# 6.1 Stoichiometry and composition  (Page 3/5)

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The standard units used for this equation are $P$ in Pa, $V$ in m ${}^{3}$ and $T$ in K. Remember also that 1000cm ${}^{3}$ = 1dm ${}^{3}$ and 1000dm ${}^{3}$ = 1m ${}^{3}$ .

A sample of gas occupies a volume of 20 dm ${}^{3}$ , has a temperature of 280 K and has a pressure of 105 Pa. Calculate the number of moles of gas that are present in the sample.

1. The only value that is not in SI units is volume. V = 0.02 m ${}^{3}$ .

2. We know that pV = nRT

Therefore,

$n=\frac{pV}{RT}$
3. $n=\frac{105×0.02}{8.31×280}=\frac{2.1}{2326.8}=0.0009\mathrm{moles}$

## Using the combined gas law

1. An enclosed gas(i.e. one in a sealed container) has a volume of 300 cm ${}^{3}$ and a temperature of 300 K. The pressure of the gas is 50 kPa. Calculate the number of moles of gas that are present in the container.
2. What pressure will 3 mol of gaseous nitrogen exert if it is pumped into a container that has a volume of 25 dm ${}^{3}$ at a temperature of 29 ${}^{0}$ C?
3. The volume of air inside a tyre is 19 litres and the temperature is 290 K. You check the pressure of your tyres and find that the pressure is 190 kPa. How many moles of air are present in the tyre?
4. Compressed carbon dioxide is contained within a gas cylinder at a pressure of 700 kPa. The temperature of the gas in the cylinder is 310 K and the number of moles of gas is 13 moles of carbon dioxide. What is the volume of the gas inside the cylinder?

## Molar concentrations of liquids

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 dm ${}^{3}$ . Therefore, the unit of concentration is mol. ${\mathrm{dm}}^{-3}$ . When concentration is expressed in mol. ${\mathrm{dm}}^{-3}$ it is known as the molarity (M) of the solution. Molarity is the most common expression for concentration.

Do not confuse molarity (M) with molar mass (M). Look carefully at the question in which the M appears to determine whether it is concentration or molar mass.
Concentration

Concentration is a measure of the amount of solute that is dissolved in a given volume of liquid. It is measured in mol.dm ${}^{-3}$ . Another term that is used for concentration is molarity (M)

If 3.5 g of sodium hydroxide (NaOH) is dissolved in 2.5 ${\mathrm{dm}}^{3}$ of water, what is the concentration of the solution in mol. ${\mathrm{dm}}^{-3}$ ?

1. $n=\frac{m}{M}=\frac{3.5}{40}=0.0875mol$
2. $C=\frac{n}{V}=\frac{0.0875}{2.5}=0.035$

The concentration of the solution is 0.035 mol.dm ${}^{-3}$ or 0.035 M

You have a 1 dm ${}^{3}$ container in which to prepare a solution of potassium permanganate (KMnO ${}_{4}$ ). What mass of KMnO ${}_{4}$ is needed to make a solution with a concentration of 0.2 M?

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

therefore

$n=C×V=0.2×1=0.2mol$
2. $m=n×M=0.2×158.04=31.61g$

The mass of KMnO ${}_{4}$ that is needed is 31.61 g.

How much sodium chloride (in g) will one need to prepare 500 ${\mathrm{cm}}^{3}$ of solution with a concentration of 0.01 M?

1. $V=\frac{500}{1000}=0.5d{m}^{3}$
2. $n=C×V=0.01×0.5=0.005mol$
3. $m=n×M=0.005×58.45=0.29g$

The mass of sodium chloride needed is 0.29 g

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