Parts per Million (ppm): Videos & Practice Problems

When measuring extremely dilute solution concentrations, the terms parts per million (ppm) and parts per billion (ppb) are used. These units can represent mass or volume. Ppm indicates the number of parts, in grams or milliliters, per one million parts, with one ppm being equivalent to one milligram per liter. The formula for ppm in terms of mass is:

grams of solutegrams of solution×10⁶ For volume, it's milliliters of solute per milliliters of solution multiplied by 10⁶. Similarly, ppb denotes the number of parts per one billion, with one ppb equal to one microgram per liter. The calculation for ppb in mass is:

grams of solutegrams of solution×10⁹ and for volume, it's milliliters of solute per milliliters of solution times 10⁹. These measurements are crucial for expressing concentrations in aqueous solutions when dealing with very low solute quantities.

Parts per Million (ppm)

In the context of extremely dilute solutions, concentrations are often expressed in parts per million (PPM) or parts per billion (PPB). These units can represent either mass or volume. Specifically, parts per million indicates the number of parts of a substance in relation to 1,000,000 parts of the solution, which can be mathematically represented as \(10^6\).

For aqueous solutions, a useful equivalence to remember is that 1 PPM is equivalent to 1 milligram of solute per 1 liter of solution. When calculating PPM in terms of mass, the formula is:

\[ \text{PPM} = \frac{\text{grams of solute}}{\text{grams of solution}} \times 10^6 \]

Conversely, when considering volume, the formula adjusts to:

\[ \text{PPM} = \frac{\text{milliliters of solute}}{\text{milliliters of solution}} \times 10^6 \]

This approach is similar to calculating mass percent, where the formula involves grams over grams multiplied by 100%. However, in the case of PPM, the multiplication factor is \(10^6\) to account for the 1,000,000 parts in the solution. Understanding these concepts is crucial when discussing very dilute concentrations in various scientific contexts.

PPM Calculation Example

To determine the concentration of DDT (dichlorodiphenyltrichloroethane) in parts per million (PPM), we can use the formula:

PPM = \(\frac{\text{grams of solute}}{\text{grams of solution}} \times 10^6\)

In this case, we have 2 milligrams of DDT in 1 kilogram of needle fish tissue. First, we need to convert these measurements to grams:

• 2 milligrams = \(2.0 \times 10^{-3}\) grams (since 1 milligram = \(10^{-3}\) grams)
• 1 kilogram = 1000 grams (since 1 kilogram = 1000 grams)

Now, substituting these values into the PPM formula:

PPM = \(\frac{2.0 \times 10^{-3} \text{ grams}}{1000 \text{ grams}} \times 10^6\)

Calculating this gives:

PPM = \(\frac{2.0 \times 10^{-3}}{1000} \times 10^6 = 2.0\)

Thus, the concentration of DDT in the needle fish tissue is 2.0 PPM.

Parts per Billion (ppb)

Parts per billion (PPB) is a unit of measurement that indicates the concentration of a substance in a solution, representing the number of parts per billion parts, either in grams or milliliters. Specifically, 1 PPB corresponds to 1 microgram of solute per liter of solution, establishing a direct relationship in aqueous solutions.

When calculating PPB in terms of mass, the formula is expressed as:

\[ \text{PPB} = \left( \frac{\text{grams of solute}}{\text{grams of solution}} \right) \times 10^9 \]

In contrast, when considering volume, the formula changes to:

\[ \text{PPB} = \left( \frac{\text{milliliters of solute}}{\text{milliliters of solution}} \right) \times 10^9 \]

It is crucial to differentiate between the two contexts—mass and volume—when working with parts per billion, as the calculations and implications can vary significantly. Understanding these distinctions is essential for accurate measurements and applications in various scientific fields.

Parts per Billion Example

To determine the concentration of ammonia in an aqueous solution expressed as parts per billion (ppb), we start with the formula for calculating ppb in terms of volume:

ppb = (Volume of solute in mL) / (Volume of solution in mL) × 10⁹

In this case, we have a 2.4 liter sample of solution containing 0.012 milliliters of ammonia. First, we need to convert the volume of the solution from liters to milliliters:

Since 1 liter equals 1,000 milliliters, we can convert:

2.4 liters = 2.4 × 1,000 mL = 2,400 mL

Now, we can substitute the values into the ppb formula:

ppb = (0.012 mL) / (2,400 mL) × 10⁹

Calculating this gives:

ppb = (0.012 / 2,400) × 10⁹ = 5,000 ppb

Thus, the concentration of ammonia in the solution is 5,000 parts per billion (ppb).

A 5.12 L sample of solution contains 0.230 g of potassium sulfate, K₂SO₄. Determine the concentration of K₂SO₄ in ppm if the density of the solution is 1.30 g/mL.

• A. 34.6 ppm
• B. 28.9 ppm
• C. 22.3 ppm
• D. 43.6 ppm

Answer: (A)

Calculate the concentration in parts per billion of the following aqueous solution:0.91 mg of caffeine in a total volume of 131 mL.

• A. 0.14 ppb
• B. 0.0069 ppb
• C. 140 ppb
• D. 6900 ppb

Answer: (D)

Glucose makes up about 0.102% by mass of human blood. Calculate this concentration in ppm.

• A. 102 ppm
• B. 0.102 ppm
• C. 0.00102 ppm
• D. 1020 ppm

Answer: (D)

The average human body contains about 5,000 grams of blood. What mass of arsenic is present in the body if the amount in blood is 0.86 ppb?

• A. 5.8 × 10¹² g
• B. 4.3 × 10¹² g
• C. 4.3 × 10^–6 g
• D. 5.8 × 10^–6 g

Answer: (C)

A water sample contains the pollutant chlorobenzene with a concentration of 16 ppm (by volume). What volume of this water contains 5.01×10² mL of chlorobenzene?

• A. 3.1 × 10⁷ mL
• B. 3.2 × 10⁴ mL
• C. 1.6 × 10⁶ mL
• D. 8.0 × 10¹⁰ mL

Answer: (A)

Here’s what students ask on this topic:

What is parts per million?

Parts per million, often abbreviated as ppm, is a unit of measurement used to express very dilute concentrations of substances. It is equivalent to 1 milligram of a substance in 1 liter of water (mg/L) or 1 milligram of a substance in 1 kilogram of a solid material. Essentially, if you imagine dividing a substance into one million equal parts, one part per million would be one of those parts. It's a way to quantify small concentrations in scientific and technical fields, such as chemistry, physics, and environmental science. For example, when measuring the amount of a pollutant in water or the concentration of a mineral in soil, ppm is a convenient and precise unit to use. It allows for easy comparison and understanding of how much of a substance is present in a larger mixture or solution.

How do you calculate parts per million?

To calculate parts per million (ppm), you're essentially determining how many parts of a specific substance are in a million parts of the total mixture or solution. Here's a simple way to do it:

1. Take the mass of the substance you're interested in (the solute) and divide it by the total mass of the solution or mixture.
2. Multiply the result by 1,000,000.

The formula looks like this:

PPM = (^{mass of solute}/_{total mass of solution}) x 1,000,000

For example, if you have 1 gram of salt dissolved in 1000 grams of water, the calculation would be:

PPM = (¹/₁₀₀₀) x 1,000,000 = 1000 ppm

Remember, this calculation assumes that the mass of the solution is the sum of the mass of the solute and the mass of the solvent. This is a common approximation for dilute solutions where the solute's mass doesn't significantly change the total mass.