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Chapter 13: Problem 39

(a) Calculate the mass percentage of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) in a solution containing \(10.6 \mathrm{~g} \mathrm{Na}_{2} \mathrm{SO}_{4}\) in \(483 \mathrm{~g}\) water. (b) An ore contains \(2.86 \mathrm{~g}\) of silver per ton of ore. What is the concentration of silver in ppm?

Short Answer

Expert verified
(a) The mass percentage of \(\mathrm{Na}_{2}\mathrm{SO}_{4}\) in the solution is \(\frac{10.6\mathrm{g}}{10.6\mathrm{g}+483\mathrm{g}} \times 100 \approx 2.15\% \). (b) The concentration of silver in the ore is \(\frac{2.86\mathrm{g}/1000}{1\mathrm{kg}} \times 10^{6}\) ppm \(\approx 2,860\) ppm.

Step by step solution

01

(Part a: Calculate the total mass of the solution)

To find the mass percentage of the solute(\(\mathrm{Na}_{2}\mathrm{SO}_{4}\)) in the solution, first calculate the total mass of the solution by adding the mass of \(\mathrm{Na}_{2}\mathrm{SO}_{4}\) and the mass of water. Total Mass = Mass of \(\mathrm{Na}_{2}\mathrm{SO}_{4}\) + Mass of Water Total Mass = \(10.6\mathrm{g}\) (solute) + \(483\mathrm{g}\) (solvent)
02

(Part a: Calculate the mass percentage of \(\mathrm{Na}_{2}\mathrm{SO}_{4}\) in the solution)

Now, we can calculate the mass percentage of \(\mathrm{Na}_{2}\mathrm{SO}_{4}\) in the solution using the formula: Mass Percentage (solute) = \(\frac{Mass~of~Solute}{Total~Mass~of~Solution} \times 100\) Mass Percentage (\(\mathrm{Na}_{2}\mathrm{SO}_{4}\)) = \(\frac{10.6\mathrm{g}}{10.6\mathrm{g}+483\mathrm{g}} \times 100\)
03

(Part b: Convert grams of silver per ton to grams of silver per kilogram)

In order to find the concentration of silver in the ore in parts per million (ppm), first convert the given mass of silver from grams per ton to grams per kilogram. There are \(1000\mathrm{kg}\) in a ton, so to find the grams of silver per kilogram, divide the given mass by \(1000\). Mass of silver in grams per kilogram = \(\frac{2.86\mathrm{g}}{1000}\)
04

(Part b: Calculate the concentration of silver in ppm)

Now, we can find the concentration of silver in the ore in parts per million (ppm) using the formula: Concentration in ppm = \(\frac{Mass~of~Silver~in~grams~per~kilogram}{1\mathrm{kg}} \times 10^{6}\) ppm Concentration in ppm = \(\frac{2.86\mathrm{g}/1000}{1\mathrm{kg}} \times 10^{6}\) ppm

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Most popular questions from this chapter

Ascorbic acid (vitamin \(\left.\mathrm{C}, \mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6}\right)\) is a water-soluble vitamin. A solution containing \(80.5 \mathrm{~g}\) of ascorbic acid dissolved in \(210 \mathrm{~g}\) of water has a density of \(1.22 \mathrm{~g} / \mathrm{mL}\) at \(55^{\circ} \mathrm{C}\). Calculate (a) the mass percentage, (b) the mole fraction, (c) the molality, (d) the molarity of ascorbic acid in this solution.

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