Foundations of Chemistry. Philippa B. Cranwell

Foundations of Chemistry

mass of a substance is the amount we measure when we weigh the substance. Mass is a measure of the quantity of a substance. In science, we use the term mass as opposed to weight of a substance to describe the amount because the weight of a substance is related to the gravitational force acting on the substance. We often use the words ‘mass’ and ‘weight’ interchangeably, but they are not really the same thing scientifically.

The SI unit of mass is the kilogram. However, in the laboratory, chemicals and other objects are usually weighed in units of grams as the gram is a far more convenient amount to work with. Even though we use a balance to weigh a substance, we report its mass in grams, not its weight.

One kilogram is equivalent to one thousand grams, 1 000 g. 1 kg = 1 000 g. Therefore 1 g =

or 0.001 kg. This can also be written as 1 × 10⁻³ kg.

Another common measure of mass is the milligram, mg. One milligram is one‐thousandth of a gram:

You should always choose a balance appropriate to the level of accuracy of the mass required. If you need ‘about two grams’, for example, a two‐figure balance is perfectly appropriate. If you are told to weigh ‘accurately approximately two grams’, this implies you need to use a four‐figure balance to weigh around two grams of substance but record its weight accurately to four decimal places, e.g. 0.0001 g.

Volume

The volume of a substance is the space that it occupies. In chemistry, we are generally most concerned with the volumes of liquids and gases.

Liquid volumes are measured relatively easily, and the type of measuring device used will depend upon the accuracy with which we need to know the volume. There is always a certain amount of uncertainty when making a measurement. Different types of measuring equipment have different levels of uncertainty associated with them. For less accurate work, chemists generally use a measuring cylinder (Figure 0.2a). These can be obtained in different sizes, but the uncertainty in the volume when using a measuring cylinder depends on the size of the measuring cylinder and the graduations. The uncertainty on a measuring cylinder is half the volume of the smallest graduations. For a 25 cm³ measuring cylinder where the graduations are 0.5 cm³, the uncertainty is ±0.25 cm³. If 25 cm³ was measured into a 25 cm³ measuring cylinder, the percentage uncertainty would be

If a 250 cm³ measuring cylinder was used to measure out 25 cm³ where the uncertainty was ±0.5 cm³, the percentage uncertainty would be

= 2%. It is therefore more accurate to use a smaller measuring cylinder for this volume of liquid.

Figure 0.2 (a) 25 cm³ measuring cylinder; (b) 25 cm³ pipette; (c) 50 cm³ burette.

Source: Eisco Labs.

If we need to know the volume of liquid measured more accurately than this, either a pipette or a burette can be used. A pipette (Figure 0.2b) measures a fixed volume of liquid, and pipettes can be obtained in various sizes. A burette (Figure 0.2c) can be used to deliver variable volumes of liquids; although burettes can be obtained in various sizes, the 50 cm³ burette is the size most commonly used. The uncertainty on a volume measurement when using a laboratory pipette is ±0.06 cm³. This means the uncertainty on measuring a volume of 25 cm³ using a pipette is

= 0.2%. For a standard burette, the uncertainty associated with each reading is ±0.05 cm³. If making one reading, then the percentage uncertainty in measuring 25 cm³ is

0.2%. When recording the amount added from a burette, we make two readings, so the total uncertainty associated with the readings is ±0.1 cm³. Thus the percentage uncertainty on the burette reading is

= 0.4%.

The derived SI unit for volume is the cubic metre or m³ because the volume of an object is obtained from the product of its height, width, and depth, which are all units of length (Figure 0.3a). As the SI unit of length is the m, the derived unit for volume has units of m³. However, a volume of 1 m³ is very large, so the m³ is not a very useful unit.

Schematic illustrations of (a) Cube of volume 1 m cubed. (b) Flask of volume 1 L.

Figure 0.3 (a) Cube of volume 1 m³. (b) Flask of volume 1 L.

Source: Eisco Labs.

In the chemistry laboratory, we often work with volumes a lot smaller than a cubic metre. A volume you will often encounter is the litre (Figure 0.3b). The symbol that represents the litre is L. However, strictly speaking, this is a non‐SI unit, although it is in common use. Chemists usually work in volumes of cm³ or dm³ where:

Therefore: 1 L = 1 dm³.

1 dm (decimetre) = 0.1 m (1 × 10⁻¹ m) (Figure 0.3c).

Remember

1 dm³ = 1 L = 1 x 10⁻³ m³ 1 000 dm³ = 1 000 L = 1 m³.

1 dm³ (decimetre cubed) = (0.1 m)³ = ( 1 × 10⁻¹ m)³ = 1 × 10⁻³ m³.

1 dm³ is therefore one thousandth of a m³. There are therefore 1 000 dm³ or 1 000 L in 1 m³.

Imagine the size of a 1 litre carton of orange juice. 1 000 cartons of 1 litre orange juice would fit in a cubic metre.

Photo depicts an orange juice packet. The label has a text that reads, grower's harvest.

Source: Dr Elizabeth Page.

Worked Example 0.4

Convert each of the following masses to grams. You may need to refer to Table 0.3 to obtain the numerical values of the prefixes used. Give your answers in scientific notation:

1 2.32 Mg

2 1 000 mg

3 400 μg

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