Calculating Mass of Aluminum Sulfate for Desired Sulfate Ion Concentration

Introduction

To determine the mass of aluminum sulfate required to achieve a specific sulfate ion concentration in a given volume of solution, it is essential to understand the relationship between moles of sulfate ions and the required amount of the salt. This calculation is crucial in various applications, from laboratory experiments to industrial processes. In this article, we will go through the-step-by-step process to find the mass of aluminum sulfate (Al2(SO4)3) needed to achieve a sulfate ion concentration of 0.45 M in 250 mL of solution.

Step-by-Step Calculation

The goal is to find the mass of aluminum sulfate needed to achieve a sulfate ion concentration of 0.45 M in 250 mL of solution. Here’s how you can do it:

Step 1: Determine the Total Moles of Sulfate Ions Needed

The volumes and concentrations are given as:

tVolume of solution 250 mL 0.250 L tConcentration of sulfate ions, [SO42-] 0.45 M

The moles of sulfate ions can be calculated as follows:

[ text{Moles of } text{SO}_4^{2-} text{Concentration} times text{Volume} 0.45 text{ mol/L} times 0.250 text{ L} 0.1125 text{ mol} ]

Step 2: Relate Moles of Sulfate Ions to Moles of Aluminum Sulfate

The formula for aluminum sulfate is Al2(SO4)3, which dissociates into 2 aluminum ions and 3 sulfate ions:

[ text{Al}_2text{SO}_4_3 rightarrow 2 text{Al}^{3 } 3 text{SO}_4^{2-} ]

Since 3 moles of sulfate ions are produced by 1 mole of aluminum sulfate, the moles of aluminum sulfate needed can be calculated as follows:

[ text{Moles of } text{Al}_2text{SO}_4_3 frac{text{Moles of } text{SO}_4^{2-}}{3} frac{0.1125 text{ mol}}{3} 0.0375 text{ mol} ]

Step 3: Calculate the Mass of Aluminum Sulfate Required

The molar mass of aluminum sulfate, Al2(SO4)3, can be calculated as follows:

tMolecular weight of Al: 26.98 g/mol tMolecular weight of S: 32.07 g/mol tMolecular weight of O: 16.00 g/mol

[ text{Molar mass of Al}_2text{SO}_4_3 (2 times 26.98 text{ g/mol}) (3 times 32.07 text{ g/mol}) (4 times 16.00 text{ g/mol}) ]

[ text{Molar mass of Al}_2text{SO}_4_3 (53.96 text{ g/mol}) (96.21 text{ g/mol}) (64.00 text{ g/mol}) 214.17 text{ g/mol} ]

The mass of aluminum sulfate needed can be calculated using the formula:

[ text{Mass} text{Moles} times text{Molar mass} 0.0375 text{ mol} times 214.17 text{ g/mol} approx 8.07 text{ g} ]

This calculation shows that to achieve a sulfate ion concentration of 0.45 M in 250 mL of solution, you would need to dissolve approximately 8.07 grams of aluminum sulfate (Al2(SO4)3) in the solution.

Alternative Solution: Addressing the Alternative Calculation

The alternative solution provided uses a different method but leads to a different result. Here is an analysis:

The equation [ 342 g/mol text{Al}_2text{SO}_4_3 ] is not directly relevant to the calculation. Using the correct relationship, the molar mass of aluminum sulfate is 342.17 g/mol, not 342 g/mol. Furthermore, the sulfate ion concentration is 0.45 M, and the stoichiometry of the dissociation is 3:1 for sulfate to aluminum sulfate.

The correct calculation should follow the steps previously outlined. However, the alternative solution attempts to use the relation:

[ text{3/5 X 0.45 M} ]

This implies a different stoichiometry, which is not correct. The correct relation is 3 moles of sulfate ions for every 1 mole of aluminum sulfate.

The correct calculation using the provided values would be:

[ text{Molality} 0.75 M ]

[ V 0.250 L ]

[ text{Mass} text{Molality} times text{Volume} times text{Molar Mass} 0.75 times 0.250 times 342.17 approx 64.12 text{ g} ]

Thus, the correct mass of aluminum sulfate needed is 64.12 grams, aligning with the correct chemical and mathematical principles.

Conclusion

The mass of aluminum sulfate required to achieve a specific sulfate ion concentration in a given volume of solution can be accurately calculated by following the principles of stoichiometry and moles. Misinterpretations of the stoichiometry or incorrect molar mass values can lead to erroneous results. Accurate calculations are crucial for laboratory and industrial applications where precise concentrations are necessary.