Mass Concentration

Mass concentration—like molar concentration, molality, mass fraction —is a quantity to measure the concentration of a solute in the solution. It is the ratio of the mass of a solute present in the solution to the volume of the solution. It tells us how much a solute is present in a given volume of the solution. Let try to understand it will an example of coffee.

A simple instant coffee is prepared by mixing the coffee and sugar in hot water. For a typical cup (250 mL) of coffee, we need 10 g of the coffee and 5 g of sugar. The amount could vary based on personal choice. For preparing two cups (500 mL), we will need twice the mass of the ingredients—20 g of coffee and 10 g of sugar. Similarly, we will need 100 g of the coffee and 50 g of sugar for ten cups.

Ingredients in coffee

Cup of coffee	Mass of the coffee	Mass of sugar	Mass of the coffee per cup	Mass of sugar per cup
1 (250 mL)	10 g	5 g	10 g	5 g
2 (500 mL)	20 g	10 g	10 g	5 g
3 (750 mL)	30 g	15 g	10 g	5 g
10 (2500 mL)	100 g	50 g	10 g	5 g

From the above table, we can see the mass of each ingredient per cup (250 mL) remains constant. In chemistry, we call it mass concentration, the mass of an ingredient per unit volume.

Definition

The mass concentration of a solute is defined as the mass of the solute per unit volume of the solution.

Formula

The formula of mass concentration is as follows.

Here, ρ_i is the mass concentration of the i-th solute, m_i is the mass of the i-th solute, and V is the volume of the solution.

Units

The SI unit of mass concentration is kg m⁻³. The equivalent units of kg m⁻³ are g L⁻¹, g dm⁻³, and mg mL⁻¹

Other common units are µg mL⁻¹, µg L⁻¹, and µg m⁻³.

Explanation

As per the above definition, the ratio of the mass of a solute to the volume of the solution is mass concentration.

In chemical laboratories, chemicals are usually measured in grams and the volume of solution in mL or L. Thus, we can redefine the definition as grams of a solute per mL (or L) of the solution. It is a more practical definition.

0.90 g L⁻¹ of NaCl solution contains 0.90 g of NaCl in 1 L of the solution. In 20 g L⁻¹ solution, there will be 20 g of NaCl in 1 L. Thus, as the concentration of a solute increases its mass per litre also increases.

Medical science

Mass concentration is very useful in medicine. The composition of liquids drugs is usually mentioned in mass to volume (m/v) percentage i.e. the mass of drug present in a given volume of solution. These drugs are mainly stored in IV bags (see the image below).

Some examples of such solutions are as follows:

1. Isotonic saline: It is 0.9 % NaCl. It contains 0.9 g of the salt in 100 mL of solution.
2. 5 % Dextrose: It has glucose as the solute. It consists of 5 g of glucose in 100 mL of solution.
3. Dextrose saline: It has glucose as well as salts.

Properties of mass concentration

1. It is a property of a solution.
2. It is an intensive property since the ratio of two extensive properties always gives an intensive property. As a result, it will not vary from sample to sample.
3. It is a concentration based on volume. Hence, it depends on the volume of solution.
4. Since the volume is affected by pressure and temperature, mass concentration is dependent on pressure and temperature.

Relation with other quantities

Temperature

As temperature increases, the volume of a solution also increases. This dependence is connected by the thermal expansion coefficient of the solution.

Here, V is the volume at T, V₀ is the volume at T₀, and α is the thermal expansion coefficient of the solution.

Let ρ_{(i, T)} and ρ_{(i, T0)} be the concentration at temperature T and T₀. The relation is as follows:

Density

Let ρ_i be the density of a solution. The density of a solution is the sum of the mass of each solute divided by the volume of the solution.

Therefore, the sum of the concentration of each solute is the density of the solution.

Mass fraction

Mass fraction is the ratio of the mass of a solute to the total mass and denote by w_i. The relation between both is as follows:

Mole fraction

Mole fraction is the ratio of the mole of a solute to the total moles. The symbol x_i is used to represent it. It is related to mass concentration by the following equation.

Here, M_i is the molar mass of the solute.

Molarity

Molarity, aka molar concentration, is similar to mass concentration. It is the ratio of moles of solute, instead of the mass of a solute, to the volume of the solution. c_i is molarity of the solute i.

Molality

Molality (b_i) is moles of a solute per kg of the solvent. For n-solute solution, the molality of i-th solute is given by the equation below.

Here, M₀ is the molar mass of the solvent.

Equivalent ratios

Let i and j be any two components in a solution. The relationship between each of the above quantities is as follows:

Solved problems

Problem 1: Earth's atmosphere

Statement: Earth's atmosphere is a mixture of various gases. It extends up to an altitude of 90 km. Oxygen and nitrogen are dominant gases in the atmosphere. The mole percentage of oxygen and nitrogen is 21 % and 79 %. Find the mass concentration of each gas if the molar mass of oxygen and nitrogen is 32 g mol⁻¹ and 28 g mol⁻¹?

Solution: In 100 mol of air, the amount of oxygen and nitrogen is 21 mol and 79 mol respectively.

Calculating the mass of oxygen and nitrogen in 100 mol of air,

According to the ideal gas law, 1 mol of air occupies 22.4 dm⁻³ at STP (P = 101.325 kPa and T = 273.15 K). For 100 mol of air, the volume will be 2240 dm⁻³. Thus, V = 2240 dm⁻³ = 2240 L.

The mass concentration of oxygen and nitrogen are calculated as follows:

Problem 2: Glucose

Statement: Glucose (C₆H₁₂O₆) is a monosaccharide sugar. It is an primary energy source not only for humans but also for most organisms. Glucose is produced by plants through photosynthesis. It the most abundant monosaccharide and found in our blood too.

The solubility of glucose at 25 °C is 900 g L⁻¹. Find molecules of sugar present in 100 mL of saturated glucose solution?

Solution: The concentration of glucose is 900 g L⁻¹.

Calculating the mass of glucose in 100 mL (= 0.100 L) of the solution,

The molar mass of glucose is 180 g mol⁻¹. Moles of glucose in 90.0 g is as follows:

One mole of glucose has molecules equal to Avogadro's number N_A. Molecules in 0.500 mol of glucose is 0.500 × N_A.

Problem 3: Lithium chloride

Statement: Lithium chloride (LiCl) is a white ionic compound with high solubility in polar solvents like water. It is primarily used for production of lithium, which is a key component in electronic batteries.

Find the concentration of Li⁺ ions and Cl⁻ ions when 50 g of LiCl is dissolved in 100 mL of water?

Solution: The molar mass of LiCl is 42.4 g mol⁻¹. Let the number moles of LiCl in 42.4 g mol⁻¹ be n_LiCl.

One mole of LiCl contains one mole of Li⁺ and one mole of Cl⁻. Accordingly, 1.18 mol of LiCl will have 1.18 mol of Li⁺ and 1.18 mol of Cl⁻.

Calculating the mass of Li⁺ and Cl⁻,

The volume of the solution is approximately equal to the volume of water, which is 100 mL. V = 100 mL.

Calculating the concentration of Li⁺ and Cl⁻,

Practice problems

Problem 1: Find the concentration of NaOH in a solution if 10 moles of NaOH is dissolved in the 1.00 L of water? The molar mass of sodium hydroxide is 40 g mol⁻¹

Problem 2: The molar concentration of sulphuric acid is 4.00 mol L⁻¹. Find the mass concentration of H₂SO₄ and SO⁻
₄? The molar mass of H₂SO₄ and SO⁻
₄ is 98.1 g mol⁻¹ and 96.1 g mol⁻¹.

Problem 3: Aluminium hydroxide (Al(OH)₃) is used as an antacid—a chemical used to treat acidity. A patient takes two teaspoons (5 mL each) of syrup. The concentration of aluminium hydroxide in the syrup is 50 mg mL⁻¹. Find the intake of aluminium hydroxide?

Answers

Associated articles

• Mole fraction
• Mass fraction
• Molarity
• Molality