Chemistry, Third edition

9 · CALCULATING CONCENTRATIONS

Other units of concentration

Parts per million

Very low concentrations of substances are usually expressed in terms of parts per

million (ppm) or even parts per billion (ppb) by mass, where:

ppm

mass of trace substance

 106 ;

mass of sample

1 ppm of a species is often expressed in the units:

1 mg of the species per kg of a sample

or

1 ppm is equivalent to 1 mg kg^1

See Box 9.3 for examples.

Trace concentrations in gaseous mixtures

If we are dealing with gaseous mixtures, it is often more convenient to express ppm

and ppb by volume, rather than by mass:

1 ppm by volume 

volume of trace substance

 106

total volume of sample

or

1 ppm by volume is equivalent to 1 cm^3 in 10^3 dm^3 of sample

These units are useful for describing the levels of pollutants in air. For example, the

concentration of NO 2 in the atmosphere around a large city was 15 ppm; this

corresponds to 15 cm^3 of the gas in a sample of 10^3 dm^3 of air.

ppm in aqueous solution

For dilute aqueous solutions at room temperature, the density of the solution is close

to the density of water (1 g cm^3 ), so the volume of the solution in cubic centimetres

9.4

146

Gravimetric analysis

The concentration of nickel ions in a solution can be determined by precipitation of scarlet

nickel dimethylglyoxime, Ni(DMG) 2. The ionic equation for the reaction is as follows:

Ni^2 (aq) + 2DMGH Ni(DMG) 2 (s) + 2H(aq)

where DMGH C 4 H 7 O 2 N 2.

A student used a 100.0 cm^3 sample of a 2000 cm^3 solution and precipitated all of the nickel

in the sample as Ni(DMG) 2. The precipitate was filtered off and heated to constant mass.

The results were:

mass of container 30.8749 g

mass of container + precipitate (1st weighing) 30.9885 g

mass of container + precipitate (2nd weighing) 30.9877 g

mass of container + precipitate (3rd weighing) 30.9877 g

(i) What was the mass of the dry precipitate?

(ii)Why were the precipitates heated to constant mass?

(iii)Calculate the concentration of nickel ions in the solution.

(iv)What was the mass of nickel in the original 2000 cm^3 of solution?

(usem(Ni)58.69 u, m(C)12.011 u, m(H)1.008 u, m(O)15.999 u, m(N)14.007 u)

Exercise 9H

ppb

mass of trace substance

 109

mass of sample

Parts per million

by mass

(i)What total mass of

mercury is present in a

fish of mass of 2.0 kg,

which has been found to

contain mercury at a

concentration of

0.60 ppm (or

0.60 mg kg^1 )?

(ii)A 5.00 kg sample of soil

is found to have a total

lead content of 2.00 g.

What is the

concentration of lead in

the soil, in ppm

(mg kg^1 )?

Exercise 9I