To calculate the weight percent of the mustard in the prepared solution, you need to use the following formula:
Weight percent = (mass of mustard / total mass of solution) x 100
In this case, the mass of mustard is given as 3.809 grams, and the total mass of the solution is 49.401 grams.
Substituting these values into the formula:
Weight percent = (3.809 / 49.401) x 100
Weight percent = 7.713%
So, the weight percent of the mustard in the prepared solution is approximately 7.713%.
Now, let's move on to the next parts of the problem. To calculate the number of grams of acetic acid in the sample of mustard solution, we need to use the given information that 3.91E-5 moles of NaOH were required to titrate a 0.775 gram sample of mustard solution.
First, we need to find the molar ratio between acetic acid and NaOH. From the balanced equation of the reaction between acetic acid (CH3COOH) and NaOH:
CH3COOH + NaOH → CH3COONa + H2O
We can see that the molar ratio is 1:1. This means that 1 mole of acetic acid reacts with 1 mole of NaOH.
Next, we can calculate the number of moles of acetic acid present in the sample using the given moles of NaOH. Since the molar ratio is 1:1, the number of moles of acetic acid is also 3.91E-5 moles.
Now, we can find the molar mass of acetic acid. The molar mass of carbon (C) is approximately 12.01 g/mol, the molar mass of hydrogen (H) is approximately 1.008 g/mol, and the molar mass of oxygen (O) is approximately 16.00 g/mol. Adding these together gives us a molar mass of acetic acid (CH3COOH) as:
12.01 + (3 x 1.008) + 16.00 = 60.05 g/mol
Finally, we can calculate the grams of acetic acid using the formula:
Grams = moles x molar mass
Grams = 3.91E-5 moles x 60.05 g/mol
Grams = 0.00234 grams
So, the number of grams of acetic acid in the sample of mustard solution is approximately 0.00234 grams.
To calculate the weight percent of acetic acid in this titrated sample, we can use the following formula:
Weight percent = (mass of acetic acid / mass of sample) x 100
In this case, the mass of acetic acid is 0.00234 grams and the mass of the sample is 0.775 grams. Substituting these values into the formula:
Weight percent = (0.00234 / 0.775) x 100
Weight percent = 0.302%
So, the weight percent of acetic acid in this titrated sample is approximately 0.302%.
Finally, to calculate the weight percent of acetic acid in the original package of mustard prepared above, we need to use the concept of conservation of mass. Since the acetic acid didn't go anywhere during the preparation of the solution, the weight percent of acetic acid in the original package must be the same as in the titrated sample, which is approximately 0.302%.
I hope this explanation helps you understand how to approach and solve these problems!