# Parts Per Million Concentration (ppm) Chemistry Tutorial

## Key Concepts

⚛ Parts Per Million is a measurement of the concentration of a soluton.

⚛ 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.

⚛ Percentage composition concentrations can be converted to parts per million concentration by multiplying by 10 000

· ppm = 10 000 × percentage concentration value

⚛ For very dilute solutions, weight/weight (w/w) and weight/volume (w/v) concentrations are sometimes expressed in parts per million.

· NOTE: weight/weight (w/w) may also be referred to as mass/mass (m/m)

· NOTE: weight/volume (w/v) may also be referred to as mass/volume (m/v) or mass concentration.

⚛ In weight of solute per volume of solution (w/v or m/v) terms,

· 1 ppm = 1g m-3 = 1 mg L-1 = 1 μg mL-1

⚛ In weight of solute per weight of solution (w/w or m/m) terms,

· 1 ppm = 1 mg kg-1 = 1 μg g-1

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## Parts per million and Percentage Concentration Calculations

Recall that, in general, concentration tells you how much solute is present in a solution.

A concentration in parts per million (ppm) tells you how many parts of solute are present in 1 000 000 parts of solution.

For example, a saline solution is a dilute aqueous solution of sodium chloride, NaCl(aq), with a concentration of 9 000 ppm.
This means that there are 9 000 parts of NaCl in every 1 000 000 parts of the solution.

But the concentration of a solution is sometimes given as a percentage.
A percentage concentration tells you how many parts of solute are present in 100 parts of solution.

For example, the ethanol content in wine is often given as about 12%(v/v), that is, 12% of the volume of the wine is ethanol, or, there are 12 parts of ethanol in every 100 parts of solution.
How would we convert that to a concentration in parts per million (ppm) ?

We could write a mathematical expression equating parts per hundred (a percentage) and parts per million (ppm) as shown below:

 x% = y ppm x   100 = y       1 000 000

To convert x% to ppm we multiply both sides of the equation by 1 000 000 as shown below:

 x   100 × 1 000 000 = y       1 000 000 × 1 000 000 x × 10 000 = y

To convert a percentage concentration to parts per million we multiply the % value (x) by 10 000.

The ethanol concentration of wine was given as 12%(v/v) so the value of x is 12. We can now convert this to a concentration in parts per million (ppm) by multiplying x by 10 000 as shown below:

 x × 10 000 = y ppm 12 × 10 000 = 120 000 ppm

This is true for other similar percentage concentrations:

For mass/volume percentage concentrations (m/v% or w/v%):
x = value of m/v%
x × 10 000 = ppm

For mass/mass percentage concentrations (m/m% or w/w%):
x = value of m/m%
x × 10 000 = ppm

y ppm = x × 10 000
where x is the value of the percentage concentration

And a word of warning ...

m/v concentration is NOT the same as a %(m/v) concentration
w/v concentration is NOT the same as a %(w/v) concentration
m/m concentration is NOT the same as a %(m/m) concentration
w/v concentration is NOT the same as a %(w/v) concentration
v/v concentration is NOT the same as a %(v/v) concentration

m/v (w/v) and m/m (w/w) concentrations and parts per million will be discussed in the following section (after the worked examples of percentage concentration and ppm below).

### Worked Examples: Converting Percentage Concentration to ppm

Follow these 4 steps to convert percentage concentration to parts. per million concentration:

Step 1: Extract the data from the question

percentage concentration = x%

parts per million concentration = y ppm

Step 2: Write the definition of ppm to be used

y ppm = x × 10 000

Step 3: Substitute in the values and solve

Step 4: Write the concentration in ppm

concentration = y ppm

Question 1. A sample of beer has an ethanol concentration of 4%(v/v).

What is the ethanol concentration of this beer in ppm?

Solution:

Step 1: Extract the data from the question

ethanol concentration = %(v/v) = 4%

x = 4

concentration = y ppm

Step 2: Write the definition of ppm to be used

y ppm = x × 10 000

Step 3: Substitute in the values and solve

y ppm = 4 × 10 000

y ppm = 40 000

Step 4: Write the concentration in ppm

ethanol concentration in beer = 40 000 ppm

Question 2. A sample of seawater has a chloride concentration of 1.94%(m/v).

What is the chloride concentration of this seawater in ppm?

Solution:

Step 1: Extract the data from the question

chloride concentration = %(m/v) = 1.94%

x = 1.94

concentration = y ppm

Step 2: Write the definition of ppm to be used

y ppm = x × 10 000

Step 3: Substitute in the values and solve

y ppm = 1.94 × 10 000

y ppm = 19 400

Step 4: Write the concentration in ppm

chloride concentration in seawater = 19 400 ppm

## Parts per million Unit Calculations

Recall that, in general, concentration tells you how much solute is present in a solution.

concentration = amount of solute ÷ amount of solution

A concentration in parts per million (ppm) may refer to the mass of solute present in the volume of solution (w/v or m/v) or it may refer to the mass of solute present in a mass of solution (w/w or m/m).

In SI units, w/w concentration (m/m concentration) would be given in kilograms of solute per kilograms of solution.
So, a 1 part per million (1 ppm) solution would be 1 kg of solute per 1 million kilograms of solution.
And these masses are just too large to be useful in Chemistry laboratory.
But we can divide the masses of solute and solution by 1 million to arrive at more useful units:

 1 ppm = 1 kg solute     1 000 000 kg solution = 1 kg solute/1 000 000     1 000 000 kg solution/1 000 000 = 10-6 kg solute     1 kg solution

Recall that there are 1 000 grams in a kilogram, so now we can write

 1 ppm = 10-6 kg solute × 1 000 g/kg 1 kg solution = 10-3 g solute 1 kg solution

Recall that 10-3 g = 1 mg (1 milligram) and now we can write

 1 ppm = 10-3 g solute 1 kg solution = 1 mg solute 1 kg solution

If we divide the masses of solute and solution by 1 000, we arrive at

 1 ppm = 1 mg solute/ 1000 1 kg solution/1000 = 10-3 mg solute 10-3 kg solution

Recall that 10-3 mg = 1 μg and 10-3 kg = 1 g so

 1 ppm = 10-3 mg solute 10-3 kg solution = 1 μg solute 1 g solution

This allows us to establish that parts per million concentration (ppm) is equivalent to the following common m/m (w/w) concentrations:

1 ppm = 1 mg solute/1 kg solution = 1 μg solute/1 g solution

In SI units, w/v concentration (m/v concentration) would be given in kilograms of solute per litres of solution.
So, a 1 part per million (1 ppm) solution would be 1 kg of solute per 1 million litres of solution.
And this mass and volume are just too large to be useful in Chemistry laboratory.
But we can divide the mass of solute and volume of solution by 1 million to arrive at more useful units:

 1 ppm = 1 kg solute     1 000 000 L solution = 1 kg solute/1 000 000     1 000 000 L solution/1 000 000 = 10-6 kg solute     1 L solution

Recall that there are 1 000 grams in a kilogram, so now we can write

 1 ppm = 10-6 kg solute × 1 000 g/kg 1 L solution = 10-3 g solute 1 L solution

Recall that 10-3 g = 1 mg (1 milligram) and now we can write

 1 ppm = 10-3 g solute 1 L solution = 1 mg solute 1 L solution

If we divide the mass of solute and volume of solution by 1 000, we arrive at

 1 ppm = 1 mg solute/ 1000 1 L solution/1000 = 10-3 mg solute 10-3 L solution

Recall that 10-3 mg = 1 μg and that 10-3 L = 1 mL then

 1 ppm = 10-3 mg solute 10-3 L solution = 1 μg solute 1 mL solution

This allows us to establish that parts per million concentration (ppm) is equivalent to the following common m/v (w/v) concentrations:

1 ppm = 1 mg solute/1 L solution = 1 μg solute/1 mL solution

To calculate the concentration of a solution in parts per million using the mass of solute and the volume or mass of solution :

⚛ weight/volume (w/v or m/v)

ppm = mass of solute (g) ÷ volume of solution (m3)

ppm = mass of solute (mg) ÷ volume of solution (L)

ppm = mass of solute (μg) ÷ volume of solution (mL)

⚛ weight/weight (w/w or m/m)

ppm = mass of solute (mg) ÷ mass of solution (kg)

ppm = mass of solute (μg) ÷ mass of solution (g)

You should practice rearranging the equations above in order to find mass of solute, volume of solution or mass of solution:

⚛ To calculate mass of solute:

mass of solute (mg) = ppm × volume of solution (L)

mass of solute (μg) = ppm × volume of solution (mL)

mass of solute (mg) = ppm × mass of solution (kg)

mass of solute (μg) = ppm × mass of solution (g)

⚛ To calculate volume of soution

volume (L) = mass (mg) of solute ÷ ppm

volume (mL) = mass (μg) of solute ÷ ppm

⚛ To calculate mass of soution

mass of solution (kg) = mass of solute (mg) ÷ ppm

mass of solution (g) = mass of solute (μg) ÷ ppm

## Converting Mass Concentrations (w/v or m/v) to ppm

Recall the definition of parts per million in mass of solute per volume of solution units derived above:

1 ppm = 1 g m-3 = 1 mg L-1 = 1 μg mL-1

Some sample questions with worked solutions of converting w/v (m/v) to ppm are given below.

Question 1. A solution has a concentration of 1.25 g L-1.

What is its concentration in ppm?

Solution:

Step 1: Extract the data from the question

concentration = w/v = m/v = 1.25 g L-1

mass of solute = 1.25 g

volume of solution = 1 L

Step 2: Write the definition of ppm to be used

1 ppm = 1 g m-3 = 1 mg L-1 = 1 μg mL-1

Step 3: Convert the mass of solute to required units

volume of solution is in litres (L) so mass of solute must be in milligrams (mg)

mass = 1.25 g = 1.25 g × 1000 mg/g = 1250 mg

Step 4: Calculate concentration: divide mass (mg) by volume (L)

concentration = mass (mg) ÷ volume (L)

concentration = 1250 mg ÷ 1 L = 1250 mg L-1

Step 5: Write the concentration in ppm

1 ppm = 1 mg L-1 therefore 1250 mg L-1 = 1250 ppm

1.25 g L-1 = 1250 ppm

Question 2. A solution has a concentration of 0.5 mg mL-1.

What is its concentration in ppm?

Solution:

Step 1: Extract the data from the question

concentration = w/v = m/v = 0.5 mg mL-1

mass of solute = 0.5 mg

volume of solution = 1 mL

Step 2: Write the definition of ppm to be used

1 ppm = 1 g m-3 = 1 mg L-1 = 1 μg mL-1

Step 3: Convert the volume of solution to required units

mass of solute is in milligrams (mg) so volume of solution must be in litres (L)

volume = 1 mL = 1 mL ÷ 1000 mL L-1 = 0.001 L

Step 4: Calculate concentration: divide mass (mg) by volume (L)

ppm = mass (mg) ÷ volume (L)

ppm = 0.5 mg ÷ 0.001 mL = 500 mg L-1

Step 5: Write the concentration in ppm

1 ppm = 1 mg L-1 therefore 500 mg L-1 = 500 ppm

0.5 mg mL-1 = 500 ppm

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

Recall the definition of parts per million in mass of solute per mass of solution units derived previously:

1 ppm = 1 mg kg-1 = 1 μg g-1

Some sample questions with worked solutions of converting w/w (m/m) to ppm are given below.

Question 1. A solution has a concentration of 0.033 g kg-1.

What is its concentration in ppm?

Solution:

Step 1: Extract the data from the question

concentration = w/w = 0.033 g kg-1

mass of solute = 0.033 g

mass of solution = 1 kg

Step 2: Write the definition of ppm to be used

1 ppm = 1 mg kg-1 = 1 μg g-1

Step 3: Convert the mass of solute to required units

mass of solution is in kilograms (kg) so mass of solute must be in milligrams (mg)

mass = 0.033 g = 0.033 g × 1000 mg/g = 33 mg

Step 4: Calculate concentration: divide mass of solute (mg) by mass of solution (kg)

concentration = mass of solute (mg) ÷ mass of solution (kg)

concentration = 33 mg ÷ 1 kg = 33 mg kg-1

Step 5: Write the concentration in ppm

1 ppm = 1 mg kg-1 therefore 33 mg kg-1 = 33 ppm

0.033 g kg-1 = 33 ppm

Question 2. A solution has a concentration of 2250 μg kg-1.

What is its concentration in ppm?

Solution:

Step 1: Extract the data from the question

concentration = w/w = 2250 μg kg-1

mass of solute = 2250 μg

mass of solution = 1 kg

Step 2: Write the definition of ppm to be used

1 ppm = 1 mg kg-1 = 1 μg g-1

Step 3: Convert the mass of solute to required units

mass of solution is in kilograms (kg) so mass of solute must be in milligrams (mg)

mass = 2250 μg = 2250 μg ÷ 1000 μg mg-1 = 2.25 mg

Step 4: Calculate concentration: divide mass of solute (mg) by mass of solution (kg)

concentration = mass of solute (mg) ÷ mass of solution (kg)

concentration = 2.25 mg ÷ 1 kg = 2.25 mg kg-1

Step 5: Write the concentration in ppm

1 ppm = 1 mg kg-1 therefore 2.25 mg kg-1 = 2.25 ppm

2250 μg kg-1 = 2.25 ppm

## Problem Solving: Parts Per Million (ppm) Concentration

We will use the following steps to solve parts per million concentration (ppm) problems:

1. Step 1: Extract the data from the question
2. Step 2: Write the definition of ppm to be used and rearrange if necessary
3. Step 3: Convert the mass of solute and/or mass or volume of solution to required units
4. Step 4: Substitute values into the ppm equation and solve
5. Step 5: Write the answer
Question 1. 150 mL of an aqueous sodium chloride solution contains 0.0045 g NaCl.

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

Solution:

Step 1: Extract the data from the question

mass of solute = 0.0045 g

volume of solution = 150 mL

concentration of solution = ? ppm

Step 2: Write the definition of ppm to be used

concentration is given as weight/volume (w/v or m/v)

1 ppm = 1 g m-3 = 1 mg L-1 = 1 μg mL-1

Step 3: Convert the mass of solute to required units

volume of solution is in milliltres (mL) so mass of solute must be in micrograms (μg)

mass = 0.0045 g = 0.0045 g × 106 μg/g = 4500 μg

Step 4: Calculate concentration: divide mass of solute (μg) by volume of solution (mL)

concentration = mass of solute (μg) ÷ volume of solution (mL)

concentration = 4500 μg ÷ 150 mL = 30 μg mL-1

Step 5: Write the concentration in ppm

1 ppm = 1 μg mL-1 therefore 30 μg mL-1 = 30 ppm

concentration = 30 ppm

Question 2. What mass in milligrams of potassium nitrate is present in 0.250 kg of a 500 ppm aqueous solution of potassium nitrate, KNO3(aq)?

Solution:

Step 1: Extract the data from the question

mass of solute = ? mg

mass of solution = 0.250 kg

concentration = 500 ppm

Step 2: Write the definition of ppm to be used

concentration is given as weight/weight (w/w or m/m)

1 ppm = 1 mg kg-1 = 1 μg g-1

rearrange this to find mass of solute (mg) :

mass solute (mg) = concentration (ppm) × mass of solution (kg)

Step 3: Convert mass and or volume units

Since mass of solution is given in kg, mass of solute will be calculated in mg and no unit conversions are necessary.

Step 4: Substitute in the values and solve for mass of solute

mass solute (mg) = concentration (ppm) × mass of solution (kg)

mass solute (mg) = 500 ppm × 0.250 kg = 125 mg

mass(KNO3) = 125 mg

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

What volume of this solution in millilitres contains 0.150 g of sucrose?

Solution:

Step 1: Extract the data from the question

volume of solution required = ? mL

mass of solute = 0.150 g

concentration = 600 ppm

Step 2: Write the definition of ppm to be used

concentration is given as weight/volume (w/v or m/v)

1 ppm = 1 g m-3 = 1 mg L-1 = 1 μg mL-1

rearrange this to find volume of solution (mL) :

volume of solution (mL) = mass of solute (μg) ÷ concentration (ppm)

Step 3: Convert mass in grams to micrograms

Since we need to find a volume in mL, we need to convert mass in g to μg

mass of solute = 0.150 g × 106 μg/g = 150 000 μg

Step 4: Substitute in the values and solve for volume of solution

volume of solution (mL) = mass of solute (μg) ÷ concentration (ppm)

volume of solution (mL) = 150 000 μg ÷ 600 ppm = 250 mL

volume of solution (mL) = 250 mL