You have a vinegar solution you believe to be 0.53 M. You are going to titrate 20.72 mL of it with a NaOH solution that you know to be 0.974 M. At what volume of added NaOH solution would you expect to see an end point?

To determine the volume of added NaOH solution at the end point, we need to calculate the number of moles of acetic acid in the vinegar solution and then determine how many moles of NaOH are required to completely react with those moles of acetic acid.

First, let's calculate the number of moles of acetic acid in the vinegar solution:

Moles of acetic acid = molarity × volume (in liters)
= 0.53 mol/L × (20.72 mL / 1000 mL/L)
= 0.011 mannols

Next, we'll determine the mole ratio between acetic acid and NaOH from the balanced chemical equation:

CH3COOH + NaOH → CH3COONa + H2O

From the equation, we can see that it takes 1 mole of acetic acid to react with 1 mole of NaOH.

So, the number of moles of NaOH needed to react with the acetic acid is also 0.011 mol.

Now, let's determine the required volume of the 0.974 M NaOH solution to reach the end point:

Moles of NaOH = molarity × volume (in liters)

0.011 mol = 0.974 mol/L × volume (in liters)

volume (in liters) = 0.011 mol / 0.974 mol/L

volume (in liters) ≈ 0.0113 L

Finally, convert the volume to milliliters:

Volume (in mL) = 0.0113 L × 1000 mL/L

Volume (in mL) ≈ 11.3 mL

Therefore, you would expect to see the end point around 11.3 mL of the NaOH solution added.