Concentration Calculations
Amount of substance calculations
- As previously discussed, the amount of substance can be defined as the number of particles in a substance, n, measured in moles (often abbreviated to mol)
- In reality, amount of substance is used as a blanket term to cover most chemical calculations, especially those that involve moles
- The two main calculations for amount of substance are:
Moles, n =
Moles, n = concentration x volume
- Other common calculations for amount of substance include:
Moles, n =
Moles, n =from the ideal gas equation (PV = nRT)
Concentration calculations
- Concentration can be defined as the amount of a substance dissolved in a quantity of liquid
- When a mass concentration is calculated, the units are usually g dm-3
- Other units are possible such as g cm-3, kg m-3 and sometimes in medicines you might see them as mg / ml
- The equation to calculate mass concentration is:
mass concentration in g dm3 =
- When a molar concentration is calculated, the units are mol dm-3
- Calculating molar concentrations requires the use of two equations:
number of moles (or amount) =
-
- Molar mass is the mass per mole of a substance in g mol-1
molar concentration in mol dm-3 =
Worked example
Mass concentration calculations
- What is the mass concentration when 6.34 g of sodium chloride is dissolved into a 0.250 dm3 solution?
- A sodium carbonate solution has a mass concentration of 5.2 g dm-3. What is the volume of the solution made when 250 g of sodium carbonate is used?
- The mass concentration of a solution is 26.7 g dm-3. What is the mass of sodium bromide in 500 cm3 of solution?
Answer 1
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- Mass concentration 25.4 g dm-3 (to 3 s.f.)
Answer 2
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- Volume of solution 48 dm3
- This answer should be given to 2 s.f. as there is a value in the question with only 2 significant figures
Answer 3
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- Mass = mass concentration (g dm-3) x volume of solution (dm3) = 26.7 x 0.5 = 13.4 g (to 3 s.f.)
- The 500 cm3 in the question has to be converted into dm3
- = 0.5 dm3
- Mass = mass concentration (g dm-3) x volume of solution (dm3) = 26.7 x 0.5 = 13.4 g (to 3 s.f.)
Worked example
Molar concentration calculations
- What is the molar concentration when 6.34 g of sodium chloride is dissolved into a 250 cm3 solution?
- A sodium carbonate solution has a molar concentration of 1.25 mol dm-3. What is the volume of the solution made when 250 g of sodium carbonate is used?
- The molar concentration of a sodium bromide solution is 0.250 mol dm-3. What is the mass of sodium bromide in 500 cm3 of this solution?
Answer 1
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- Number of moles of NaCl 0.1084 moles
- Molar concentration in mol dm-3 0.434 mol dm-3
Answer 2
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- Number of moles of Na2CO3 2.358 moles
- Volume of solution in dm3
1.89 dm3
Answer 3
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- Number of moles of NaBr = molar concentration x volume of solution
= 0.250 x 0.500 = 0.125 moles
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- Mass of NaBr = number of moles of NaBr x molar mass
= 0.125 x (23.0 + 79.9) = 12.9 g
Parts per million
- When expressing extremely low concentrations a unit that can be used is parts per million or ppm
- This is useful when giving the concentration of a pollutant in water or the air when the absolute amount is tiny compared the the volume of water or air
- 1 ppm is defined as
- A mass of 1 mg dissolved in 1 dm3 of water
- Since 1 dm3 weighs 1 kg we can also say it is
- A mass of 1 mg dissolved in 1 kg of water, or 10-3 g in 103 g which is the same as saying the concentration is 1 in 106 or 1 in a million
Worked example
The concentration of chlorine in a swimming pool should between between 1 and 3 ppm. Calculate the maximum mass, in kg, of chlorine that should be present in an olympic swimming pool of size 2.5 million litres.
Answer:
Step 1: calculate the total mass in mg assuming 3ppm(1 litre is the same as 1 dm3)
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- 3 x 2.5 x 106 = 7.5 x 106 mg
Step 2: convert the mass into kilograms (1 mg = 10-6 kg)
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- 7.5 x 106 x 10-6 kg = 7.5 kg
Atmospheric gas concentration
- The concentration of atmospheric gases, particularly pollutants, can be measured in parts per million, ppm
- Instead of using mass, the comparison of gas is done by volume
- You might see the values quoted in ppmv - the v shows that the value relates to concentration by volume
- A concentration of 1 ppmv means that there is 1 cm3 of a particular gas in 1000000cm3 or 1000 dm3
- The equation to calculate the concentration of a gas in ppm is:
-
- The volumes can be given in any units but they must be the same units, otherwise one of them will need to be converted
Worked example
Atmospheric gas concentration calculations
Calculate the concentration, in ppm, of the following:
- A volume of 2.5 dm3 of carbon dioxide in 10000 dm3 of air
- A volume of 2.5 dm3 of sulfur dioxide in 4000 dm3 of air
- A volume of 152 cm3 of ozone in 112 dm3 of air
Answer 1
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- Concentration in ppm
250 ppm
Answer 2
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- Concentration in ppm
625 ppm
Answer 3
A volume of 152 cm3 of ozone in 112 dm3 of air
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- Concentration in ppm 1360 ppm
Examiner Tip
When completing atmospheric gas calculations, the gas involved does not affect the calculation as shown by worked examples 1 and 2