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

The mass percentage of Na2SO4 in the solution is calculated as follows: \(Mass~Percentage = \frac{10.6~g}{10.6~g + 483~g} \times 100 = 2.15\% \). The concentration of silver in ppm in the ore is calculated as follows: \( Concentration~(ppm) = \frac{2.86~g}{2000 \times 453.592~g/ton} \times 10^6 = 3.16~ppm \).

Step-by-step solution

Write the mass percentage formula.

Mass percentage of a solute in a solution can be calculated using the following formula: \[Mass~Percentage = \frac{mass~of~solute}{mass~of~solution} \times 100\] We are given the mass of Na2SO4 (10.6 g) and mass of water (483 g). We need to calculate the mass percentage of Na2SO4 in this solution.

Calculate the mass of the solution.

The mass of the solution can be calculated by adding the mass of the solute (Na2SO4) and the mass of the solvent (water). In this case, the mass of the solution is: \[Mass~of~solution = 10.6~g (Na_{2}SO_{4}) + 483~g (Water)\]

Calculate the mass percentage of Na2SO4.

Now, we can use the mass percentage formula to calculate the mass percentage of Na2SO4 in the solution. We have the mass of Na2SO4 (10.6 g) and the mass of the solution (calculated in step 2). So, the mass percentage is: \[Mass~Percentage = \frac{10.6~g}{10.6~g + 483~g} \times 100\] Now for part (b),

Write the formula to find the concentration of silver in ppm.

The formula to find the concentration of a solute in ppm (parts per million) is as follows: \[Concentration (ppm) = \frac{mass~of~solute}{mass~of~solution} \times 10^6\] In this case, we are given the mass of silver (2.86 g) per ton of ore and asked to find the concentration of silver in ppm.

Convert the mass of ore to grams.

We are given the mass of ore is 1 ton. To use the formula, we need the mass of the ore in grams. We know that 1 ton equals 2000 pounds and 1 pound is 453.592 grams. So, 1 ton of ore equals (2000 x 453.592) grams.

Calculate the concentration of silver in ppm.

Now we can use the concentration formula to find the concentration of silver in ppm in the ore. We have the mass of silver (2.86 g) per ton of ore and the mass of the ore (in grams, calculated in step 2). So, the Concentration of silver in ppm is: \[Concentration~(ppm) = \frac{2.86~g}{2000 \times 453.592~g/ton} \times 10^6\]