Chapter 1.4, Problem 21P

You have prepared $42\text{mL}$ of distilled water, $18\text{mL}$ of vinegar and $47\text{mL}$ of salt water for an experiment.

a. How many milliliters of solution will you have if you first pour the distilled water, then the salt water, and finally the vinegar into your beaker?

b. How many milliliters of solution will you have if you first pour the salt water, then the vinegar, and finally the distilled water into your beaker?

c. Explain why the amounts described in parts (a) and (b) are equal.

To determine

How many milliliters of solution will you have if you first pour the distilled water, then the salt water, and finally the vinegar into your beaker?

Answer to Problem 21P

The volume of solution is 107 mL.

Explanation of Solution

Given:

The volume of distilled water 42 mL , volume of vinegar is 18 mL and volume of salt water is 47 mL.

Concept Used:

The total volume of the solution is calculates by adding the amount of distilled water, salt water and vinegar.

Calculation:

The total volume of the solution = amount of distilled water + amount of salt water + amount of vinegar.

The volume of solution is:

  $\begin{array}{l}{V}_{saltwater}=47mL\\ V_{vinegar}=18mL\\ V_{distilledwater}=42mL\\ V_1=V_{distilledwater}+V_{saltwater}+V_{vinegar}\\ =42+47+18=107mL\mathrm{.....................................................}(1)\end{array}$

Conclusion:

The volume of solution is 107 mL .

To determine

How many milliliters of solution will you have if you first pour the salt water, then the vinegar, and finally the distilled water into your beaker?

Answer to Problem 21P

The volume of solution is 107 mL.

Explanation of Solution

Given:

The volume of distilled water 42 mL , volume of vinegar is 18 mL and volume of salt water is 47 mL.

Concept Used:

The total volume of the solution is calculates by adding the amount of salt water, vinegar and distilled water.

Calculation:

The total volume of the solution = amount of salt water + amount of vinegar + amount of distilled water .

The volume of solution is:

  $\begin{array}{l}{V}_{saltwater}=47mL\\ V_{vinegar}=18mL\\ V_{distilledwater}=42mL\\ V_2=V_{saltwater}+V_{vinegar}+V_{distilledwater}\\ =47+18+42=107mL\mathrm{.....................................................}(2)\end{array}$

Conclusion:

The volume of solution is 107 mL .

To determine

Explain why the amounts described in parts (a) and (b) are equal.

Explanation of Solution

As we see from the equation (1)&(2) the volumes are equal this shows that the addition is a cumulative property

The commutative property of addition means that by changing the order of addends the sum does not change.

  $a+(b+c)=b+(c+a)$