Science You're Expected to Know · Lesson 2

States of matter, density, pH and solutions

A few chemistry facts come up again and again. Pure water freezes (and ice melts) at 0 °C and boils at 100 °C at sea level. While a substance is melting or boiling, its temperature stays level even though heat is still being added.

Density = mass ÷ volume, usually in g/cm³ or g/mL. An object floats in a liquid that is denser than the object and sinks in one that is less dense. Mass alone doesn’t decide it: a large, heavy log floats while a small pebble sinks.

The pH scale tells you how acidic or basic a solution is. Below 7 is acidic, exactly 7 is neutral (pure water), and above 7 is basic. A lower pH means more acidic.

A solute dissolves in a solvent to make a solution. A solution that holds as much solute as it can at that temperature is saturated; extra solute stays undissolved. For many solids, warmer water dissolves more. Dissolved substances also change a liquid’s properties, and the passage’s data tell you by how much.

Dissolving Solid S

Students studied Solid S, a white crystalline solid that dissolves in water. All of the work was done at sea level.

Study 1: The students found the greatest mass of Solid S that would dissolve in 100 g of water at five temperatures. A solution holding that greatest mass was called saturated; any extra solid stayed undissolved at the bottom. Figure 1 shows the results.

Study 2: The students dissolved 0, 5, 10 or 15 g of Solid S in 100 g of water. For each solution they measured the density at 25 °C, the temperature at which it began to freeze, and the temperature at which it boiled (Table 1).

Study 3: The students measured the mass and volume of four small plastic objects, A to D (Table 2).

Figure 1
Figure 1Line graph of the greatest mass of Solid S that dissolves in 100 g of water versus water temperature. The mass rises as temperature rises: 20 g at 0 °C, 32 g at 20 °C, 50 g at 40 °C, 76 g at 60 °C and 110 g at 80 °C.020406080100120020406080Water temperature (°C)Solid S dissolved at saturation (g per 100 g water)
  • Solid S
Show the data as a table
Figure 1: data
Water temperature (°C)Solid S (g per 100 g water)
020
2032
4050
6076
80110

Line graph of the greatest mass of Solid S that dissolves in 100 g of water versus water temperature. The mass rises as temperature rises: 20 g at 0 °C, 32 g at 20 °C, 50 g at 40 °C, 76 g at 60 °C and 110 g at 80 °C.

Table 1
Solid S in 100 g water (g)Density at 25 °C (g/cm³)Freezing temperature (°C)Boiling temperature (°C)
01.000.0100.0
51.04−1.5100.4
101.07−3.0100.8
151.11−4.5101.2
For 0, 5, 10 and 15 g of Solid S in 100 g of water: density 1.00, 1.04, 1.07 and 1.11 g/cm³; freezing temperature 0.0, −1.5, −3.0 and −4.5 °C; boiling temperature 100.0, 100.4, 100.8 and 101.2 °C. More dissolved solid raises density and boiling temperature and lowers freezing temperature.
Table 2
ObjectMass (g)Volume (cm³)
A2730
B2120
C1210
D4050
Mass and volume of four plastic objects. Object A: 27 g, 30 cm³. Object B: 21 g, 20 cm³. Object C: 12 g, 10 cm³. Object D: 40 g, 50 cm³. Object D has the most mass and the most volume.

Worked example Easy

Show the whole passage

Dissolving Solid S

Students studied Solid S, a white crystalline solid that dissolves in water. All of the work was done at sea level.

Study 1: The students found the greatest mass of Solid S that would dissolve in 100 g of water at five temperatures. A solution holding that greatest mass was called saturated; any extra solid stayed undissolved at the bottom. Figure 1 shows the results.

Study 2: The students dissolved 0, 5, 10 or 15 g of Solid S in 100 g of water. For each solution they measured the density at 25 °C, the temperature at which it began to freeze, and the temperature at which it boiled (Table 1).

Study 3: The students measured the mass and volume of four small plastic objects, A to D (Table 2).

Figure 1
Figure 1Line graph of the greatest mass of Solid S that dissolves in 100 g of water versus water temperature. The mass rises as temperature rises: 20 g at 0 °C, 32 g at 20 °C, 50 g at 40 °C, 76 g at 60 °C and 110 g at 80 °C.020406080100120020406080Water temperature (°C)Solid S dissolved at saturation (g per 100 g water)
  • Solid S
Show the data as a table
Figure 1: data
Water temperature (°C)Solid S (g per 100 g water)
020
2032
4050
6076
80110

Line graph of the greatest mass of Solid S that dissolves in 100 g of water versus water temperature. The mass rises as temperature rises: 20 g at 0 °C, 32 g at 20 °C, 50 g at 40 °C, 76 g at 60 °C and 110 g at 80 °C.

Table 1
Solid S in 100 g water (g)Density at 25 °C (g/cm³)Freezing temperature (°C)Boiling temperature (°C)
01.000.0100.0
51.04−1.5100.4
101.07−3.0100.8
151.11−4.5101.2
For 0, 5, 10 and 15 g of Solid S in 100 g of water: density 1.00, 1.04, 1.07 and 1.11 g/cm³; freezing temperature 0.0, −1.5, −3.0 and −4.5 °C; boiling temperature 100.0, 100.4, 100.8 and 101.2 °C. More dissolved solid raises density and boiling temperature and lowers freezing temperature.
Table 2
ObjectMass (g)Volume (cm³)
A2730
B2120
C1210
D4050
Mass and volume of four plastic objects. Object A: 27 g, 30 cm³. Object B: 21 g, 20 cm³. Object C: 12 g, 10 cm³. Object D: 40 g, 50 cm³. Object D has the most mass and the most volume.

Based on Tables 1 and 2, which objects would float in pure water (the 0 g solution)?

  1. Object A only
  2. Objects A and DAnswer
  3. Objects B and C
  4. Object D only

How to solve it

  1. From the passage: the 0 g row of Table 1 gives water’s density, 1.00 g/cm³; Table 2 gives each object’s mass and volume.
  2. From background: density = mass ÷ volume, and an object floats in a denser liquid.
  3. A 0.90, B 1.05, C 1.20, D 0.80 g/cm³. Below 1.00: A and D.

Why each choice is right or wrong

  • A. Incorrect. This drops Object D because it has the most mass, 40 g. Floating depends on density, and D’s density is only 40 ÷ 50 = 0.80 g/cm³.
  • B. Correct. From Table 1, pure water’s density is 1.00 g/cm³ (passage). From background, density = mass ÷ volume: A is 27 ÷ 30 = 0.90 and D is 40 ÷ 50 = 0.80 g/cm³, both less than water, so they float. B (1.05) and C (1.20) sink.
  • C. Incorrect. B and C have the least mass (21 g and 12 g), but floating depends on density, mass ÷ volume: 1.05 and 1.20 g/cm³, both denser than water, so both sink.
  • D. Incorrect. Object D does float, but so does Object A, at 0.90 g/cm³. Size isn’t the test; density below 1.00 g/cm³ is.

Worked example Medium

Show the whole passage

Dissolving Solid S

Students studied Solid S, a white crystalline solid that dissolves in water. All of the work was done at sea level.

Study 1: The students found the greatest mass of Solid S that would dissolve in 100 g of water at five temperatures. A solution holding that greatest mass was called saturated; any extra solid stayed undissolved at the bottom. Figure 1 shows the results.

Study 2: The students dissolved 0, 5, 10 or 15 g of Solid S in 100 g of water. For each solution they measured the density at 25 °C, the temperature at which it began to freeze, and the temperature at which it boiled (Table 1).

Study 3: The students measured the mass and volume of four small plastic objects, A to D (Table 2).

Figure 1
Figure 1Line graph of the greatest mass of Solid S that dissolves in 100 g of water versus water temperature. The mass rises as temperature rises: 20 g at 0 °C, 32 g at 20 °C, 50 g at 40 °C, 76 g at 60 °C and 110 g at 80 °C.020406080100120020406080Water temperature (°C)Solid S dissolved at saturation (g per 100 g water)
  • Solid S
Show the data as a table
Figure 1: data
Water temperature (°C)Solid S (g per 100 g water)
020
2032
4050
6076
80110

Line graph of the greatest mass of Solid S that dissolves in 100 g of water versus water temperature. The mass rises as temperature rises: 20 g at 0 °C, 32 g at 20 °C, 50 g at 40 °C, 76 g at 60 °C and 110 g at 80 °C.

Table 1
Solid S in 100 g water (g)Density at 25 °C (g/cm³)Freezing temperature (°C)Boiling temperature (°C)
01.000.0100.0
51.04−1.5100.4
101.07−3.0100.8
151.11−4.5101.2
For 0, 5, 10 and 15 g of Solid S in 100 g of water: density 1.00, 1.04, 1.07 and 1.11 g/cm³; freezing temperature 0.0, −1.5, −3.0 and −4.5 °C; boiling temperature 100.0, 100.4, 100.8 and 101.2 °C. More dissolved solid raises density and boiling temperature and lowers freezing temperature.
Table 2
ObjectMass (g)Volume (cm³)
A2730
B2120
C1210
D4050
Mass and volume of four plastic objects. Object A: 27 g, 30 cm³. Object B: 21 g, 20 cm³. Object C: 12 g, 10 cm³. Object D: 40 g, 50 cm³. Object D has the most mass and the most volume.

At 40 °C, a student stirs 60 g of Solid S into 100 g of water. Based on Figure 1, what happens?

  1. All 60 g dissolve, and the solution is not saturated.
  2. About 32 g dissolve, and about 28 g stay solid.
  3. About 50 g dissolve, and about 10 g stay solid.Answer
  4. About 10 g dissolve, and about 50 g stay solid.

How to solve it

  1. From the passage: Figure 1 at 40 °C reads 50 g per 100 g of water.
  2. Background: past saturation, extra solute stays undissolved.
  3. 60 g added − 50 g dissolved = 10 g left as solid; the solution is saturated.

Why each choice is right or wrong

  • A. Incorrect. At 40 °C, Figure 1 shows a limit of 50 g, less than the 60 g added, so not all of it dissolves and the solution is saturated.
  • B. Incorrect. 32 g is the limit at 20 °C, the neighboring point on Figure 1, not at 40 °C.
  • C. Correct. Figure 1 shows 50 g dissolving in 100 g of water at 40 °C (passage). The passage defines a saturated solution as one holding that greatest mass, so 50 g dissolve and 60 − 50 = 10 g stay at the bottom.
  • D. Incorrect. This reverses the two amounts. 50 g is how much dissolves, and the extra 10 g is what stays solid.

Trap When a fact you know meets the data, the data win

“Water freezes at 0 °C” is true for pure water. Table 1 shows that water with Solid S dissolved in it begins to freeze lower, at −1.5, −3.0 or −4.5 °C. Use a background fact to read the data, never to overrule it. If a choice gives a textbook value that the table contradicts, it’s a trap.