Question

(a) Calculate the mass percentage of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) in a solution containing \(10.6 \mathrm{~g}\) of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) in \(483 \mathrm{~g}\) of 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 Na2SO4 in the solution is \(2.148\%\). (b) The concentration of silver in the ore is \(2.86 \ ppm\).

Step-by-step solution

(a) Finding mass percentage of Na2SO4

To find the mass percentage of Na2SO4 in the given solution, we can use the formula: Mass percentage = (Mass of solute / Total mass) × 100 Here, the mass of Na2SO4 (solute) is 10.6 g and the total mass of the solution is the sum of the mass of Na2SO4 and the mass of water (483 g).

Calculate the total mass of the solution

To calculate the total mass of the solution, we can simply add the mass of Na2SO4 (10.6 g) and the mass of water (483 g): Total mass = mass of Na2SO4 + mass of water Total mass = 10.6 g + 483 g = 493.6 g

Calculate the mass percentage of Na2SO4

Now, we can calculate the mass percentage of Na2SO4 using the formula: Mass percentage = (Mass of Na2SO4 / Total mass) × 100 Mass percentage = (10.6 g / 493.6 g) × 100 = 2.148%

(b) Finding the concentration of silver in ppm

In this part, we need to find the concentration of silver in parts per million (ppm) in an ore. To do this, we will use the formula: Concentration in ppm = (Mass of silver / Mass of ore) × 10^6 Here, the mass of silver in the ore is given as 2.86 g per ton of ore. A ton is equal to 1000 kg, so we need to convert the mass of ore from tons to grams.

Convert the mass of ore to grams

We can convert the mass of ore from tons to grams as follows: 1 ton = 1000 kg = 1000 × 1000 g = 10^6 g So, the mass of ore is 10^6 g.

Calculate the concentration of silver in ppm

Now, we can use the formula to calculate the concentration of silver in ppm: Concentration in ppm = (Mass of silver / Mass of ore) × 10^6 Concentration in ppm = (2.86 g / 10^6 g) × 10^6 = 2.86 ppm So, the concentration of silver in the ore is 2.86 ppm.

Key concepts

Molar Mass

Understanding molar mass is essential in chemistry as it helps relate the mass of substances to the number of molecules or atoms contained within. Molar mass is the mass of one mole of a compound and is calculated by summing the atomic masses of all the atoms present in the compound's formula. This value is expressed in grams per mole (g/mol). For example, the molar mass of sodium sulfate (\(\mathrm{Na}_2\mathrm{SO}_4\)) is determined by adding twice the atomic mass of sodium, the atomic mass of sulfur, and four times the atomic mass of oxygen. Here's how we calculate it:

• The atomic mass of sodium (Na) is 23 g/mol.
• The atomic mass of sulfur (S) is 32 g/mol.
• The atomic mass of oxygen (O) is 16 g/mol.

Thus, the molar mass of \(\mathrm{Na}_2\mathrm{SO}_4\) is \(2 \times 23 + 32 + 4 \times 16 = 142\, \text{g/mol}\) .Understanding molar mass allows chemists to convert between the mass of a substance and the amount it contains, providing a bridge between theoretical calculations and practical applications.

Solution Concentration

Solution concentration is a measure that describes the amount of solute present in a given quantity of solvent or solution. It's vital for defining how saturated or diluted a solution is. There are various expressions of concentration, such as molarity, molality, and mass percentage. The mass percentage is a simple concentration metric calculated by dividing the mass of the solute by the total mass of the solution, multiplied by 100. This expresses how much of a solution's mass comes from the solute. Let's say we dissolve \(10.6\, \text{g}\) of \(\mathrm{Na}_2\mathrm{SO}_4\) in \(483\, \text{g}\) of water, the mass percentage can be calculated as follows:

• Calculate the total solution mass: \(10.6\, \text{g} + 483\, \text{g} = 493.6\, \text{g}\)
• Determine the mass percentage: \(\frac{10.6}{493.6} \times 100 = 2.148\,%\)

This shows that \(2.148\,%\) of the solution's mass consists of \(\mathrm{Na}_2\mathrm{SO}_4\) . Such concentration measures are crucial when preparing solutions for experiments or industrial processes.

Parts Per Million (PPM)

Parts per million (ppm) is a unit of measurement for quantifying very dilute concentrations. It's often used for measuring contaminants in air, water, and soil. PPM represents the mass of a substance per one million units of mass of the total solution or mixture. This metric is crucial in environmental science as it helps ensure substances are within permissible limits.To calculate ppm, use the formula:Concentration in ppm = \(\left(\frac{\text{mass of solute}}{\text{mass of solution}}\right) \times 10^{6}\)This calculation can be illustrated using the example of determining the silver concentration in an ore. Here, 2.86 grams of silver are contained in one ton of ore, which is equivalent to \(10^{6}\, \text{g}\). The calculation is as follows:

• Use the formula: \(\frac{2.86}{10^{6}} \times 10^{6} = 2.86\, \text{ppm}\)

This means that for every million grams of ore, there are 2.86 grams of silver. Applying ppm calculations helps in analyzing trace amounts of various substances accurately.