What was the concentration of HBr in the original HBr solution in mol L-1 ?

Question

A 22.6 mL solution of HBr (a strong acid) of unknown concentration was titrated using 0.4383 mol L^-1 NaOH using phenolphthalein as a pH indicator. At the moment when the solution turned a consistent light pink colour, the burette volume read 28.95 mL. The initial burette reading before the experiment was 7.97 mL. What was the concentration of HBr in the original HBr solution in mol L^-1 ?

Answer 1

This is a titration problem where the reaction of HBr in the unknown solution with a known volume and concentration of base, NaOH (referred to as the titrant) is used to determine the amount of HBR in the unknown solution. First, you need to establish the mole ratio of HBr to NaOH in the reaction:

HBr + NaOH → H₂O + NaBr (for simplicity NaBr, HBr and NaOH are not shown ionized, although they are all completely ionized in solution, since they are strong electrolytes)

The mole ratio of HBr to NaOH is 1:1, so this makes our calculation pretty simple.

The moles of NaOH used to completely neutralize the HBr should be equal to the number of moles of HBr in the unknown solution. So let’s calculate the moles of NaOH used.

We know that molarity (M) = moles per liter and we can calculate the volume of NaOH used by subtracting the initial burette reading from the final burette reading:

V_NaOH = 28.95 – 7.97 mL = 20.98 mL. Convert this to liters in order to be consistent with the dimension of molarity, which is moles/liter.

(20.98 mL)(1 L/1000 mL) = 0.02098 L NaOH

We get the moles of NaOH by multiplying this volume by the known titrant molarity:

Moles NaOH = (.02098 L)(0.4383 moles/L) = 9.196 x 10^-3 moles = moles HBr

because mole ratio of NaOH to HBr is 1:1.

Given that the volume of the unknown HBr solution is 22.6 mL, we can obtain its molarity by dividing number of moles by number of liters. As with NaOH, convert volume to liters (L).

(22.6 mL)(1 L/1000 mL) = 0.0226 L

9.196 x 10^-3 moles HBr         = 0.407 moles/L  HBr – this is the concentration of the original

    .0226 L HBr                                                                                  HBr solution

The last step in solving any problem is to evaluate your answer to see if it makes sense. First check the unit (moles/L is correct). Next, given that the mole ratio of HBr to NaOH is 1:1 and the volume of the unknown solution is slightly more than the volume of NaOH used to neutralize it, we are expecting the molarity of the unknown solution to be slightly LESS than that of the titrant. The calculated answer satisfies this condition, indicating that our problem solving process is most likely right.