What is the molality of a solution that has 6 mol of [tex]$CaCl_2$[/tex] in 3 kg of water?

A. [tex]6 \, m[/tex]
B. [tex]2 \, m[/tex]
C. [tex]3 \, m[/tex]
D. [tex]0.5 \, m[/tex]



Answer :

Let's solve the problem step-by-step:

1. Understanding Molality:
Molality (m) is a measure of the concentration of a solute in a solution. It is defined as the number of moles of solute per kilogram of solvent.

2. Given Values:
- Moles of [tex]\( \text{CaCl}_2 \)[/tex]: 6 mol
- Mass of water (solvent): 3 kg

3. Calculate Molality:
The formula for molality (m) is:
[tex]\[ m = \frac{\text{moles of solute}}{\text{mass of solvent in kg}} \][/tex]

Substituting the given values:
[tex]\[ m = \frac{6 \text{ mol}}{3 \text{ kg}} \][/tex]

4. Perform the Division:
[tex]\[ m = 2 \text{ mol/kg} \][/tex]

Thus, the molality of the solution is [tex]\( 2 \text{ mol/kg} \)[/tex] or [tex]\( 2 \, m \)[/tex].

The correct answer is:
B. [tex]\( 2 \, m \)[/tex]