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Chapter 1: Problem 71

The volume of seawater on Earth is about \(330,000,000 \mathrm{mi}^{3} .\) If seawater is \(3.5 \%\) sodium chloride by mass and has a density of \(1.03 \mathrm{g} / \mathrm{mL}\), what is the approximate mass of sodium chloride, in tons, dissolved in the seawater on Earth ( 1 ton \(=\) 2000 lb)?

Short Answer

Expert verified
To solve this problem, first the total mass of the seawater is calculated using the given volume and density. After that, the mass of the sodium chloride is computed as a percentage of the total seawater mass and finally, this mass is converted from grams to tons using the proper conversion factors.

Step by step solution

01

Find the total mass of seawater

The problem provides the volume of seawater in cubic miles, and the seawater's density in grams per milliliter. Convert the volume of seawater into milliliters \((1 \mathrm{mi}^{3} = 4.16818183 x 10^{15} \mathrm{mL})\), and then multiply by the density to find the total mass of the seawater in grams. Mass = volume x density = \(330,000,000 \mathrm{mi}^{3}\) x \(4.16818183 x 10^{15} \mathrm{mL/mi}^{3}\) x \(1.03 \mathrm{g/mL}\).
02

Calculate the mass of sodium chloride

We find the mass of sodium chloride in the sea water using the percentage given. According to the problem, seawater is \(3.5%\%\) sodium chloride by mass. That means 3.5g of every 100g of seawater is sodium chloride. So, to find the mass of sodium chloride in the seawater, we only need to find \(3.5\%\) of the total seawater mass calculated in Step 1.
03

Convert the mass to tons

Lastly, we convert the mass obtained in Step 2 from grams to tons. We know that 1 lb = 453.592g and 2000 lbs = 1 ton. Therefore, using these conversions factors, we transform the mass from grams into tons. Mass (in tons) = Mass (in grams) / \(453.592 \times 2000\) .

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