule? — answer key

Check meaning, not exact wording. These are teaching points, not official Cambridge marks.

1. RQ1 · Practice

Model answer. The relative atomic mass is the average mass of the isotopes of an element compared to 1/12 of the mass of an atom of carbon-12. It is an average, so it can be 35.5 for chlorine, and it is a comparison, so it has no unit.

A full answer includes

I chose the average mass of its isotopes, compared to 1/12 of the mass of a carbon-12 atom.
I did not choose the mass of the most common isotope: every isotope counts in the average.

Also accept

The average mass of the isotopes compared to 1/12 of the mass of a carbon-12 atom.

Watch for

“The relative atomic mass is the mass number of the atom.” — The mass number counts the protons and neutrons in one atom of one isotope. A_r is the average of all the isotopes, so it need not be a whole number.
“Relative masses are in grams.” — A_r and M_r compare masses with 1/12 of the mass of a carbon-12 atom, so they have no unit.
“A_r is the mass of the most common isotope.” — The most common isotope pulls the average towards it, but every isotope counts.

2. RQ2 · Practice

Model answer. (a) Every silver atom is either silver-107 or silver-109, and any sample is a mixture of the two. A_r is the average mass of the atoms in the mixture, so it need not be the mass of any single atom. (b) 108 is exactly halfway between 107 and 109. A more common isotope would pull the average towards its own mass, so neither is more common: the two isotopes are about equally common. (Real silver is about 52 % silver-107 and 48 % silver-109.)

A full answer includes

(a) I wrote that silver is a mixture of two isotopes, silver-107 and silver-109.
(a) I wrote that A_r is the average mass of the atoms in a sample.
(a) I did not write that 108 is the mass number of a silver atom.
(b) I wrote that 108 is exactly halfway between 107 and 109.
(b) I wrote that the two isotopes are about equally common.

Also accept

(a) A mixture of silver-107 and silver-109; A_r is their average. (b) 108 is halfway, so they are about equally common.

Watch for

“The relative atomic mass is the mass number of the atom.” — The mass number counts the protons and neutrons in one atom of one isotope. A_r is the average of all the isotopes, so it need not be a whole number.
“108 is the mass of a third isotope, silver-108.” — Silver has only two isotopes, 107 and 109. 108 is their average, not a third kind of atom.
“The heavier isotope is always more common.” — If silver-109 were more common, the average would be above 108. Exactly halfway means about equal amounts.

3. RQ3 · Practice

Model answer. If the two isotopes were equally common, the average would be halfway, 70. 69.7 is nearer 69, so the average is pulled towards gallium-69: there are more gallium-69 atoms than gallium-71 atoms.

A full answer includes

I chose: gallium-69 atoms are more common.
I compared 69.7 with 70, the halfway point between 69 and 71.
I saw that 69.7 is below 70, so nearer 69.
I did not choose gallium-71 just because it is heavier.

Also accept

Gallium-69, because the average is nearer 69.

Watch for

“The heavier isotope is always more common.” — The average is pulled towards whichever isotope is more common; here it is the lighter one.
“The isotopes are equally common, because 69.7 is between 69 and 71.” — Equal amounts would give exactly 70. Any average lies between the isotopes; its position shows which one is more common.
“A_r tells you nothing about how common each isotope is.” — It does: where the average lies between 69 and 71 shows which isotope is more common.

4. RQ4 · Practice

Model answer. CH₄: 12 + 4 × 1 = 16. K₂O: 2 × 39 + 16 = 94. Potassium oxide is ionic, a lattice of K⁺ and O²⁻ ions with no molecules, so its M_r is called the relative formula mass. Row C.

A full answer includes

I chose row C.
I worked out CH₄ as 12 + 4 × 1 = 16.
I worked out K₂O as 2 × 39 + 16 = 94.
I named the M_r of the ionic compound its relative formula mass.
I did not count only one potassium atom in K₂O.

Also accept

Row C

Watch for

“Row A.” — K₂ means two potassium atoms: 2 × 39 + 16 = 94, not 39 + 16 = 55.
“Row B.” — CH₄ has four hydrogen atoms: 12 + 4 × 1 = 16. The small 4 counts the atoms of the element before it.
“Row D.” — Potassium oxide is made of ions and has no molecules, so its M_r is a relative formula mass.

5. RQ5 · Practice

Model answer. M_r is the sum of the relative atomic masses. An ionic compound is a lattice of ions with no molecules, so its sum is called the relative formula mass. It has the same symbol, M_r.

A full answer includes

(1) I wrote "sum" (or "total").
(2) I wrote "formula".
(1) I did not write "average": that word belongs to A_r.

Also accept

sum (or total); formula

Watch for

“M_r is the average of the relative atomic masses.” — A_r is an average of isotopes; M_r adds up the A_r of every atom in the formula.
“Ionic compounds have a relative molecular mass.” — An ionic compound has no molecules, so the sum is its relative formula mass.

6. RQ6 · Practice

Model answer. Work out the mass inside the bracket first, multiply it by the number after the bracket, then add the rest. Fe(OH)₃: OH is 17, so 56 + 3 × 17 = 107. Ca(NO₃)₂: NO₃ is 14 + 48 = 62, so 40 + 2 × 62 = 164. Al₂(SO₄)₃: SO₄ is 32 + 64 = 96, so 2 × 27 + 3 × 96 = 54 + 288 = 342.

Checked automatically

M_r of Fe(OH)₃: 107 (exact value)
- Common wrong answer 73 : The 3 multiplies the whole OH group: 56 + 3 × 17.
- Common wrong answer 75 : The 3 multiplies the oxygen too, not only the hydrogen: 56 + 3 × (16 + 1).
M_r of Ca(NO₃)₂: 164 (exact value)
- Common wrong answer 102 : The 2 doubles the whole NO₃ group: 40 + 2 × 62.
M_r of Al₂(SO₄)₃: 342 (exact value)
- Common wrong answer 150 : The 3 multiplies the whole SO₄ group: 2 × 27 + 3 × 96.

A full answer includes

I worked out each bracket group first: OH 17, NO₃ 62, SO₄ 96.
I multiplied each group by the number after its bracket.
I wrote 107 for Fe(OH)₃.
I wrote 164 for Ca(NO₃)₂.
I wrote 342 for Al₂(SO₄)₃.
I did not multiply only the last symbol in a bracket.

Also accept

107, 164, 342

Watch for

“The number after a bracket multiplies only the last symbol.” — The number after a bracket multiplies everything inside the bracket.

7. RQ7 · Practice

Model answer. CoCl₂ is 59 + 2 × 35.5 = 130. Each water molecule is 2 × 1 + 16 = 18, and there are six: 6 × 18 = 108. The dot means "together with", so add: 130 + 108 = 238.

Checked automatically

(a) M_r of CoCl₂·6H₂O: 238 (exact value)
- Common wrong answer 148 : There are six water molecules: 130 + 6 × 18.
- Common wrong answer 14040 : The dot means "with": add, do not multiply.
(b) Water in it: 108 (exact value)
- Common wrong answer 18 : That is one water molecule; there are six.

A full answer includes

(a) I found CoCl₂: 59 + 2 × 35.5 = 130.
(a) I added six water molecules: 6 × 18 = 108.
(a) I wrote 238.
(b) I wrote 108.
(a) I did not multiply across the dot.

Also accept

(a) 238 (b) 108

Watch for

“The dot in a hydrate formula means multiply.” — The dot means "together with": add the mass of the water molecules to the rest.
“Only one water molecule counts.” — The 6 in front of H₂O counts six water molecules: 6 × 18.

8. RQ8 · Practice

Options as numbered on the pupil sheet: 1 — Relative molecular mass; 2 — Relative formula mass.

Model answer. Sulfur dioxide, SO₂, and ammonia, NH₃, are made of non-metals only: they are covalent and made of molecules, so their M_r is the relative molecular mass. Potassium bromide, lithium fluoride and calcium chloride are ionic: a metal with a non-metal, a lattice of ions with no molecules, so their M_r is the relative formula mass. Both are worked out in the same way.

A full answer includes

I matched sulfur dioxide and ammonia to relative molecular mass.
I matched potassium bromide, lithium fluoride and calcium chloride to relative formula mass.
I did not call the sum for every compound a relative molecular mass.

Also accept

SO₂, NH₃: molecular; KBr, LiF, CaCl₂: formula.

Watch for

“Every compound has a relative molecular mass.” — Ionic compounds have no molecules, so their sum is a relative formula mass.
“A compound of two non-metals is made of ions.” — Non-metals share electrons and form molecules; ions form when a metal reacts with a non-metal.

9. RQ15 · Practice

Model answer. Think of 100 atoms: 95 of mass 32, 1 of mass 33 and 4 of mass 34. Their total mass is 32 × 95 + 33 × 1 + 34 × 4 = 3040 + 33 + 136 = 3209. One atom on average: 3209 ÷ 100 = 32.09, which is 32.1 to one decimal place. Check: it lies between 32 and 34 and very near 32, because almost all the atoms are sulfur-32.

Checked automatically

A_r of sulfur: 32.1 (3 significant figures)
- Common wrong answer 33 : That is the plain average of 32, 33 and 34. Each mass counts as often as its percentage.
- Common wrong answer 3209 : That is the total mass of 100 atoms. Divide by 100 for the average of one atom.
- Common wrong answer 32 : That is the mass number of the most common isotope. The heavier atoms pull the average up a little: give one decimal place.

A full answer includes

I multiplied each mass by its percentage and added: 32 × 95 + 33 × 1 + 34 × 4 = 3209.
I divided by 100: 32.09.
I wrote 32.1, to one decimal place.
I did not take the plain average of 32, 33 and 34.

Also accept

32.1

Watch for

“A_r is the plain average of the isotope masses.” — Each isotope counts as often as its percentage, so the most common isotope pulls the average towards its own mass.
“The relative atomic mass is the mass number of the atom.” — The mass number counts the protons and neutrons in one atom of one isotope. A_r is the average of all the isotopes, so it need not be a whole number.
“A_r is the total mass of the atoms.” — 3209 is the mass of 100 atoms. Divide by 100 for the average of one atom.

10. RT1 · Apply

Model answer. Ozone has three oxygen atoms: 3 × 16 = 48. An oxygen molecule, O₂, is 2 × 16 = 32, and 48 ÷ 32 = 1.5, so an ozone molecule is one and a half times as heavy. A carbon-12 atom is 12 on the same scale, and 48 ÷ 12 = 4: an ozone molecule is four times as heavy as a carbon-12 atom.

Checked automatically

(a) M_r of O₃: 48 (exact value)
- Common wrong answer 16 : Ozone has three oxygen atoms.
(b) Times as heavy as O₂: 1.5 (exact value)
- Common wrong answer 3 : An O₂ molecule is 32, not 16: 48 ÷ 32.
- Common wrong answer 0.67 : Divide the heavier mass by the lighter one: 48 ÷ 32.
(c) Times as heavy as carbon-12: 4 (exact value)
- Common wrong answer 3 : Compare with carbon-12, which is 12 on this scale, not with one oxygen atom.
- Common wrong answer 0.25 : Divide the heavier mass by the lighter one: 48 ÷ 12.

A full answer includes

(a) I multiplied the A_r of oxygen by 3.
(a) I wrote 48.
(b) I divided 48 by 32, the M_r of O₂.
(b) I wrote 1.5.
(c) I divided 48 by 12, the value of a carbon-12 atom on this scale.
(c) I wrote 4.
(b) I did not divide by 16, the mass of one oxygen atom.

Also accept

(a) 48 (b) 1.5 (c) 4

Watch for

“Ozone is O₂ with one more atom, so it is 16 heavier and the ratio cannot be found.” — All relative masses are on the carbon-12 scale, so dividing one by another gives how many times as heavy.
“Relative masses are in grams.” — A_r and M_r compare masses with 1/12 of the mass of a carbon-12 atom, so they have no unit.

11. RT3 · Apply

Model answer. (a) A group that matches the ratio has 1 lithium-6 atom and 12 lithium-7 atoms, 13 atoms in all. Their total mass is 6 + 12 × 7 = 6 + 84 = 90, so the average is 90 ÷ 13 = 6.923… = 6.92. (b) Now the group has 1 + 30 = 31 atoms with a total mass of 6 + 30 × 7 = 6 + 210 = 216, so the average is 216 ÷ 31 = 6.967… = 6.97. The second sample has a smaller share of the lighter isotope, so its average is pulled nearer to 7. A_r is the average for one mixture of isotopes, so it changes when the mixture changes.

Checked automatically

(a) A_r of natural lithium: 6.92 (3 significant figures)
- Common wrong answer 6.5 : That is the plain average of 6 and 7. There are 12 lithium-7 atoms for every lithium-6 atom.
- Common wrong answer 7.5 : You divided by 12. The group has 13 atoms: count the lithium-6 atom too.
- Common wrong answer 6.08 : You gave the 12 atoms a mass of 6. Lithium-7 is the common isotope.
(b) A_r of the second sample: 6.97 (3 significant figures)
- Common wrong answer 7.2 : You divided by 30. The group has 31 atoms: count the lithium-6 atom too.
- Common wrong answer 6.03 : You gave the 30 atoms a mass of 6. Lithium-7 is the common isotope.
- Common wrong answer 6.5 : That is the plain average of 6 and 7. Each isotope counts as often as its atoms appear.

A full answer includes

(a) I took a group of 13 atoms: 1 of mass 6 and 12 of mass 7.
(a) I divided their total mass, 90, by 13.
(a) I wrote 6.92.
(b) I divided the total mass of 31 atoms, 216, by 31.
(b) I wrote 6.97.
I explained that the second sample has a smaller share of lithium-6, so its average is nearer 7.
I did not divide by 12 or 30: the lithium-6 atom counts too.

Also accept

(a) 6.92 (b) 6.97; the second sample has fewer lithium-6 atoms, so its average is nearer 7.

Watch for

“A_r is the plain average of the isotope masses.” — Each isotope counts as often as its atoms appear, so the common lithium-7 pulls the average towards 7.
“Divide by the number of atoms of the common isotope only.” — Every atom in the group counts: 1 + 12 = 13 atoms, not 12.
“Every sample of an element has the same A_r.” — A_r is the average of a mixture. Change the mixture and the average changes.