"An aqueous sodium borate solution is titrated to the second endpoint with 0.225 mol/l nitric acid in the presence of a suitable indicator. If an average of 12.6mL of titrant are required to reach the second endpoint for a 25.0 mL sample, what is the base concentration?"
My calculations:
nHNO3: (0.225 mol/l)(12.6 mL)/1000
= 2.835 x 10^-3 mol
nNa3BO3: (2.835 x 10^-3 mol)(1/3)
= 9.45 x 10^-4 mol
[Na3BO3]: (9.45 x 10^-4 mol)/(25 mL)(1000)
= 0.0378 mol/L
Is this correct? Because the answer given is different (0.0567 mol/L).
nHNO3: (0.225 mol/l)(12.6 mL)/1000
= 2.835 x 10^-3 mol
This step is ok.
nNa3BO3: (2.835 x 10^-3 mol)(1/3)
= 9.45 x 10^-4 mol
This step is in error. The problem says that Na3BO3 was titrated to the second end point (meaning two H ions were added) but you divided by 3. You should have divided by 2
[Na3BO3]: (9.45 x 10^-4 mol)/(25 mL)(1000)
= 0.0378 mol/L
Is this correct? Because the answer given is different (0.0567 mol/L).
Another way to approach the problem is to say if 12.6 mL were used to add 2 Hs, then 6.3 would have been used to add 1 H, then go through the remainder of the calculation. I think the answer of 0.0567 M is correct.
Your calculations seem to be correct, but it appears that you made a mistake in the final calculation for the concentration of sodium borate ([Na3BO3]).
To calculate the concentration of sodium borate, you correctly determined the moles of sodium borate (nNa3BO3) to be 9.45 x 10^-4 mol. However, when calculating the concentration, you divided by the volume of the sample in liters (25 mL * 1000), which is incorrect.
To calculate the concentration, you should divide the moles of sodium borate (9.45 x 10^-4 mol) by the volume of titrant used for the second endpoint (12.6 mL * 1000) since the second endpoint refers to when the reaction is complete. Therefore, the correct calculation for the concentration of sodium borate should be:
[Na3BO3] = (9.45 x 10^-4 mol) / (12.6 mL * 1000)
= 0.0567 mol/L
So, it seems that the correct answer is indeed 0.0567 mol/L, which matches the given answer.