Molarity And Mole Fraction: Definition, Formula, Questions

Molarity And Mole Fraction: Definition, Formula, Questions

Edited By Shivani Poonia | Updated on Jul 02, 2025 07:40 PM IST

In chemistry, a homogenous mixture of two or more substances in relative amounts can be varied continuously up to what is called the limit of solubility. The term solution is commonly applied to the liquid state of matter, but solutions of gases and solids are possible. Many reactions take place in solutions. In solution generally, one component is present in lesser amounts and is called solute while the other present in access is called solvent.

This Story also Contains
  1. Solution:
  2. Concentration:
  3. Types of concentration terms:
  4. Some Solved Examples
  5. Conclusion
Molarity And Mole Fraction: Definition, Formula, Questions
Molarity And Mole Fraction: Definition, Formula, Questions

The concentration of the solution is usually expressed in the following ways: mass percentage or volume percentage, molarity, molality, mole fraction, and normality. In this article, we will cover the concept of reactions in solutions. This topic falls under the broader category of some basic concepts of chemistry which is a crucial chapter in Class 11 chemistry.

Solution:

The solution is a homogeneous mixture of two or more chemically non-reacting substances whose composition can be varied within certain limits.

Solute and Solvent:

The solution is present in the same physical state as that of the solvent.

In case the species forming a solution are all present in the same physical state then the component that is present in a smaller amount is called the solute and the other present in a larger amount is called the solvent.

Concentration:

The concentration of a solution is a measure of the amount of solute that has been dissolved in a given amount of solvent or solution

Types of concentration terms:

(I) Mass fraction or % (w/w)

The mass percentage of a component of a solution is defined as:
Mass % of a component = Mass of the component in the solution Total mass of the solution ×100
For example, if a solution is described as 10% glucose in water by mass, it means that 10 g of glucose is dissolved in 90 g of water resulting in a 100 g solution. Concentration described by mass percentage is commonly used in industrial chemical applications. For example, a commercial bleaching solution contains a 3.62 mass percentage of sodium hypochlorite in water.

Example: A 10 mg effervescent tablet containing sodium bicarbonate and oxalic acid releases 0.25 ml of CO2 at T = 298.15 K and p = 1 bar. If the molar volume of CO2 is 25.9 L under such conditions, what is the percentage of sodium bicarbonate in each tablet?
[Molar mass of NaHCO3 = 84 g mol-1]

1) 0.84

2) 8.4

3) 16.8

4) 33.6

Solution:

2NaHCO3+H2C2O4→Na2C2O4+2CO2+2H2O

Here, number of moles of CO2=0.25×10−325.9≈10−5

Now, one mole of CO2 is produced by one mole of NaHCO3.

∴ the number of moles of NaHCO3 in the given reaction
= number of moles of CO2=10−5

∴% Mass =84×10−510×10−3×100=8.4%

Hence, the answer is (8.4%).

(II) Mole fraction:

The commonly used symbol for mole fraction is x and the subscript used on the right-hand side of x denotes the component.
It is defined as:Mole fraction of a component = Number of moles of the component Total number of moles of all the components

It is expressed by X for example, for a binary solution with two components A and B.

XA=nA/nA+nB

XB=nB/nA+nB
XA+XB=1

Here nA and nB represent moles of solvent and solute respectively. Mole fraction does not depend upon temperature as both solute and solvent are expressed by weight.

(III) Molality

It is the number of moles or gram moles of solute dissolved per kilogram of the solvent. It is denoted by 'm'.m= Weight of solute in gram Molar mass × wt. of solvent in Kg

  • If molality is one solution, it is called molal solution.
  • One molal solution is less than one molar solution.
  • Molality is preferred over molarity during experiments as molality is temperature-independent while molarity is temperature-dependent.

Example: Calculate the molality of a solution containing Acetic acid in Ethanol if the mass of solute = 10g and the density of Ethanol = 0.789 gmL-1.

1) 0.2112

2) 0.2012

3) 0.1992

4) 0.2002

Solution

We know.

Molality (m) = (number of moles of solute)/(mass of solvent in kg)

Now,

Moles of solute Acetic acid = mass / molar mass

=1060 moles

If Volume of ethanol = 1 L

Formula, Density = mass/volume

So,

Weight of ethanol = 1000 x 0.789 = 789g = 0.789 Kg

Molality = mass of solute mass of solution in kg

Molality =1060×7891000=0.2112 m/kg

Hence, the answer is (0.2112 m/kg).

(IV) Mass by volume percentage (w/V):

Another unit that is commonly used in medicine and pharmacy is mass by volume percentage. It is the mass of solute dissolved in 100 mL of the solution.

(V) Molarity:

It is the number of moles or gram moles of solute dissolved per liter of the solution. Molarity is denoted by 'M'.
M= Weight of solute in gram Molar mass × volume in litre

  • When the molarity of a solution is one, it is called a molar solution and when it is 0.1, the solution is called a decimolar solution.
  • Molarity depends upon temperature and its unit is mol/liter.
  • The number of moles of solute if the Molarity and the Volume in liters are given, is calculated as
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Moles = M $\times$ V

In case the volume is given in ml then the millimoles of solute will be given by the above formula

  • On dilution water is added and the final volume is made to V2 , then the moles of solute will remain constant and hence the following formula can be used (V1 is the volume before dilution, V2 is the volume after dilution)

M1V1 = M2V2

  • When a mixture of different solutions having different concentrations is taken the molarity of the mixture is calculated as follows: M=M1V1+M2V2……
  • When density and % by weight of a substance in a solution are given, molarity is found as follows:
    M=% by weight ×d×10 Molecular weight
    Here d = density

Example: What volume (in L) of solution of 2M BaSO4 contains 192 g of SO42- ion?

1) 0.5

2) (correct) 1

3) 2

4) 1.5

Solution

Molarity -

Molarity (M) = (Number of moles of solute)/(volume of solution in litres)

- wherein

It is defined as the number of moles of the solute in 1 liter of the solution.

192 g of SO42- = 2 moles of SO42-

2 moles of SO42-\rightarrow 2 moles of BaSO4

Volume = no.of moles molarity =22=1L

Hence, the answer is an option (2).

(VI) Normality

It is the number of gram equivalents of solute present in one liter of the solution and it is denoted by 'N'.N= Weight of solute in gram Equivalent mass × volume in litre

  • When the normality of a solution is one, the solution is called a normal solution and when it is 0.1, the solution is called a decinormal solution.

Normality Equation:

N1 V1=N2 V2

  • Volume Of water added = V2 - V1
    Here V2 = volume after dilution
    V1 = volume before dilution
  • When density and % by weight of a substance in a solution are given, normality is found as follows:

    N=% by weight ×d×10 Equivalent weight
    Here d = density of solution

When a mixture of different solutions having different concentrations is taken the normality of the mixture is calculated as follows: N=N1V1+N2V2

(VII) Strength :

It is the amount of solute present in one liter of solution. It is denoted by C or S.
C or S= Weight of solute in gram Volume in litre C=N×E

Here N= normality and E= Eq. wt.

(VIII) The relation between Normality and Molarity :

N = molarity x n-factor

N x Eq wt. = molarity x molar mass

Recommended topic video on (Molarity And Mole Fraction )

Some Solved Examples

Example: A sample of KCl is placed in 50 ml of solvent. What should be the mass (in gm) of the sample for the molarity to be 2M ?

1) 7.45

2) 7.81

3) 6.81

4) 7

Solution

Number of Moles = molarity x volume

= 2 x 0.05 = 0.1

So, mass = (39 + 35.5) x 0.01g = 7.45 g

Hence, the answer is an option (1).

Example: The amount (in g) of sugar (C12H22O11) required to prepare 2L of its 0.1 M aqueous solution is

1) 17.1

2) 68.4

3) 136.8

4) 34.2

Solution

Molarity -Molarity (M) = (Number of moles of solute)/(volume of solution in litres)

It is defined as the number of moles of the solute in 1 liter of the solution.

As we have learned in the mole concept.

The formula of molarity = (n)solute Vsolution ( in lit )

0.1=wt3422

wt(C12H22O11) = 68.4 gram

Hence, the answer is the option (2).

Conclusion

From the discussion of molarity and molality, it is evident that in molarity we consider the volume of the solution while in molality we consider the mass of the solvent. Therefore, the two are never equal. Molality is considered better for expressing the concentration as compared to molarity because the molarity changes with temperature because of the expansion or contraction of the liquid with temperature. However, molality does not change with temperature because the mass of the solvent does not change in temperature.

Frequently Asked Questions (FAQs)

1. How does the mole fraction of a component in a solution relate to its activity?
In ideal solutions, the activity of a component is equal to its mole fraction. However, in real solutions, there are often deviations from this ideal behavior due to interactions between molecules. The activity coefficient is used to account for these deviations, relating the actual activity to the mole fraction. Understanding this relationship is crucial in thermodynamics and chemical equilibrium studies.
2. How does adding more solvent affect the molarity of a solution?
Adding more solvent to a solution decreases its molarity. This is because molarity is defined as moles of solute per liter of solution. When you add more solvent, you increase the total volume of the solution while keeping the amount of solute constant, thus diluting the solution and lowering its molarity.
3. How does the concept of molarity apply to titrations?
Molarity is crucial in titrations because it allows us to determine the amount of one reactant based on the known amount of another. In a titration, we typically know the molarity and volume of the titrant (the solution in the burette) and use this to determine the concentration or amount of the analyte (the solution being analyzed). The equivalence point in a titration occurs when the moles of titrant added equal the moles of analyte present.
4. What's the relationship between molarity and density of a solution?
Molarity and density are related, but not directly proportional. Density is mass per unit volume, while molarity is moles of solute per unit volume. To calculate molarity from density, you need to know the molecular weight of the solute and the mass percentage of the solute in the solution. The relationship is: Molarity = (Density × % mass × 10) / (Molecular weight of solute).
5. Can you have a negative molarity or mole fraction?
No, neither molarity nor mole fraction can be negative. Molarity represents the number of moles of solute per liter of solution, which cannot be less than zero. Similarly, mole fraction represents the proportion of a component in a mixture, which must be between 0 and 1 inclusive. A negative value for either would not have physical meaning in the context of solutions.
6. What is the relationship between mole fraction and Gibbs free energy of mixing?
The Gibbs free energy of mixing is related to the mole fractions of the components in a mixture. For an ideal solution, the change in Gibbs free energy upon mixing is given by the equation ΔG = RT(x1lnx1 + x2lnx2), where x1 and x2 are the mole fractions of the two components. This relationship is fundamental in understanding the thermodynamics of mixing and predicting whether mixing will occur spontaneously.
7. What is the significance of partial molar quantities in relation to mole fraction?
Partial molar quantities, such as partial molar volume or partial molar Gibbs energy, represent how an extensive property of a solution changes with the addition of a small amount of one component while keeping the amounts of other components constant. These quantities are often expressed as functions of mole fraction. Understanding partial molar quantities is crucial in thermodynamics for predicting the behavior of multicomponent systems and in explaining phenomena like volume contraction upon mixing.
8. What is the relationship between mole fraction and activity in non-ideal solutions?
In non-ideal solutions, the activity of a component is related to its mole fraction through the activity coefficient: a = γx, where a is the activity, γ is the activity coefficient, and x is the mole fraction. The activity coefficient accounts for deviations from ideal behavior due to interactions between molecules. Understanding this relationship is crucial in thermodynamics, particularly in predicting equilibrium constants and other properties of real solutions.
9. What is molarity and how is it different from mole fraction?
Molarity is the number of moles of solute per liter of solution, while mole fraction is the ratio of moles of one component to the total moles of all components in a solution. Molarity focuses on the concentration of solute in a specific volume, whereas mole fraction compares the amount of one component to the total amount of all components.
10. Why is molarity commonly used in chemistry labs?
Molarity is widely used in chemistry labs because it directly relates the amount of solute to a specific volume of solution, making it easy to prepare solutions and perform calculations. It's particularly useful for reactions that occur in solution, as it allows chemists to quickly determine the amounts of reactants needed.
11. How does temperature affect molarity?
Temperature changes can affect molarity because they can cause the volume of the solution to expand or contract. As molarity is defined as moles of solute per liter of solution, changes in volume due to temperature fluctuations can alter the molarity. This is why it's important to specify the temperature when reporting molarity.
12. Can molarity be greater than 1? If so, what does this mean?
Yes, molarity can be greater than 1. This means there is more than one mole of solute per liter of solution. For example, a 2 M (molar) solution contains 2 moles of solute per liter of solution. This is common for highly soluble substances or concentrated solutions.
13. What's the difference between molarity and molality?
Molarity is moles of solute per liter of solution, while molality is moles of solute per kilogram of solvent. Molarity depends on volume, which can change with temperature, while molality is based on mass and is therefore independent of temperature. Molality is often preferred in certain thermodynamic calculations for this reason.
14. How does mole fraction relate to percent composition?
Mole fraction and percent composition are both ways to express the relative amounts of components in a mixture, but they use different units. Mole fraction expresses the ratio of moles of one component to total moles, while percent composition typically expresses the mass of a component as a percentage of the total mass. They can be converted between each other using molecular weights.
15. Why is the sum of all mole fractions in a solution always equal to 1?
The sum of all mole fractions in a solution is always 1 because mole fraction represents the proportion of each component relative to the total. Since all components together make up the entire solution, their fractions must sum to the whole, which is represented by 1.
16. Can mole fraction be used for gases as well as liquids and solids?
Yes, mole fraction can be used for gases, liquids, and solids. It's a versatile concept that applies to any mixture, regardless of its physical state. In fact, mole fraction is particularly useful in gas mixtures, where it's directly related to the partial pressure of each gas component.
17. How does mole fraction help in understanding Raoult's law?
Mole fraction is crucial in understanding Raoult's law, which states that the partial pressure of each component in an ideal solution is directly proportional to its mole fraction in the solution. This law helps predict the vapor pressure of solutions and is fundamental in understanding vapor-liquid equilibria.
18. How does the concept of mole fraction apply to colligative properties?
Mole fraction is fundamental in understanding colligative properties, which depend on the ratio of solute particles to solvent particles, not on the nature of the particles. For example, the freezing point depression and boiling point elevation of a solution are directly proportional to the mole fraction of the solute. This concept helps explain why adding salt to water changes its freezing and boiling points.
19. Why is it important to distinguish between mole fraction and volume fraction?
Mole fraction and volume fraction are different concepts that can lead to different results. Mole fraction is based on the number of particles, while volume fraction is based on the volume occupied by each component. They're not always equivalent, especially for mixtures of substances with different molecular sizes or densities. Understanding this distinction is crucial for accurate calculations and predictions in chemistry.
20. What's the difference between molar concentration and normal concentration?
Molar concentration (molarity) is based on the number of moles of solute per liter of solution, while normal concentration (normality) is based on the number of equivalents of solute per liter of solution. The key difference is that normality takes into account the reactivity of the solute, particularly useful for acid-base or redox reactions where the number of reactive species per molecule matters.
21. How does the mole fraction concept apply to Dalton's law of partial pressures?
Dalton's law states that the total pressure of a gas mixture is the sum of the partial pressures of each gas. The partial pressure of each gas is directly proportional to its mole fraction in the mixture. Specifically, the partial pressure of a gas component is equal to its mole fraction multiplied by the total pressure. This relationship makes mole fraction a powerful tool in gas mixture calculations.
22. Why is it important to specify whether a solution is volume/volume (v/v), weight/volume (w/v), or weight/weight (w/w) when discussing concentration?
Specifying v/v, w/v, or w/w is crucial because these notations indicate how the concentration is measured, which affects calculations and preparation methods. V/v is volume of solute per volume of solution, w/v is weight of solute per volume of solution, and w/w is weight of solute per weight of solution. Using the wrong notation can lead to significant errors in solution preparation and subsequent experiments.
23. How does the concept of molarity apply to buffer solutions?
Molarity is essential in preparing and understanding buffer solutions. A buffer typically consists of a weak acid or base and its conjugate. The ratio of their molarities determines the pH of the buffer. The Henderson-Hasselbalch equation, which relates pH to the pKa of the acid and the ratio of concentrations of the acid and its conjugate base, uses molarity directly. Proper calculation of molarities is crucial for creating buffers with specific pH values.
24. What is the relationship between molarity and osmolarity?
Molarity and osmolarity are related but distinct concepts. Molarity is the number of moles of solute per liter of solution, while osmolarity is the number of osmoles of solute particles per liter of solution. For ideal, dilute solutions of non-dissociating compounds, molarity and osmolarity are numerically equal. However, for solutions of dissociating compounds (like salts), osmolarity is higher than molarity because each molecule produces multiple particles. Understanding this difference is crucial in biological and medical applications.
25. How does the mole fraction concept apply to phase diagrams?
Mole fraction is fundamental in constructing and interpreting phase diagrams for mixtures. In a binary system, the mole fraction of one component is often plotted on the x-axis, with temperature or pressure on the y-axis. The resulting diagram shows how the phases present change with composition and temperature or pressure. This is particularly important in understanding eutectic mixtures, azeotropes, and other complex phase behaviors.
26. Why is molarity preferred over molality in many practical applications?
Molarity is often preferred in practical applications because it relates directly to volume, which is easier to measure accurately in a lab setting using volumetric glassware. Most reactions are carried out by combining volumes of solutions, making molarity more convenient. However, molality has the advantage of being independent of temperature, which is why it's preferred in certain thermodynamic calculations.
27. How does the concept of mole fraction relate to Henry's law?
Henry's law states that the amount of dissolved gas in a liquid is proportional to its partial pressure above the liquid. The proportionality constant, known as Henry's constant, relates the partial pressure of the gas to its mole fraction in the solution. This relationship is crucial in understanding gas solubility in liquids and has applications in fields ranging from carbonated beverages to environmental science.
28. What is the significance of infinite dilution in the context of mole fraction?
Infinite dilution refers to the theoretical state where the mole fraction of solute approaches zero. This concept is important in understanding the behavior of solutions at extreme dilutions. Many thermodynamic properties, such as partial molar quantities and activity coefficients, are often reported at infinite dilution as reference states. This helps in predicting solution behavior across a range of concentrations.
29. How does the concept of molarity apply to electrochemistry, particularly in the Nernst equation?
Molarity is crucial in electrochemistry, especially in the Nernst equation, which relates the reduction potential of an electrochemical reaction to the standard electrode potential and the activities (often approximated by concentrations) of the species involved. In dilute solutions, these activities are often replaced directly with molarities. This allows for the calculation of cell potentials based on solution concentrations, which is fundamental in understanding and predicting electrochemical behavior.
30. What is the relationship between mole fraction and vapor pressure in non-ideal solutions?
In non-ideal solutions, the relationship between mole fraction and vapor pressure deviates from Raoult's law. This deviation is quantified using activity coefficients. The actual vapor pressure is related to the product of the mole fraction, the activity coefficient, and the vapor pressure of the pure component. Understanding these deviations is crucial in distillation processes, azeotrope formation, and other separation techniques.
31. How does the concept of molarity apply to reaction kinetics?
Molarity is fundamental in reaction kinetics as reaction rates are typically expressed in terms of changes in concentration over time. The rate laws for chemical reactions are usually written in terms of molar concentrations. For example, in a second-order reaction, the rate is proportional to the square of the concentration of a reactant. Understanding and manipulating molarities is therefore crucial in studying reaction mechanisms and determining rate constants.
32. What is the significance of mole fraction in understanding colligative properties of non-electrolyte solutions?
For non-electrolyte solutions, colligative properties (like freezing point depression, boiling point elevation, vapor pressure lowering, and osmotic pressure) are directly proportional to the mole fraction of the solute. This relationship allows for simple predictions of these properties based on solution composition. It's a powerful concept that demonstrates how the number of particles, rather than their nature, affects these properties.
33. How does the concept of molarity apply to spectrophotometry and Beer-Lambert law?
Molarity is central to spectrophotometry and the Beer-Lambert law, which states that the absorbance of a solution is directly proportional to the concentration of the absorbing species. In practice, this often means the molarity of the solution. This relationship allows for the determination of unknown concentrations by measuring absorbance, making it a fundamental tool in analytical chemistry and biochemistry for quantitative analysis.
34. How does the concept of molarity apply to acid-base equilibria and pH calculations?
Molarity is crucial in acid-base equilibria and pH calculations. The pH of a solution is defined as the negative logarithm of the hydrogen ion concentration (in mol/L). In weak acid or base solutions, the molarity of the acid or base is used to calculate the equilibrium concentrations of all species, which in turn determines the pH. Understanding how to manipulate molarities in these calculations is essential for predicting and controlling pH in various chemical and biological systems.
35. How does the concept of molarity apply to chemical equilibrium and Le Chatelier's principle?
Molarity is fundamental in understanding chemical equilibrium and applying Le Chatelier's principle. The equilibrium constant is typically expressed in terms of molar concentrations for reactions in solution. When the concentration (molarity) of a species is changed, Le Chatelier's principle predicts how the equilibrium will shift to counteract this change. This concept is crucial in optimizing reaction conditions in industrial processes and understanding complex equilibria in biological systems.
36. How does the concept of molarity apply to solubility and precipitation reactions?
Molarity is key in understanding solubility and precipitation reactions. The solubility product constant (Ksp) is expressed in terms of molar concentrations of ions. When the product of ion concentrations exceeds the Ksp, precipitation occurs. Manipulating molarities allows chemists to predict when precipitation will occur, calculate the amount of precipitate formed, or determine the solubility of a compound under various conditions. This is crucial in fields ranging from water treatment to geochemistry.
37. What is the significance of mole fraction in understanding and applying Gibbs' phase rule?
Gibbs' phase rule relates the number of degrees of freedom in a system to the number of components and phases present. The mole fraction is crucial in defining the composition variable in this rule. For a two-component system, one mole fraction is sufficient to specify the composition, which is why binary phase diagrams often use mole fraction as one of the axes. Understanding this helps in analyzing complex phase equilibria and designing separation processes.
38. How does the concept of molarity apply to redox reactions and electrochemical cells?
Molarity is essential in redox reactions and electrochemical cells. In the Nernst equation, which relates cell potential to concentration, the activities of species are often approximated by their molarities. In concentration cells, the potential difference is directly related to the logarithm of the ratio of molarities. Understanding how to manipulate molarities in these contexts is crucial for

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