Why is my actual percent of sulfate in alum a lot less than my theoretical percent of sulfate in alum?

Actual Percent SO4= 1.68%
Theoretical Percent SO4= 40.5%

I don't know without seeing all of your work. One possibility is that you lost some of the BaSO4 ppt. A second possibility is that you didn't ppt all of the sulfate in the sample due to the conditions; i.e., pH not right, not adding enough BaCl2, etc. Your calculations could be wrong.

Well the questions are confusing, the first question asks to find the mass of sulfate in my 1 gram sample of alum based off of the mass of BaSO4 (0.52g).

The second question then asks to calculate the percent sulfate in my alum, and I don't know if that means my sample of alum or the total mass of alum the reaction produced which was 11.28.

I think the first question is % SO4 in your 1 grams sample.

That is 0.52 x (molar mass SO4/molar mass BaSO4)*100 = about 21% (The mass is about 0.21g)

I think the second question is to calculate the theoretical percent SO4 in your 1 g sample (or any mass sample) so you can compare your experimental value with the theoretical value.
The theoretical % SO4 in alum is about 40%. (96.064*2/474.39)*100 = ?

That sounds right to me..thanks for all of your help.

The difference between the actual and theoretical percent of sulfate in alum could be due to several factors. Here are a few possible reasons:

1. Experimental error: In a laboratory setting, there can be various sources of error, including imprecise measurements, incomplete reactions, or loss of the product during handling or transfer. Such errors can result in a lower actual percentage of sulfate compared to the calculated theoretical value.

2. Impurities: Alum might contain impurities that can affect the measurement of sulfate content. For example, the presence of other compounds or contaminants in the alum sample can interfere with the accurate determination of sulfate content, leading to a lower measured value.

3. Incomplete reaction: The chemical reaction used to produce alum from its precursor compounds may not always proceed to completion. If the reaction is not allowed to reach its equilibrium or if the conditions are not ideal, it can result in an incomplete reaction, leading to a lower yield of sulfate.

4. Sampling error: The sample you used for analysis might not be representative of the entire alum sample. If the sample was poorly chosen or not mixed thoroughly before analysis, it can lead to inaccurate results.

To pinpoint the exact reason for the discrepancy between the actual and theoretical values of sulfate in your alum sample, it would be necessary to further investigate and consider these potential factors. Sometimes repeating the experiment or analyzing multiple samples can help identify and minimize these sources of error.