In the following questions, two statements (Assertion) A and Reason (R) are given.

(A) : Molarity of a solution and molality of a solution both change with density

(R) : Density of the solution changes when percentage by mass of solution changes.

Choose the correct answer from the options given below:

A and R both are correct and R is the correct explanation of A

The correct answer is option 1. A and R both are correct and R is the correct explanation of A.

Statement (A): Molarity of a solution and molality of a solution both change with density. - This statement is true. Both molarity (M) and molality (m) are concentration units defined as:

Molarity (M) = moles of solute / liters of solution (depends on volume)

Molality (m) = moles of solute / kg of solvent (independent of volume)

However, both M and m depend on the density (ρ) of the solution through the relationship between volume (V) and mass of solvent (m_s) for a given solution:

\(V = \frac{m_s}{ρ}\)

Reason (R): Density of the solution changes when percentage by mass of solution changes. - This statement is also true. The density of a solution depends on the concentration of the solute and solvent. As the percentage by mass of the solute changes, the density of the solution will also change.

Connecting A and R:

Since the density of the solution affects both the volume (for molarity) and the mass of solvent (for molality) through the \(V = \frac{m_s}{ρ}\) relationship, a change in density will indeed lead to a change in both molarity and molality.

Therefore, both statement (A) and reason (R) are correct, and reason (R) explains why statement (A) is true.