Concentration of Solution is a measure of the amount of solute that has been dissolved in the given amount of solvent. In simple words, it means determining how much of one substance is mixed with another substance. As Concentration is a frequently used term in chemistry and other relevant fields, although it is most commonly used in the context of solutions, where it refers to the quantity of solute dissolved in a solvent. Concentration can be expressed in both qualitative or quantitative (numerically) terms.
Concentration of a Solution Definition
Concentration of a solution is defined as the amount of solute dissolved in the solution. It is given by the ratio of the amount of solute to the amount of solution or solvent sometimes. However, we can express it in percentages, Parts per Million, and several other ways. The concentration of a solution can be expressed both qualitatively and quantitatively which we will see in the below topics. Before learning more about concentration let’s understand some of the general types of solution
Solution of Solid and Liquid
Solutions of solids and liquids involve the dissolution of a solid solute in a liquid solvent or a liquid solute in a liquid solvent. Examples include:
a. Solid in Liquid: Dissolving table salt (NaCl) in water.
b. Liquid in Liquid: Mixing ethanol and water to form a homogeneous solution.
Solution of Gas
Solutions of gases involve the dissolution of a gas in a liquid solvent or another gas. Examples include:
a. Gas in Liquid: Dissolving carbon dioxide (CO_{2}) in water to form carbonated water.
b. Gas in Gas: Mixing different gases, such as oxygen and nitrogen, in the atmosphere to form a homogeneous mixture.
Qualitative Expressions of Concentration
To qualitatively express concentration, a solution can be classified as a dilute solution or a concentrated solution, which are explained as follows:
Dilute Solution
Dilute Solution contains a smaller proportion of solute than the proportion of solvent. For example, if 2 grams of salicylic acid is dissolved in 100 ml of water and in another container, 8 grams of salicylic acid is dissolved in the same amount of water then a 2-gram solution of salicylic acid is a dilute solution compared to 8 grams solution of salicylic acid.
Concentrated Solution
Concentrated Solution contains a much greater proportion of solute than the proportion of solvent. For example, if 2 grams of salicylic acid is dissolved in 100 ml of water and in another container, 8 grams of salicylic acid is dissolved in the same amount of water then 8 grams solution of salicylic acid is a concentrated solution compared to 2 grams solution of salicylic acid.
Semi-Qualitative Expressions of Concentration
To semi-qualitatively express concentration, a solution can be classified as a saturated solution or an unsaturated solution, which are explained as follows:
Saturated Solution
A saturated solution is one in which the greatest quantity of solute is dissolved in a solvent at a given temperature. When a solution reaches saturation, it can no longer dissolve any more solute at that temperature. Undissolved chemicals settle to the bottom. The saturation point is determined as the point at which no more solute can be dissolved in the solvent.
Unsaturated Solution
An unsaturated solution is one that contains less solute than the maximum possible solute it can dissolve before the solution reaches the saturation level. When more solute is dissolved in this solution, there are no residual substances at the bottom, indicating that all of the solutes have been dissolved in the solvent. An unsaturated solution is a chemical solution in which the solute concentration is less than the corresponding equilibrium solubility.
Solubility
Solubility is defined as the greatest amount of solute that may dissolve in a certain quantity of solvent at a given temperature.
A solution is a liquid that is a homogeneous combination of one or more solutes and a solvent. A typical example of a solution is, sugar cubes added to a cup of tea or coffee. Here, solubility is the characteristic that allows sugar molecules to dissolve.
As a result, the term solubility may be defined as a substance’s (solute’s) ability to dissolve in a particular solvent.
Quantitative Expressions of Concentration
Qualitative expressions of concentration are relative terms, which do not provide the exact concentration of the solution. To characterize the concentrations of various solutions around us in an accurate and precise manner, we require quantitative expressions of concentration.
Generally, concentration is represented in both ways:
Concentration = Quantity of Solute / Quantity of Solution
or
Concentration = Quantity of Solute / Quantity of Solvent
To quantitatively express concentration, we use the following terms:
- Mass Percentage
- Volume Percentage
- Mass by Volume Percentage
- Parts per Million and Parts per Billion
- Molarity
- Molality
- Mole Fraction
Mass Percentage (w/w%)
Mass percentage which is also called weight by weight concentration of solute and is defined as the amount of solute (in grams) present in 100 gm of the solution.
Mass Percentage = (Mass of Solute / Mass of Solution) × 100
Mass percentage has no unit as it is the ratio of the mass of solute and solution.
Volume Percentage (v/v%)
Volume Percentage which is also called volume by volume concentration of solute and is defined as the amount of solute (in ml) present in 100 ml of the solution.
Volume Percentage = (Volume of Solute / Volume of Solution) × 100
Volume percentage has no unit as it is the ratio of the volume of solute and solution.
Mass by Volume Percentage(w/v %)
It is defined as the amount of solute (in grams) present in the 100ml of the solution.
Mass by Volume Percentage = (Mass of Solute(in gm) / Volume of Solution(in ml) × 100
Unit of mass by volume percentage is gram per milliliter as it is the ratio of the mass of the solute and volume of the solution.
Parts per Million (PPM)
Parts Per Million or PPM is used to measure the very small amount of solute dissolved in the Solvent. Drinking water, air, soils, etc. are the solvents that have very fewer amounts of solutes in them, which can’t be measured in percentage as a percentage only calculates the concentration out of 100. If we represent concentrations of these solvents in percentage it looks like 0.00002 %, which is not an effective way. That’s why parts per million were introduced to make a representation of these concentrations.
PPM of solute = Mass of solute (in milligrams)/Mass of solution(In Kg)
Parts per Billion
Like, Parts per million, Parts Per Billion are also used to represent solute available in trace quantities. Parts Per Billion represents the amount of solute in 1 billion parts of the solution.
PPB of solute = Mass of solute (in micrograms)/Mass of solution(In Kg)
Molarity
Molarity of a given solution is defined as the number of moles present in the 1 liter of solution. For example, if 2 moles of NaCl are dissolved in 1 liter of water, the molarity of the resulting solution would be 2M, and the Formula for Molarity is given as follows:
Molarity (M) = Moles of solute /Volume of solution(in Liter)
Molality
Molality of a given solution is defined as the number of moles present in 1 kg of solution. For example, if 3 moles of KOH are dissolved in 3 Liters of water (density of water 1 kg/L), the molality of the resulting solution would be 1 m, as there is 1 mole of KOH present in each Kg of water. The formula for molality is given as follows:
Molality (m) = Moles of solute / Mass of solvent(in Kg)
Mole Fraction
Mole fraction i.e., X is defined as the ratio of the number of moles of one component to the total number of moles present in the solution. It is a dimensionless quantity. The mole fraction of solute A in a solution containing n components such as A, B, C, . . ., N can be calculated using the following formula:
Mole fraction of A (X_{A}) = Moles of A / (Moles of A + Moles of B + . . . + Moles of N)
The mole fraction of other solvents (B, C, D, . . .N) in a solution can be calculated using a similar formula.
Normality
Normality is a measure of concentration equivalent to the number of equivalents per liter of solution. It is often used for reactions that involve acid-base neutralization, precipitation reactions, or redox reactions, and it takes into account the stoichiometry of the reaction.
Normality (N) = Equivalents of solute / Volume of solution in liters
For example, for an acid-base reaction, normality can be calculated using:
Normality = Molarity × Basicity or Acidity of the compound
Where basicity or acidity is the number of hydrogen ions (H⁺) or hydroxide ions (OH⁻) that can be released per molecule of the compound.
Formality
Formality is similar to molarity in that it measures the number of moles of solute per liter of solution. However, formality is used when the solute undergoes a reaction or dissociation in solution. Formality measures the concentration based on the initial composition of the solution, not the final dissolved state.
Formality (F) = Moles of solute / Volume of solution in liters
Temperature Dependence of Quantitative Expressions of Concentration
The following table shows the temperature dependence of the Quantitative Expressions of Concentration.
Expression of Concentration |
Required Parameters |
Dependence on Temperature |
---|---|---|
Mass by Mass percentage (w/w%) |
Mass of solute and mass of solution |
No (mass is not affected by temperature) |
Mass by Volume percentage (w/v%) |
Mass of solute and volume of solution |
Yes (volume is affected by temperature) |
Parts per Million/Parts per Billion |
Mass of solute and Mass of Solution |
No (mass is not affected by temperature) |
Mole Fraction |
Moles of Solute and Moles of Solvent |
No (mass and moles are not affected by temperature) |
Molarity |
Moles of Solute and Volume of Solvent |
Yes (volume is affected by temperature) |
Molality |
Moles of Solute and Mass of Solvent |
No (mass and moles are not affected by temperature) |
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Sample Problems on Concentration of Solution
Problem 1: 15 g of common salt is dissolved in 400 g of water. Calculate the concentration of the solution by expressing it in Mass by Mass percentage (w/w%).
Solution:
Given that,
Mass of solute (common salt) = 15 g …(1)
Mass of Solvent (water) = 400 g …(2)
It is known that,
Mass of Solution = Mass of Solute + Mass of Solvent …(3)
So,
Substituting (1) and (2) in (3), we obtain the following,
Mass of Solution = 15 g + 400 g = 415 g …(4)
From Figure 4, we know
Mass by Mass Percentage = ( Mass of Solute / Mass of Solution ) × 100 …(5)
Substituting (1) and (4) in (5), we obtain the following,
Mass by Mass Percentage = ( 15 g / 415 g ) × 100 = ( 0.0361 ) × 100 = 3.61
Answer is:
( w / w % ) = 3.61
Problem 2: 15 g of common salt is dissolved in a solution of 300 mL, calculate the Mass by Volume percentage (w/v%).
Solution:
Given that,
Mass of solute (common salt) = 15 g . . . (1)
Mass of Solution (salt solution) = 300 mL . . . (2)
From Figure 5, we know
Mass by Volume Percentage = ( Mass of Solute / Volume of Solution ) × 100 . . . (3)
Substituting (1) and (2) in (3), we obtain the following,
Mass by Volume Percentage = ( 15 g / 300 mL ) × 100 = ( 0.05 ) × 100 = 5 g/mL
Answer is:
( w / v % ) = 5 g/mL
Problem 3: Richard dissolved 70 g of sugar in 750 mL of sugar solution. Calculate the Mass by Volume percentage (w/v%).
Solution:
Given that,
Mass of solute (common salt) = 70 g . . . (1)
Mass of Solution (salt solution) = 750 mL . . . (2)
From Figure 5, we know
Mass by Volume Percentage = ( Mass of Solute / Volume of Solution ) × 100 . . . (3)
Substituting (1) and (2) in (3), we obtain the following,
Mass by Volume Percentage = ( 70 g / 750 mL ) * 100 = ( 0.933 ) × 100 = 93.3 g/mL
Answer is:
( w / v % ) = 93.3 g/mL
Problem 4: What is the molarity of a solution containing 0.5 moles of NaCl dissolved in 500 mL of water?
Solution:
Given, Moles of NaCl = 0.5, Volume of Solution = 500 mL = 0.5 Liter
As, Molarity (M) = moles of solute / liters of solution
⇒ M = 0.5 moles / 0.5 liters = 1 M
So the molarity of the solution is 1 M.
Problem 5: What is the molality of a solution containing 20 g of glucose dissolved in 500 g of water?
Solution:
Given: Mass of Glucose = 20 g, Mass of water = 500 g = 0.5 kg,
Molar mass of glucose (C_{6}H_{12}O_{6}) = 180 g/mol
Number of Moles = Mass/Molar Mass
⇒ Moles of Glucose = 20 / 180 = 1/9 ≈ 0.111 moles of glucose
As, Molality (m) = moles of solute / kilograms of solvent
⇒ m = 0.111 / 0.5 = 0.222 mol/kg
So the molality of the solution is 0.222 mol/kg.
Problem 6:How many moles of HCl are present in 250 mL of a 0.2 M HCl solution?
Solution:
Given: Molarity of solution = 0.2 M, Volume of solution = 250 mL = 0.25 liters
Molarity (M) = moles of solute / liters of solution
⇒ Moles of solute = Molarity x liters of solution
⇒ Moles of HCl = 0.2 M x 0.25 L = 0.05 moles
So there are 0.05 moles of HCl present in 250 mL of the solution.
Problem 7:What is the ppm of lead in a sample that contains 20 mg of lead in 10 L of water?
Solution:
Given : mass of solute(in mg) = 20 mg and Volution of solvent = 10 L
Mass of solution = Mass of water = 10 L x 1 Kg/L = 10 Kg (density of water is 1Kg/L or 1g/mL)
ppm (parts per million) = Mass of solute(in mg)/Mass of solution (in Kg)
⇒ ppm = 20 / 10 = 2
So the ppm of lead in the sample is 2ppm.
Problem 8: What is the ppb of mercury in a sample that contains 0.01 g of mercury in 1000 L of air?
Solution:
Given : mass of solute(in mg) = 0.01 g = 10,000 μg and Volution of solvent = 1000 L
Mass of solution = Mass of water = 1000 L x 1 Kg/L = 1000 Kg (density of water is 1Kg/L or 1g/mL)
ppb (parts per million) = Mass of solute(in μg)/Mass of solution (in Kg)
⇒ ppm = 10000 / 1000 = 10
So the ppm of lead in the sample is 10 ppb.
FAQs on Concentration of Solution
What is Solubility?
Solubility is defined as the greatest amount of solute that may dissolve in a certain quantity of solvent at a given temperature.
What is a Dilute Solution?
A dilute solution is solution which contains a smaller proportion of solute as compared to the proportion of solvent.
What is the difference between PPM and PPB?
PPM and PPB are both represents the concentration of very small scale and only difference between them is that PPM is 1000 times greater scale then PPB or PPB is 1000 times smaller scale then PPM i.e., 1 PPM = 1000 PPB
What is the difference between Molarity and Molality?
Molarity is the number of moles of solute per liter of solution, whereas molality is the number of moles of solute per kilogram of solvent.