Problem 35 - Chemistry: The Central Science

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?

Step-by-Step Solution

Answer

(a) The mass percentage of Na2SO4 in the solution is 2.15 %. (b) The concentration of silver in the ore is 2.86 ppm.

Step 1: Calculate the total mass of the Na2SO4 solution

The solution contains 10.6 g of Na2SO4 dissolved in 483 g of water. To find the total mass of the solution, we add the masses of the solute (Na2SO4) and the solvent (water). Total mass of the solution = Mass of Na2SO4 + Mass of water Total mass = 10.6 g + 483 g Total mass = 493.6 g

Step 2: Calculate the mass percentage of Na2SO4

Now that we know the total mass of the solution, we can calculate the mass percentage of Na2SO4. The mass percentage is the mass of the solute divided by the total mass of the solution, multiplied by 100. Mass percentage of Na2SO4 = (Mass of Na2SO4 / Total mass of the solution) x 100 Mass percentage = (10.6 g / 493.6 g) x 100 Mass percentage = (0.0215) x 100 Mass percentage = 2.15 % (a) The mass percentage of Na2SO4 in the solution is 2.15 %.

Step 3: Convert the mass of silver per ton of ore to grams

In the second part of the exercise, we are given that there are 2.86 g of silver in one ton of ore. Since we will need to express the concentration of silver in ppm, we should first convert the mass of silver to grams. One ton is equal to 1,000,000 grams. Mass of silver = 2.86 g Mass of ore = 1 ton = 1,000,000 g

Step 4: Calculate the concentration of silver in ppm

Now that we have the mass of silver and the mass of ore in grams, we can easily calculate the concentration of silver in ppm. Silver concentration in ppm = (Mass of silver / Mass of ore) x 1,000,000 Silver concentration in ppm = (2.86 g / 1,000,000 g) x 1,000,000 Silver concentration in ppm = 2.86 ppm (b) The concentration of silver in the ore is 2.86 ppm.