1.2.1 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

   Answer 1

• • Mass concentration 25.4 g dm^-3 (to 3 s.f.)

   Answer 2

• • 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

• • 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 

Worked Example

   Answer 1

• • Number of moles of NaCl 0.1084 moles
  • Molar concentration in mol dm^-3 0.434 mol dm^-3 

   Answer 2

• • Number of moles of Na₂CO₃ 2.358 moles
  • Volume of solution in dm³

1.89 dm³ 

   Answer 3

• • Number of moles of NaBr = molar concentration x volume of solution

= 0.250 x 0.500 = 0.125 moles 

• • Mass of NaBr = number of moles of NaBr x molar mass

= 0.125 x (23.0 + 79.9) = 12.9 g

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

   Answer 1

• • Concentration in ppm

250 ppm 

   Answer 2

• • Concentration in ppm

625 ppm 

   Answer 3

A volume of 152 cm³ of ozone in 112 dm³ of air

• • Concentration in ppm 1360 ppm 

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