Concentration of Solutions

Concentrations of Solutions

There are a number of ways to express the relative amounts of solute and solvent in a solution. This page describes calculations for four different units used to express concentration:

• Percent Composition (by mass)
• Molarity
• Molality
• Mole Fraction
• Parts per Million
• Mass Per Unit Volume
• Percent by Volume

Percent Composition (by mass)

We can consider percent by mass (or weight percent, as it is sometimes called) in two ways:

• The parts of solute per 100 parts of solution.
• The fraction of a solute in a solution multiplied by 100.

We need two pieces of information to calculate the percent by mass of a solute in a solution:

• The mass of the solute in the solution.
• The mass of the solution.

Use the following equation to calculate percent by mass:

Molarity

Molarity tells us the number of moles of solute in exactly one liter of a solution. (Note that molarity is spelled with an "r" and is represented by a capital M.)

We need two pieces of information to calculate the molarity of a solute in a solution:

• The moles of solute present in the solution.
• The volume of solution (in liters) containing the solute.

To calculate molarity we use the equation:

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Molality

Molality, m, tells us the number of moles of solute dissolved in exactly one kilogram of solvent. (Note that molality is spelled with two "l"'s and represented by a lower case m.)

We need two pieces of information to calculate the molality of a solute in a solution:

• The moles of solute present in the solution.
• The mass of solvent (in kilograms) in the solution.

To calculate molality we use the equation:

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Mole Fraction

The mole fraction, X, of a component in a solution is the ratio of the number of moles of that component to the total number of moles of all components in the solution.

To calculate mole fraction, we need to know:

• The number of moles of each component present in the solution.

The mole fraction of A, X_A, in a solution consisting of A, B, C, ... is calculated using the equation:

To calculate the mole fraction of B, X_B, use:

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Parts per Million

Parts per million - ppm -  is commonly used as a measure of small levels of pollutants in air, water, body fluids, etc. Parts per million is the mass ratio between the pollutant component and the solution and ppm is defined as

ppm = 1,000,000 m_c / m_s         (1)

where

m_c = mass of component (kg, lb_m)

m_s = mass of solution (kg, lb_m)

In the metric system ppm can be expressed in terms of milligram versus kg where

·         1 mg/kg = 1 part per million

Alternatively mass related units to measure very small concentration levels used are

·         ppb - parts per billion (1 / 1,000,000,000)

·         ppt - parts per trillion (1 / 1,000,000,000,000)

An alternatively mass related unit to measure larger concentration levels are weight percent which can be expressed like

weight percent = 100 m_c / m_s         (1)

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Volume related Concentration Units

Mass per Unit Volume

The concentration of a component can be measured as mass per unit volume as mg/liter, mg/cm³, etc.

Weight of substance added to one unit volume of water to give one part per million (ppm)

1 ppm

    = 2.72 pounds per acre-foot

    = 1,233 grams per acre-foot

    = 1.233 kilograms per acre-foot

    = 0.0283 grams per cubic foot

    = 0.0000624 pounds per cubic foot

    = 0.0038 grams per US gallon

    = 0.058419 grains per US gallon

    = 0.07016 grains per Imperial gallon

    = 1 milligram per liter

    = 1 microlitre ( μL ) per liter

    = 0.001 gram per litre

    = 8.345 pounds per million gallons of water

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Percent by Volume

Volume percent can be expressed as volume per unit volume as

percent by volume = 100 v_c /(v_c + v_s)         (3)

where

v_c = volume component

v_s = volume solvent

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