Calculate the pH at the equivalence point in titrating 0.100 M solutions of each of the following with 0.038 M NaOH.
(a) hydrobromic acid (HBr)
(b) lactic acid (HC3H5O3)
(c) sodium hydrogen chromate (NaHCrO4)
You have three problems here. The secret to each is to recognize that the pH at the equivalence point is determined by the salt present at that point and what that salt does upon hydrolysis.
a. HBr + NaOH ==> NaBr + H2O
b. HL + NaOH ==> NaL + H2O
c. NaHCrO4 + NaOH ==> Na2CrO4 + H2O
a. Neither Na^+ nor Br^- is hydrolyzed since it is the salt of a strong acid and a strong base; therefore, you have a salt in pure water and the water has a pH of 7.
b. NaL is the salt of a weak acid and a strong base. First you want to find the concn of lactate ion. You don't list a value for volume for the acid so you can't do that. I'll just make up a number of say 0.2M and show you how to do it. The lactate ion is hydrolyzed as follows:
......L- + HOH ==> HL + OH^-
I....0.2...........0.....0
C.....-x...........x.....x
E...0.2-x..........x.....x
Kb for L^- = (Kw/Ka for HL) = (x)(x)/(0.2-x)
Solve for x = (OH-) and convert to pH.
c is the same.
Post your work if you get stuck.
To calculate the pH at the equivalence point in these acid-base titrations, we need to first determine the nature of the equivalence point. The equivalence point occurs when the moles of acid are equal to the moles of base added, resulting in a neutral solution. At this point, the hydronium ion concentration (H3O+) equals the hydroxide ion concentration (OH-), resulting in a pH of 7.
Now let's go through each of the given examples to determine the nature of the equivalence point.
(a) Hydrobromic acid (HBr):
Hydrobromic acid is a strong acid that completely dissociates into its constituent ions in water. Therefore, it produces H3O+ ions in solution. When titrating with a strong base like NaOH, the reaction will proceed as follows:
HBr + NaOH -> NaBr + H2O
Since HBr is a strong acid, it will completely react with NaOH, resulting in a neutral solution at the equivalence point. Therefore, the pH at this point is 7.
(b) Lactic acid (HC3H5O3):
Lactic acid is a weak acid, and it does not completely dissociate in water. To determine the pH at the equivalence point, we need to consider the dissociation constant of lactic acid, Ka. According to the equation below:
HC3H5O3 + H2O -> C3H5O3- + H3O+
The Ka expression for lactic acid is given by:
Ka = [C3H5O3-][H3O+]/[HC3H5O3]
Since we are dealing with a 0.100 M solution, we can assume that the initial concentration of HC3H5O3 is equal to its molarity.
At the equivalence point, all the moles of lactic acid will react with an equal number of moles of NaOH to form sodium lactate (C3H5O3-) and water (H2O). As a result, the concentration of HC3H5O3 will be zero, while the concentrations of C3H5O3- and NaOH will be equal.
Therefore, we can rewrite the Ka expression as:
Ka = [C3H5O3-][H3O+]/0
Since the concentration of HC3H5O3 is zero, the equilibrium shifts to the right, producing more C3H5O3- ions. In this case, taking the logarithm of both sides of the Ka expression and solving for pH gives us the pH at the equivalence point. However, since we have a strong base added, the OH- ion concentration will exceed the H3O+ ion concentration, resulting in a basic solution. Therefore, the exact pH value at the equivalence point of lactic acid and NaOH cannot be accurately determined without considering the initial concentration and Ka value of lactic acid.
(c) Sodium hydrogen chromate (NaHCrO4):
Sodium hydrogen chromate is a salt composed of a weak acid (HCrO4-) and its conjugate base (CrO4^2-). The reaction between NaHCrO4 and NaOH can be expressed as follows:
NaHCrO4 + NaOH -> Na2CrO4 + H2O
At the equivalence point, all the moles of NaHCrO4 will react with an equal number of moles of NaOH to form Na2CrO4 and water. The resulting solution will contain only the conjugate base, CrO4^2-, making the solution basic. However, since NaHCrO4 is a salt composed of a weak acid and a weak base, the exact pH value at the equivalence point cannot be accurately determined without considering the initial concentrations and relevant equilibrium constants.
In summary, the pH at the equivalence point for:
(a) Hydrobromic acid (HBr) is 7 (neutral).
(b) Lactic acid (HC3H5O3) is higher than 7 (basic), but the exact pH value cannot be determined without additional information.
(c) Sodium hydrogen chromate (NaHCrO4) is higher than 7 (basic), but the exact pH value cannot be determined without additional information.
To calculate the pH at the equivalence point, we need to determine the species present in the solution at that point. At the equivalence point, the moles of acid will be equal to the moles of base added. Let's calculate the number of moles of each compound first.
(a) Hydrobromic acid (HBr):
Moles of HBr = concentration * volume = 0.100 M * volume
(b) Lactic acid (HC3H5O3):
Moles of HC3H5O3 = concentration * volume = 0.100 M * volume
(c) Sodium hydrogen chromate (NaHCrO4):
Moles of NaHCrO4 = concentration * volume = 0.100 M * volume
Since we are titrating with NaOH, the moles of the acid/base will react with the same number of moles of the base/acid, resulting in a neutral solution at the equivalence point. To find the volume at the equivalence point, we can use the formula:
Moles of HBr / Volume at equivalence point = Moles of NaOH / Volume of NaOH added
Similarly, we can set up the same equation for lactic acid and sodium hydrogen chromate.
Now let's calculate the volume of NaOH needed to reach the equivalence point for each compound:
(a) Volume at equivalence point for HBr = (0.100 M * volume) / 0.038 M
(b) Volume at equivalence point for HC3H5O3 = (0.100 M * volume) / 0.038 M
(c) Volume at equivalence point for NaHCrO4 = (0.100 M * volume) / 0.038 M
At the equivalence point, the moles of acid will react completely with the moles of the base, resulting in a neutral solution. To calculate the pH at the equivalence point, we need to consider the dissociation of the acid or base in water.
(a) For HBr:
HBr is a strong acid, so it dissociates completely in water. The resulting solution will contain only H+ ions, making it acidic. Thus, the pH at the equivalence point will be less than 7.
(b) For HC3H5O3:
Lactic acid is a weak acid, so it does not dissociate completely in water. The resulting solution will contain a mixture of HC3H5O3 and HC3H5O3-, making it slightly acidic. Thus, the pH at the equivalence point will be slightly less than 7.
(c) For NaHCrO4:
NaHCrO4 is a salt formed by the reaction between a strong base (NaOH) and a weak acid (HCrO4-). The HCrO4- ion will react with water to form H3O+ ions, making the solution slightly acidic. Thus, the pH at the equivalence point will be slightly less than 7.
In summary:
(a) pH at the equivalence point for HBr: less than 7
(b) pH at the equivalence point for HC3H5O3: slightly less than 7
(c) pH at the equivalence point for NaHCrO4: slightly less than 7