To solve this problem, we need to follow these steps:
(a) Calculate the percent of BaS in the precipitate:
Let's denote:
- W₁ = weight of BaSO₄ precipitate obtained (0.4604 g)
- W₂ = weight of BaS formed during the heating process
We know that the total initial weight of the compound was 0.2841 g (Na₂SO₄). After the heating process, some BaSO₄ converted to BaS, so the total weight will still be 0.2841 g:
0.4604 g (BaSO₄) + W₂ (BaS) = 0.2841 g (initial weight)
Solving for W₂:
W₂ = 0.2841 g - 0.4604 g
W₂ = -0.1763 g
This negative weight doesn't make physical sense in this context, indicating there might be an error in the problem setup or data.
(b) Calculate the percent error of the analysis:
Percent error is calculated using the formula:
Percent Error = (|Experimental Value - Theoretical Value| / Theoretical Value) * 100
In this case, the experimental value is the weight of the precipitate obtained (0.4604 g), and the theoretical value would be the expected weight of BaSO₄ if all the BaSO₄ in the sample had precipitated and none had converted to BaS.
The theoretical weight of BaSO₄ can be calculated by considering the molar mass of Na₂SO₄ and BaSO₄:
Molar mass of Na₂SO₄ = 22.99 * 2 + 32.07 + 15.999 * 4 = 142.04 g/mol
Molar mass of BaSO₄ = 137.33 + 32.07 + 15.999 * 4 = 233.39 g/mol
Using the molar ratios of Na₂SO₄ and BaSO₄, the theoretical weight of BaSO₄ in the sample would be:
Theoretical Weight of BaSO₄ = (Molar mass of BaSO₄ / Molar mass of Na₂SO₄) * Initial Weight of the Sample
Theoretical Weight of BaSO₄ = (233.39 g/mol / 142.04 g/mol) * 0.2841 g
Theoretical Weight of BaSO₄ = 0.4665 g
Now we can calculate the percent error:
Percent Error = (|0.4604 g - 0.4665 g| / 0.4665 g) * 100
Solving this will give you the percent error of the analysis.
Please note that the negative value obtained for the weight of BaS in part (a) indicates a problem with the problem setup or data provided. Double-check the values and equations to ensure accuracy.