Question

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 (1.00 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 3.74 × 10-8 M. What is the volume of water in the pool in liters? The molar mass of methylene blue is 319.854 g/mol.

Answer 1

• 83,700 liter (rounded to 3 significant figures)

Step-by-step explanation:

1) Data:

a) Solution of a dye:

• m₁ = 1.00 g of methylene blue, C₁₆H₁₈ClN₃S

• V₁ = 50.0 mL

• MM₁ = 319.854 g/mol

b) Water of the pool, after mixing the dye:

• M₂ = 3.74 × 10⁻⁸ M.

• V₂ = ?

2) Formulae:

a) Molarity: M = n / V in liter

b) Molar mass: MM = mass in grams / number of moles

3) Solution:

a) Number of moles of methylene blue in the prepared solution:

• n₁ = mass in grams / molar mass = = 1.00 g / 319.854 g/mol = 0.00313 mol

b) Number of moles of methylen blue in the pool = number of moles of methylen blue in the prepared solution

• n₂ = n₁ = 0.00313 mol

c) Volume of the pool:

• M₂ = n₂ / V₂ ⇒ V₂ = n₂ / M₂ = 0.00313 mol /( 3.74 × 10⁻⁸ M) = 83,700 liter

And that is the answer, which has to be rounded to 3 significant figures, since the data are expressed with 3 significant figures.

Note: For all the effects, the 50.0 mL of the dye solution are neglictible in front of the volume of the pool.