Chapter 6, Problem 6.30CP

Box (a) represents 1.0 mL of a solution of particles at a given concentration. Which of the boxes (b)–(d) represents 1.0 mL of the solution that results after (a) has been diluted by doubling the volume of its solvent?

Interpretation Introduction

Interpretation:

Among the given boxes (b)-(d), the box that represents the result of box (a) after being diluted with double the volume of its solvent has to be identified.

Concept Introduction:

Diluting Concentrated Solutions:

On diluting concentrated solutions, the product of molarity and volume of an initial solution will be equal to the product of molarity and volume of a final solution and hence the number of moles of solute remains constant.

${\text{M}}_{\text{i}}\times {\text{V}}_{\text{i}}{\text{ = M}}_{\text{f}}\times {\text{V}}_{\text{f}}$

Where,

${\text{M}}_{\text{i}}{\text{ and M}}_{\text{f}}$ are initial and final molarity respectively

${\text{V}}_{\text{i}}{\text{ and V}}_{\text{f}}$ are initial and final volume respectively

Answer to Problem 6.30CP

The box that gives the result of box (a) after dilution is box (b)

Explanation of Solution

Given data:

The given box (a) and the optional boxes (b)-(d) which forms the result of dilution of box (a) are shown in the below figure 1.

Figure 1

Box (a) represents $\text{1}\text{.0 mL}$ of solution of particles at a given concentration.

Box (b)-(d) represents $\text{1}\text{.0 mL}$ of solution that results after dilution of box (a) with double the volume of its solvent.

Reason for correct option:

The correct option that results after dilution is box (b)

The green spheres in each box represents, the number of particles present in it which in turn corresponds to the concentration of each solution.

• Box (a) contains 14 green spheres representing the concentration of solution contained in it.
• Box (b) contains 7 green spheres representing the concentration of solution contained in it.

When the volume of a solution is doubled, the concentration is halved.

Hence, box (b) represents half the concentration of box (a) that is 7 green spheres which is half of 14 spheres.

Therefore, the correct option is box (b)

Reason for incorrect options:

Box (c) contains 14 green spheres.  This implies that the concentration remains same even after dilution.  But in actual after doubling the volume, concentration will be halved.

Box (d) represents formation of molecules which will not happen in actual on dilution.

Hence, the incorrect options are box (c) and box (d).

Conclusion

The box that represents the result of box (a) after being diluted with double the volume of its solvent was identified as box (b)