We did a titration lab, and one of the post-lab questions says: "the manufacturer of the vinegar used in this experiment claims that the vinegar contains 5% acetic acid by weight. Use your results and a density of 1g/mL to determine if this claim is true or false.

So the concentration of acetic acid I found in my experiment was 0.8655 M, and i used the molar mass of acetic acid to find that the acetic acid would be 51.98g/mL.

I known that I need to have the mass of the acetic acid and the mass of the vinegar solution to find the percent I'll need, but how do I go from the 51.98 g/mL to just g and how would I find the g of the vinegar solution? (and where does the density come in??)

Thank you in advance!

I don't believe you have 51.98 g/mL but I might believe it is 51.98 g/L.

0.8655 mols/L x 60.05 g/mol = 51.97 by my calculations and that is g/L.
Since you want %, that is 5.197 g/100 mL and since the density is 1 g/mL that is 5.197 g/100 g solution and that is 5.197% by weight.

To determine if the manufacturer's claim about the vinegar's acetic acid content is true or false, you need to calculate the mass percentage of acetic acid using the results of your titration experiment and the given density of 1g/mL.

To proceed, you need to understand how to convert between grams per milliliter (g/mL) and just grams (g).

1. Conversion from g/mL to g:
The given molar mass of acetic acid is 51.98 g/mol. However, you mentioned that you found the molarity of acetic acid to be 0.8655 M. The molarity (M) is defined as the number of moles of solute divided by the volume of the solution in liters (L).
So, you need to find the volume of acetic acid in the titration solution. Assuming you used a specific volume of vinegar in your titration (let's say V_vinegar in mL), and if the stoichiometry between acetic acid and the titrant is 1:1 (which is usually the case), then the volume of acetic acid is also V_vinegar in mL.

Now, you can use the following equation to convert from g/mL to g:
(g/mL) = (g/mol) × (mol/mL) × (mL),
where (g/mol) is the molar mass of acetic acid and (mol/mL) is the molarity of acetic acid.

In your case, you'll use:
(g) = (51.98 g/mol) × (0.8655 mol/mL) × (V_vinegar mL).

2. Calculation of vinegar solution mass:
To determine the mass of the vinegar solution, you need to know the volume of vinegar used in your titration. Let's denote this volume as V_solution in mL.

The density of the vinegar is given as 1g/mL, which means 1mL of vinegar weighs 1g. So, the mass of the vinegar solution is simply:
(g_vinegar solution) = (V_solution mL).

3. Determining the acetic acid mass and percentage:
To calculate the mass of acetic acid in the vinegar solution, subtract the mass of the vinegar solution from the mass of acetic acid calculated using the conversion formula in step 1:
(g_acetic acid) = (g) - (g_vinegar solution).

Finally, to find the percentage of acetic acid by weight, divide the mass of acetic acid by the mass of the vinegar solution and multiply by 100:
(Percentage acetic acid) = [(g_acetic acid) / (g_vinegar solution)] × 100.

By following these steps, you can determine if the manufacturer's claim of 5% acetic acid by weight is true or false based on your titration results and the given density. Remember to substitute the appropriate volumes (V_vinegar and V_solution) from your experiment into the equations for accurate results.