Final answer:
To determine the purity of the alum preparation, calculate the moles of Al2O3, convert it to moles of pure alum using the mole ratio, and then use the molar mass of alum to determine the mass of pure alum. Divide the mass of pure alum by the initial sample mass and multiply by 100 to get the purity percentage, which is approximately 51%.
Step-by-step explanation:
To determine the purity of the alum preparation, one must first understand the reaction that took place. The aluminum in alum reacts to form aluminum oxide (Al2O3) upon ignition. Now, we calculate the moles of Al2O3 produced using its molar mass (101.96 g/mol).
The moles of Al2O3 will be 0.1357 g divided by 101.96 g/mol, which gives us approximately 0.00133 moles. Since the mole ratio of alum to aluminum oxide is 1:1, this would also be the moles of pure alum.
Next, we use the molar mass of alum, K2SO4Al(SO4)3*24H2O, which is 474.39 g/mol to determine the theoretical mass of the pure alum that would produce the measured amount of Al2O3.
Multiplying the moles of alum by its molar mass gives us the expected mass of pure alum, which is 0.00133 moles * 474.39 g/mol = 0.6317 g.
Finally, to calculate the % purity, we divide the expected mass of pure alum (0.6317 g) by the initial sample mass (1.2391 g) and multiply by 100.
This calculation gives us a purity percentage of about 51%.