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## Converting weight/volume (w/v) concentrations to ppm

ppm = 1 g m^{-3} = 1 mg L^{-1} = 1 μg mL^{-1}

**Question 1.** A solution has a concentration of 1.25 g L^{-1}.

What is its concentration in ppm?

- Convert the mass in grams to a mass in milligrams:
1.25 g = 1.25 × 1000 mg = 1250 mg

- Re-write the concentration in mg L
^{-1}
concentration in mg L^{-1} = 1250 mg L^{-1} = 1250 ppm

**Question 2.** A solution has a concentration of 0.5 mg mL^{-1}.

What is its concentration in ppm?

- Convert the volume in millilitres to litres:
volume = 1 mL = 1 mL ÷ 1000 mL L^{-1} = 0.001 L

- Re-write the concentration in mg L
^{-1}
concentration in mg L^{-1} = 0.5 mg ÷ 0.001 L = 500 mg L^{-1} = 500 ppm

## Converting weight/weight (w/w) concentrations to ppm

1 ppm = 1 mg kg^{-1} = 1 μg g^{-1}

**Question 1.** A solution has a concentration of 0.033 g kg^{-1}.

What is its concentration in ppm?

- Convert the mass in grams to mass in milligrams:
0.033 g = 0.033 g × 1000 mg g^{-1} = 33 mg

- Re-write the concentration in mg kg
^{-1}
concentration in mg kg^{-1} = 33 mg kg^{-1} = 33 ppm

**Question 2.** A solution has a concentration of 2250 μg kg^{-1}.

What is its concentration in ppm?

- Convert the mass in micrograms to mass in milligrams:
2250 μg = 2250 μg ÷ 1000 μg mg^{-1} = 2.25 mg

- Re-write the concentration in mg kg
^{-1}
concentration in mg kg^{-1} = 2.25 mg kg^{-1} = 2.25 ppm

## Parts Per Million (ppm) Concentration Calculations

**Question 1.** 150 mL of an aqueous sodium chloride solution contains 0.0045 g NaCl.

Calculate the concentration of NaCl in parts per million (ppm).

- Write an equation representing the ppm concentration:
ppm = mass solute (mg) ÷ volume solution (L)

- Extract the data from the question:
mass solute (NaCl) = 0.0045 g

volume of solution = 150 mL

- Convert the mass in grams to a mass in milligrams:
mass NaCl = 0.0045 g = 0.0045 g × 1000 mg/g = 4.5 mg

- Convert the volume in millilitres to a volume in litres
volume solution = 150 mL = 150 mL ÷ 1000 mL/L = 0.150 L

- Calculate the ppm concentration of the NaCl solution:
concentration of NaCl = 4.5 mg ÷ 0.150 L = 30 mg L^{-1} = 30 ppm

**Question 2.** What mass in milligrams of potassium nitrate is present in 0.25 kg of a 500 ppm aqueous solution of KNO_{3}?

- Write an equation representing the ppm concentration:
ppm = mass solute (mg) ÷ mass solution (kg)

- Re-arrange this equation to find the mass of solute:
mass solute (mg) = ppm × mass solution (kg)

- Extract the data from the question:
concentration = 500 ppm = 500 mg/kg

mass of solute (KNO_{3}) = 0.25 kg

- Substitute in the values and solve:
mass KNO_{3} = 500 mg/kg × 0.25 kg = 125 mg

**Question 3.** A student is provided with 500 mL of 600 ppm solution of sucrose.

What volume of this solution in millilitres contains 0.15 g of sucrose?

- Write an equation representing the ppm concentration:
ppm = mass solute (mg) ÷ volume solution (L)

- Re-arrange this equation to find volume of solution:
volume solution (L) = mass solute (mg) ÷ ppm

- Extract the data from the question:
mass solute (sucrose) required = 0.15 g

ppm concentration of solution = 600 ppm = 600 mg L^{-1}

(the total volume of solution provided, that is 500 mL, is not relevant to the question)

- Convert the mass in grams to a mass in milligrams:
mass solute (sucrose) = 0.15 g × 1000 mg/g = 150 mg

- Substitute in the values and solve:
volume solution (L) required = 150 mg ÷ 600 mg L^{-1} = 0.25 L

- Convert the volume in litres to a volume in millilitres:
volume solution required = 0.25 L × 1000 mL/L = 250 mL