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Chapter 1: Problem 66

A solution containing \(12.0 \%\) sodium hydroxide by mass in water has a density of \(1.131 \mathrm{g} / \mathrm{mL}\). What volume of this solution, in liters, must be used in an application requiring \(2.25 \mathrm{kg}\) of sodium hydroxide?

Short Answer

Expert verified
So, the volume of the sodium hydroxide solution required is approximately \(16.6 \, L\).

Step by step solution

01

Calculate Mass of Sodium Hydroxide in the Solution

From the exercise, the mass percentage of sodium hydroxide (NaOH) in the solution is \(12.0 \%\). This means that 100 g of the solution contains 12.0 g of NaOH. Thus, for a solution containing \(2.25 \, kg = 2250 \, g\) of NaOH, it can be calculated as: \[ \text{Mass of the solution} = \frac{\text{mass of NaOH}}{\text{% of NaOH by mass}} = \frac{2250 \, g}{0.12} = 18750 \, g\].
02

Calculate Volume of the Solution

\(\mathrm{Density} = \frac{\mathrm{Mass}}{\mathrm{Volume}}\), therefore we can solve for volume: \[ \mathrm{Volume} = \frac{\mathrm{Mass}}{\mathrm{Density}}=\frac{18750 \, g}{1.131 \, g/mL} = 16580.2 \, mL \].
03

Convert Volume to Liters

To convert the volume from milliliters (mL) to liters (L), remember that \(1 \, L = 1000 \, mL\). So, \[ \text{Volume} = 16580.2 \, mL × \frac{1 \, L}{1000 \, mL} = 16.58 \, L. \] The volume should be rounded to three significant figures since the least precise data given in the question was to three significant figures.

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