Question

If ‘m’ is the molality, ‘M’ is the molarity, ‘d’ is the density in g/cm\(^3\) and ‘M\(_2\)’ is the molarity of solute. What is the relation between them?

Hint:

Remember: The relationship between molality and molarity depends on the density of the solution and the volume of the solvent.

Answer 1

Step 1: Define the terms.
- Molality (m) is defined as the number of moles of solute per kilogram of solvent: \[ m = \frac{\text{moles of solute}}{\text{mass of solvent in kg}} \] - Molarity (M) is defined as the number of moles of solute per liter of solution: \[ M = \frac{\text{moles of solute}}{\text{volume of solution in L}} \] - Density (D) is the mass per unit volume of the solution in g/cm\(^3\).
Step 2: Relate molality and molarity.
To derive a relation between molality and molarity, we use the following:
- The mass of the solution = volume of the solution \(\times\) density (in grams).
- The moles of solute are the same for both molality and molarity.
Let \(V\) be the volume of the solution and \(m_2\) be the molarity of the solute, then: \[ M = \frac{m}{d \times V} \] By using the above formula, the relation between molality (m), molarity (M), and density (D) is established.