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# Amount of substance

## 19.3 Amount of substance (ESAGC)

### Molar Volumes of Gases (ESAGD)

Molar volume of gases

One mole of gas occupies $$\text{22,4}$$ $$\text{dm^{3}}$$ at standard temperature and pressure.

Standard temperature and pressure (S.T.P.) is defined as a temperature of $$\text{273,15}$$ $$\text{K}$$ and a pressure of $$\text{0,986}$$ $$\text{atm}$$.

For example, $$\text{2}$$ $$\text{mol}$$ of $$\text{H}_{2}$$ gas will occupy a volume of $$\text{44,8}$$ $$\text{dm^{3}}$$ at standard temperature and pressure (S.T.P.). and $$\text{67,2}$$ $$\text{dm^{3}}$$ of ammonia gas ($$\text{NH}_{3}$$) contains $$\text{3}$$ $$\text{mol}$$ of ammonia.

### Molar concentrations of liquids (ESAGE)

A typical solution is made by dissolving some solid substance in a liquid. The amount of substance that is dissolved in a given volume of liquid is known as the concentration of the liquid. Mathematically, concentration ($$C$$) is defined as moles of solute ($$n$$) per unit volume ($$V$$) of solution.

$C = \frac{n}{V}$

For this equation, the units for volume are $$\text{dm^{3}}$$ (which is equal to litres). Therefore, the unit of concentration is $$\text{mol·dm^{-3}}$$.

Concentration

Concentration is a measure of the amount of solute that is dissolved in a given volume of liquid. It is measured in $$\text{mol·dm^{-3}}$$.

## Worked example 12: Concentration calculations 1

If $$\text{3,5}$$ $$\text{g}$$ of sodium hydroxide ($$\text{NaOH}$$) is dissolved in $$\text{2,5}$$ $$\text{dm^{3}}$$ of water, what is the concentration of the solution in $$\text{mol·dm^{-3}}$$?

### Find the number of moles of sodium hydroxide

\begin{align*} n & = \frac{m}{M} \\ & = \frac{\text{3,5}\text{ g}}{\text{40,01}\text{ g·mol$^{-1}$}} \\ & = \text{0,0875}\text{ mol} \end{align*}

### Calculate the concentration

\begin{align*} C & = \frac{n}{V} \\ & = {\text{0,0875}\text{ mol}}{\text{2,5}\text{ dm$^{3}$}} \\ & = \text{0,035}\text{ mol·dm$^{-3}$} \end{align*}

The concentration of the solution is $$\text{0,035}$$ $$\text{mol·dm^{-3}}$$.

## Worked example 13: Concentration calculations 2

You have a $$\text{1}$$ $$\text{dm^{3}}$$ container in which to prepare a solution of potassium permanganate ($$\text{KMnO}_{4}$$). What mass of $$\text{KMnO}_{4}$$ is needed to make a solution with a concentration of $$\text{0,2}$$ $$\text{mol·dm^{-3}}$$?

### Calculate the number of moles

$$C = \frac{n}{V}$$ therefore:

\begin{align*} n & = \frac{C}{V} \\ & = \frac{\text{0,2}\text{ mol·dm$^{-3}$}}{\text{1}\text{ dm$^{3}$}} \\ & = \text{0,2}\text{ mol} \end{align*}

### Find the mass

\begin{align*} m & = nM \\ & = (\text{0,2}\text{ mol})(\text{158}\text{ g·mol$^{-1}$}) \\ & = \text{31,6}\text{ g} \end{align*}

The mass of $$\text{KMnO}_{4}$$ that is needed is $$\text{31,6}$$ $$\text{g}$$.

## Worked example 14: Concentration calculations 3

How much sodium chloride (in g) will one need to prepare $$\text{500}$$ $$\text{cm^{3}}$$ of solution with a concentration of $$\text{0,01}$$ $$\text{mol·dm^{-3}}$$?

### Convert the given volume to the correct units

$V = \text{500}\text{ cm^{3}} \times \frac{\text{1}\text{ dm^{3}}}{\text{1 000}\text{ cm^{3}}} = \text{0,5}\text{ dm^{3}}$

### Find the number of moles

\begin{align*} n & = \frac{C}{V} \\ & = \frac{\text{0,01}\text{ mol·dm$^{-3}$}}{\text{0,5}\text{ dm$^{3}$}} \\ & = \text{0,005}\text{ mol} \end{align*}

### Find the mass

\begin{align*} m & = nM \\ & = (\text{0,005}\text{ mol})(\text{58,45}\text{ g·mol$^{-1}$}) \\ & = \text{0,29}\text{ g} \end{align*}

The mass of sodium chloride needed is $$\text{0,29}$$ $$\text{g}$$

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## Concentration of solutions

Exercise 19.6

$$\text{5,95}$$ $$\text{g}$$ of potassium bromide was dissolved in $$\text{400}$$ $$\text{dm^{3}}$$ of water. Calculate its concentration.

Solution not yet available

$$\text{100}$$ $$\text{g}$$ of sodium chloride ($$\text{NaCl}$$) is dissolved in $$\text{450}$$ $$\text{cm^{3}}$$ of water.

1. How many moles of $$\text{NaCl}$$ are present in solution?

2. What is the volume of water (in $$\text{dm^{3}}$$)?

3. Calculate the concentration of the solution.

Solution not yet available

What is the molarity of the solution formed by dissolving $$\text{80}$$ $$\text{g}$$ of sodium hydroxide ($$\text{NaOH}$$) in $$\text{500}$$ $$\text{cm^{3}}$$ of water?

Solution not yet available

What mass (g) of hydrogen chloride ($$\text{HCl}$$) is needed to make up $$\text{1 000}$$ $$\text{cm^{3}}$$ of a solution of concentration $$\text{1}$$ $$\text{mol·dm^{-3}}$$?

Solution not yet available

How many moles of $$\text{H}_{2}\text{SO}_{4}$$ are there in $$\text{250}$$ $$\text{cm^{3}}$$ of a $$\text{0,8}$$ $$\text{mol·dm^{-3}}$$ sulphuric acid solution? What mass of acid is in this solution?

Solution not yet available