0.9 Quantitative aspects of chemical change (Page 7/10)

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Aluminium trichloride ( ${AlCl}_{3}$ ) is an ionic substance that forms crystals in the solid phase. Water molecules may be trapped inside the crystal lattice. We represent this as: ${AlCl}_{3} \cdot n H_{2} O$ . A learner heated some aluminium trichloride crystals until all the water had evaporated and found that the mass after heating was $2,8 g$ . The mass before heating was $5 g$ . What is the number of moles of water molecules in the aluminium trichloride?

Work out the mass of water molecules lost
We first need to find n, the number of water molecules that are present in the crystal. To do this we first note that the mass of water lost is $5 - 2,8 = 2,2$ .
Work out the mass ratio and mole ratio
The next step is to work out the mass ratio of aluminium trichloride to water and the mole ratio. The mass ratio is:
$2,8 : 2,2$
To work out the mole ratio we divide the mass ratio by the molecular mass of each species:
$\frac{2,8}{133} : \frac{2,2}{18} = 0,021 : 0,12$
Next we do the following:
$0,021 \frac{1}{0,021} = 1$
and
$\frac{0,12}{0,021} = 6$
So the mole ratio of aluminium trichloride to water is:
$1 : 6$
Write down the final answer
And now we know that there are 6 moles of water molecules in the crystal.

Khan academy video on molecular and empirical formulae - 1

Khan academy video on mass composition - 1

Moles and empirical formulae

Calcium chloride is produced as the product of a chemical reaction.
1. What is the formula of calcium chloride?
2. What percentage does each of the elements contribute to the mass of a molecule of calcium chloride?
3. If the sample contains $5 g$ of calcium chloride, what is the mass of calcium in the sample?
4. How many moles of calcium chloride are in the sample?
13 g of zinc combines with 6,4 g of sulphur. What is the empirical formula of zinc sulphide?
1. What mass of zinc sulphide will be produced?
2. What percentage does each of the elements in zinc sulphide contribute to its mass?
3. Determine the formula of zinc sulphide.
A calcium mineral consisted of 29,4% calcium, 23,5% sulphur and 47,1% oxygen by mass. Calculate the empirical formula of the mineral.
A chlorinated hydrocarbon compound was analysed and found to consist of 24,24% carbon, 4,04% hydrogen and 71,72% chlorine. From another experiment the molecular mass was found to be $99 g \cdot mol^{- 1}$ . Deduce the empirical and molecular formula.

Molar volumes of gases

It is possible to calculate the volume of one mole of gas at STP using what we know about gases.

Write down the ideal gas equation $pV = nRT$ , therefore $V = \frac{n R T}{p}$
Record the values that you know, making sure that they are in SI units You know that the gas is under STP conditions. These are as follows: $p = 101,3 kPa = 101300 Pa$ $n = 1 mol$ $R = 8,31 J \cdot K^{- 1} \cdot mol^{- 1}$ $T = 273 K$
Substitute these values into the original equation.
$V = \frac{n R T}{p}$

$V = \frac{1 mol \times 8, 31 J \cdot K^{- 1} \cdot {mol}^{- 1} \times 273 K}{101300 Pa}$
Calculate the volume of $1 mole$ of gas under these conditions The volume of $1 mole$ of gas at STP is $22,4 \times 10^{- 3} m^{3} = 22,4 dm^{3}$ .

The standard units used for this equation are

P

Pa

V

m^{3}

and

T

K

. Remember also that

1 000 cm^{3} = 1 dm^{3}

and

1 000 dm^{3} = 1 m^{3}

A sample of gas occupies a volume of $20 dm^{3}$ , has a temperature of $200 K$ and has a pressure of $105 Pa$ . Calculate the number of moles of gas that are present in the sample.

Convert all values into SI units
The only value that is not in SI units is volume. $V = 0,02 m^{3}$ .
Write the equation for calculating the number of moles in a gas
We know that $pV = nRT$

Therefore,

$n = \frac{p V}{R T}$
Substitute values into the equation to calculate the number of moles of the gas
$n = \frac{105 \times 0, 02}{8, 31 \times 280} = \frac{2, 1}{2326, 8} = 0, 0009 moles$

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Source: OpenStax, Chemistry grade 10 [caps]. OpenStax CNX. Jun 13, 2011 Download for free at http://cnx.org/content/col11303/1.4

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