Calculate the pH at the equivalence point for the titration of 0.180 M methylamine (CH3NH2) with 0.180 M HCl. The Kb of methylamine is 5.0× 10^–4.
At the equivalence point we have the salt, CH3NH3Cl and it will hydrolyze to give you an acidic solution. (salt) at the equivalence point is 0.09M.
.........CH3NH3^+ + H2O == H3O^+ + CH3NH2
I.........0.09..............0........0
C...........-x..............x........x
E.......0.09-x..............x........x
Kb = (CH3NH2)(H3O^+)/((CH3NH3^+)
Substitute and solve for x = (H3O^+) and convert to pH.
To calculate the pH at the equivalence point of the titration between methylamine (CH3NH2) and HCl, we first need to determine the stoichiometry of the reaction.
The balanced chemical equation for the reaction between methylamine and HCl is:
CH3NH2 + HCl -> CH3NH3+ + Cl-
In this reaction, one mole of methylamine reacts with one mole of HCl to form one mole of methylammonium ion (CH3NH3+) and one mole of chloride ion (Cl-).
At the equivalence point, the moles of methylamine will be equal to the moles of HCl. Therefore, we need to determine the volume of HCl required to reach the equivalence point.
To calculate the volume of HCl required, we can use the Molarity (M) and volume (V) relationship:
M1V1 = M2V2
Where:
M1 = initial molarity of HCl
V1 = initial volume of HCl
M2 = final molarity of HCl (which is 0.180 M in this case)
V2 = volume of HCl at the equivalence point (unknown)
Let's assume the initial volume of HCl is V1 and solve for V2:
(0.180 M)(V1) = (0.180 M)(V2)
V2 = V1
This means that at the equivalence point, the volumes of HCl and methylamine will be the same.
Now, let's determine the number of moles of methylamine at the equivalence point. We can use the molarity and volume relationship again, knowing that the volume of methylamine will also be V1:
(0.180 M)(V1) = moles of methylamine
Now that we know the moles of methylamine at the equivalence point, we can calculate the concentration of the methylammonium ion (CH3NH3+) at the equivalence point. Since one mole of methylamine reacts to form one mole of methylammonium ion, the concentration of methylammonium ion will be equal to the moles of methylamine divided by the total volume of the solution (V1 + V2):
[CH3NH3+] = moles of methylamine / (V1 + V2)
Now, let's calculate [CH3NH3+]:
[CH3NH3+] = moles of methylamine / (V1 + V1)
[CH3NH3+] = moles of methylamine / (2V1)
[CH3NH3+] = (0.180 M)(V1) / (2V1)
[CH3NH3+] = 0.090 M
Now, since the equilibrium reaction between methylamine and water can be represented as:
CH3NH3+ + H2O <=> CH3NH2 + H3O+
The equilibrium constant for this reaction is the Kb of methylamine, which is given as 5.0× 10⁻⁴.
Since we have found the concentration of methylammonium ion ([CH3NH3+]), we can use the Kb value to calculate the concentration of hydronium ion (H3O+).
Kb = ([CH3NH2][H3O+]) / [CH3NH3+]
We can rearrange this equation to solve for [H3O+] as follows:
[H3O+] = (Kb * [CH3NH3+]) / [CH3NH2]
[H3O+] = (5.0× 10⁻⁴ * 0.090 M) / 0.180 M
Now, let's calculate [H3O+]:
[H3O+] = 2.50× 10⁻⁴ M
Finally, to find the pH at the equivalence point, we can use the formula:
pH = -log[H3O+]
pH = -log(2.50× 10⁻⁴)
Now, let's calculate the pH:
pH ≈ 3.60 (rounded to two decimal places)
Therefore, the pH at the equivalence point for the titration of 0.180 M methylamine with 0.180 M HCl is approximately 3.60.
To calculate the pH at the equivalence point of a titration, you need to determine the concentration of the resulting salt formed at the equivalence point. In this case, the titration is between methylamine (CH3NH2) and hydrochloric acid (HCl).
Methylamine (CH3NH2) is a weak base, and hydrochloric acid (HCl) is a strong acid. The reaction between them can be represented as follows:
CH3NH2 + HCl → CH3NH3+Cl-
Since both the initial concentration of methylamine and hydrochloric acid are the same (0.180 M), the equivalence point is reached when the number of moles of methylamine is equal to the number of moles of hydrochloric acid.
First, let's determine the concentration of methylamine (CH3NH2) and hydrochloric acid (HCl) at the equivalence point:
Number of moles of methylamine at equivalence point = Number of moles of HCl at equivalence point
Let "x" be the number of moles of methylamine reacted. Since the initial concentration of methylamine is 0.180 M and the volume of the solution is not given, we can assume that the volume is V L.
Number of moles of methylamine = 0.180 * V * x
Since the reaction is 1:1, the number of moles of hydrochloric acid at equivalence point is also equal to x.
Number of moles of hydrochloric acid = x
Now, let's calculate the concentration of the resulting salt, methylammonium chloride (CH3NH3+Cl-), at the equivalence point:
Concentration of methylammonium chloride = (Number of moles of CH3NH3+Cl- at equivalence point) / (Volume of solution)
At the equivalence point, the moles of methylammonium chloride formed will be equal to the moles of methylamine initially present:
Concentration of methylammonium chloride = (0.180 * V * x) / V
Concentration of methylammonium chloride = x
Since methylamine (CH3NH2) is a weak base, it can react with water to undergo hydrolysis and produce hydronium ions (H3O+). This reaction can be represented as follows:
CH3NH2 + H2O ⇌ CH3NH3+ + OH-
The Kb for methylamine is given as 5.0 × 10^–4. Kb is the equilibrium constant for the hydrolysis reaction, and it can be used to calculate the concentration of hydroxide ions (OH-) at equilibrium.
Kb = [CH3NH3+][OH-] / [CH3NH2]
Since the concentration of methylammonium chloride at the equivalence point is equal to the moles of methylamine reacted (x), we can substitute the values into the Kb expression:
5.0 × 10^–4 = (x * [OH-]) / 0.180
Simplifying the equation, we get:
x * [OH-] = 5.0 × 10^–4 * 0.180
x * [OH-] = 9.0 × 10^–5
The concentration of hydroxide ions ([OH-]) can be approximated as twice the concentration of methylammonium chloride at equilibrium:
[OH-] = 2 * x
Substituting the value of x, we get:
[OH-] = 2 * 9.0 × 10^–5
[OH-] = 1.8 × 10^–4
Now, let's calculate the concentration of hydronium ions (H3O+) at equilibrium, which is equal to the concentration of hydroxide ions ([OH-]):
[H3O+] = [OH-] = 1.8 × 10^–4
Using the definition of pH, we can calculate the pH at the equivalence point:
pH = -log[H3O+]
pH = -log(1.8 × 10^–4)
pH ≈ 3.74
Therefore, the pH at the equivalence point for the titration of 0.180 M methylamine (CH3NH2) with 0.180 M HCl is approximately 3.74.