Question

(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

(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

(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)

(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 (\(\mathrm{Na}_{2}\mathrm{SO}_{4}\)) = \(\frac{10.6\mathrm{g}}{10.6\mathrm{g}+483\mathrm{g}} \times 100\)

(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 = \(\frac{2.86\mathrm{g}}{1000}\)

(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

Key concepts

Solution Concentration

Solution concentration refers to how much solute is dissolved in a solvent. It tells us the ratio of solute-to-water in a solution. The concentration can be expressed in various units, such as molarity, molality, mass percentage, or ppm, depending on what aspect is most useful for us to understand or calculate. When calculating the concentration, the

• solute is the substance being dissolved
• solvent is the medium in which the solute is dissolved, often water in many chemistry problems

To find the solution's overall concentration, one needs to consider the amount of dissolved solute and the total volume or mass of the solution. A good understanding of different concentration metrics helps interpret and solve problems in chemistry effectively, just like deciding which units of concentration are appropriate for a given context.

Parts Per Million (ppm)

Parts per million (ppm) is a measurement unit used to describe the concentration of a substance in a solution, especially when that substance is present in very small amounts. Imagine you have one million pieces, and only a few of those are the solute—this would be described using ppm.It's particularly useful in fields like environmental science, where pollutants in water or air might be in tiny quantities. For example:

• 1 ppm means 1 part substance per 1,000,000 parts of the solution.
• In practice, when dealing with solutions, 1 ppm often equates to 1 milligram per liter since water has a density of approximately 1 kg/L.
• To calculate ppm when given grams in a certain volume, you can use: \[ \text{ppm} = \frac{Mass~of~Substance~(in~g)}{Mass~of~Solution~(in~kg)} \times 10^{6} \]

Utilizing the ppm metric makes it simpler to express very dilute concentrations in a manageable way, as with determining trace silver amount in an ore.

Mass Percentage

Mass percentage is another way to express concentration. It tells us how much of the solute is present per 100 parts of the solution, expressed in percentage.Calculating mass percentage helps when it's essential to know what portion of the solution is made up from the solute. It’s a straightforward approach that doesn’t require knowing the volume or density of the solution, only the masses of the solute and solution.To calculate mass percentage, use the formula:\[\text{Mass Percentage (solute)} = \frac{\text{Mass of Solute}}{\text{Total Mass of Solution}} \times 100\%\]Let’s say there is 10.6 g of \(\text{Na}_2\text{SO}_4\) in a solution where the total mass (including \(\text{Na}_2\text{SO}_4\) and water) is 493.6 g. The mass percentage would be calculated by dividing 10.6 g by 493.6 g and then multiplying by 100 to convert it to a percentage. This simple calculation provides significant insights into the composition of a given solution in practical and laboratory settings.