# Parts Per Million (ppm) Concentration

## Key Concepts

• Parts Per Million (ppm) is a measurement of the concentration of a soluton.
• For very dilute solutions, weight/weight (w/w) and weight/volume (w/v) concentrations are sometimes expressed in parts per million.
• parts per million is abbreviated as ppm
• 1 ppm is one part by weight, or volume, of solute in 1 million parts by weight, or volume, of solution.
• In weight/volume (w/v) terms,
1 ppm = 1g m-3 = 1 mg L-1 = 1 μg mL-1
• In weight/weight (w/w) terms,
1 ppm = 1 mg kg-1 = 1 μg g-1

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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?

1. Convert the mass in grams to a mass in milligrams:
1.25 g = 1.25 × 1000 mg = 1250 mg
2. 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?

1. Convert the volume in millilitres to litres:
volume = 1 mL = 1 mL ÷ 1000 mL L-1 = 0.001 L
2. 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

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## 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?

1. Convert the mass in grams to mass in milligrams:
0.033 g = 0.033 g × 1000 mg g-1 = 33 mg
2. 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?

1. Convert the mass in micrograms to mass in milligrams:
2250 μg = 2250 μg ÷ 1000 μg mg-1 = 2.25 mg
2. Re-write the concentration in mg kg-1
concentration in mg kg-1 = 2.25 mg kg-1 = 2.25 ppm

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## 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).

1. Write an equation representing the ppm concentration:
ppm = mass solute (mg) ÷ volume solution (L)
2. Extract the data from the question:
mass solute (NaCl) = 0.0045 g
volume of solution = 150 mL
3. Convert the mass in grams to a mass in milligrams:
mass NaCl = 0.0045 g = 0.0045 g × 1000 mg/g = 4.5 mg
4. Convert the volume in millilitres to a volume in litres
volume solution = 150 mL = 150 mL ÷ 1000 mL/L = 0.150 L
5. 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 KNO3?

1. Write an equation representing the ppm concentration:
ppm = mass solute (mg) ÷ mass solution (kg)
2. Re-arrange this equation to find the mass of solute:
mass solute (mg) = ppm × mass solution (kg)
3. Extract the data from the question:
concentration = 500 ppm = 500 mg/kg
mass of solute (KNO3) = 0.25 kg
4. Substitute in the values and solve:
mass KNO3 = 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?

1. Write an equation representing the ppm concentration:
ppm = mass solute (mg) ÷ volume solution (L)
2. Re-arrange this equation to find volume of solution:
volume solution (L) = mass solute (mg) ÷ ppm
3. 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)
4. Convert the mass in grams to a mass in milligrams:
mass solute (sucrose) = 0.15 g × 1000 mg/g = 150 mg
5. Substitute in the values and solve:
volume solution (L) required = 150 mg ÷ 600 mg L-1 = 0.25 L
6. Convert the volume in litres to a volume in millilitres:
volume solution required = 0.25 L × 1000 mL/L = 250 mL

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