   # You need to know the volume of water in a small swimming pool, but, owing to the pool’s irregular shape, it is not a simple matter to determine its dimensions and calculate the volume. To solve the problem, you stir in a solution of a dye (1.0 g of methylene blue. C 16 H 18 ClN 3 S, in 50.0 mL of water). After the dye has mixed with the water in the pool, you take a sample of the water. Using a spectrophotometer, you determine that the concentration of the dye in the pool is 4.1 × 10 −8 M. What is the volume of water in the pool? ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640

#### Solutions

Chapter
Section ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640
Chapter 4, Problem 115GQ
Textbook Problem
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## You need to know the volume of water in a small swimming pool, but, owing to the pool’s irregular shape, it is not a simple matter to determine its dimensions and calculate the volume. To solve the problem, you stir in a solution of a dye (1.0 g of methylene blue. C16H18ClN3S, in 50.0 mL of water). After the dye has mixed with the water in the pool, you take a sample of the water. Using a spectrophotometer, you determine that the concentration of the dye in the pool is 4.1 × 10−8 M. What is the volume of water in the pool?

Interpretation Introduction

Interpretation:

The volume of water in the pool has to be calculated.

Concept introduction:

• Concentration of a solution is the amount of solute present in a given volume of solution and it can be expressed in many different ways such as mole per liter, mass per liter.

Therefore,

Volume=MassConcentartion

• The molar mass of an element or compound is the mass in grams of 1 mole of that substance, and it is expressed in the unit of grams per mol (g/mol).

Numberofmole=GivenmassofthesubstanceMolarmass

• Massofthesubstance=Amountofthesubstance×Molarmassofthesubstance

### Explanation of Solution

From the given description the pool is irregular in shape.  The volume of water in the pool can be calculated on the basis of concentration of the dye added into the water and the mass of dye added.

Molar mass of the dye, methylene blue C16H18CIN3S is 319.58g/mol

Last concentration of the dye is 1.31×10-5g/L

Here volume of water ×Conxcentration=1g

Volume=

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