The concentration of a solution may be defined as the amount of solute present in the given quantity of the solution.

The concentration of solution may be expressed in several ways as discussed below:

Mass Percentage

The mass percentage of a component in a given solution is the mass of the component per 100 g of the solution.

\[\text{Mass percentage of a component = }\frac{\text{Mass of the component in the solution}}{\text{Total mass of the solution}} × 100\]

Volume percentage

In the case of a liquid dissolved in another liquid, it is convenient to express the concentrations in volume percentage. The volume percentage is defined as the volume of the component per 100 parts by the volume of the solution.

Mass by volume percentage (w/v)

Sometimes, we express the concentrations as weight/volume. It is the mass of solute dissolved in 100 mL of the solution

Molarity of a solution

The molarity of a solution is defined as the number of moles of the solute dissolved per litre of the solution.It is represented as ′M′. Mathematically,

\[Molarity = \frac{\text{Moles of solute}}{\text{Volume of the solution (in mL)}} × 1000\]

Molarity of a solution

The molarity of a solution is defined as the number of moles of the solute dissolved per litre of the solution.

Molality of the solution

The molality of a solution is defined as the number of moles of the solute dissolved per 1000 g (or 1 kg) of the solvent.

Which of the following statement is correct?

Sum of the mole fractions of all components in a solution is always exactly one

The correct answer is option 3. Sum of the mole fractions of all components in a solution is always exactly one.

Let us explain each statement in detail to understand why the correct answer is that the sum of the mole fractions of all components in a solution is always exactly one.

1. Molecular weight changes with valency

Molecular weight is a fixed property of a molecule. It is the sum of the atomic weights of all atoms in a molecule. For example, the molecular weight of water \((H_2O)\) is 18 g/mol (2×1 for hydrogen + 16 for oxygen). This value does not change with the valency of the atoms in the molecule. Valency is the combining capacity of an element. While valency determines how atoms combine to form molecules, it does not affect the molecular weight once the molecule is formed.

2. Molar concentration of a solution in water is always equal to normality of a solution

Molarity \((M)\) is defined as the number of moles of solute per liter of solution. Normality \((N)\) is defined as the number of equivalents of solute per liter of solution. For many substances, molarity and normality can be different because normality depends on the type of reaction. For example, in an acid-base reaction, the normality of an acid depends on how many protons \((H^+)\) it can donate. A 1 \(M\) solution of sulfuric acid \((H_2SO_4)\) has a normality of 2 \(N\) because each molecule of \(H_2SO_4\) can donate 2 \(H^+\) ions.

3. Sum of the mole fractions of all components in a solution is always exactly one

Mole fraction \((X)\) of a component in a solution is defined as the ratio of the number of moles of that component to the total number of moles of all components in the solution. Mathematically, for a solution with \( n \) components:

\(X_i = \frac{n_i}{\sum_{i=1}^{n} n_i}\)

where \( n_i \) is the number of moles of component \( i \).

The sum of the mole fractions of all components in the solution is:

\(\sum_{i=1}^{n} X_i = \sum_{i=1}^{n} \frac{n_i}{\sum_{i=1}^{n} n_i} = \frac{\sum_{i=1}^{n} n_i}{\sum_{i=1}^{n} n_i} = 1\)

This is a fundamental property of mole fractions.

4. Equivalent weight of an element is not variable

Equivalent weight of an element is variable and depends on the specific reaction it participates in. It is defined as the mass of the element that combines with or displaces 1 mole of hydrogen or 8 grams of oxygen or 35.5 grams of chlorine. For example, the equivalent weight of sulfur in \(H_2SO_4\) (where sulfur has an oxidation state of +6) is different from its equivalent weight in \(H_2S\) (where sulfur has an oxidation state of -2).

Conclusion

The correct statement is: Sum of the mole fractions of all components in a solution is always exactly one

This is a fundamental property of solutions and mole fractions. No matter how many components are present, the sum of their mole fractions will always equal one, reflecting the entire solution.