What ratio [CH3NH3+]/[CH3NH2] is needed to prepare a buffer solution with a pH of 8.60 from methylamine, CH3NH2, and methylammonium chloride, CH3NH3Cl? Kb of CH3NH2 = 3.7e-4.
pH = pKa + log(base/acid)
Subsitute pH, convert pKb to pKa and calculate the ratio of base/acid and reverse that since you want the ratio of acid to base.
To prepare a buffer solution with a pH of 8.60 using methylamine, CH3NH2, and methylammonium chloride, CH3NH3Cl, we need to calculate the ratio [CH3NH3+]/[CH3NH2].
Step 1: Write the equation for the ionization of methylamine in water:
CH3NH2 + H2O ⇌ CH3NH3+ + OH-
Step 2: Calculate the pOH of the buffer solution using the given pH:
pOH = 14 - pH = 14 - 8.60 = 5.40
Step 3: Calculate the concentration of OH- ions using the pOH:
OH- concentration = 10^(-pOH) = 10^(-5.40) = 3.98 × 10^(-6) M
Step 4: Using the concentration of OH- ions, calculate the concentration of CH3NH3+ ions in the buffer solution. Since this is a weak base, we can assume that [OH-] ≈ [CH3NH3+]:
[CH3NH3+] = 3.98 × 10^(-6) M
Step 5: Use the given value of Kb for CH3NH2 to calculate the concentration of CH3NH2. The Kb expression for CH3NH2 is:
Kb = ([CH3NH3+][OH-]) / [CH3NH2]
Plugging in the known values:
3.7 × 10^(-4) = (3.98 × 10^(-6))^2 / [CH3NH2]
Solving for [CH3NH2]:
[CH3NH2] = (3.98 × 10^(-6))^2 / 3.7 × 10^(-4)
= 4.31 × 10^(-8) M
Step 6: Calculate the ratio [CH3NH3+]/[CH3NH2]:
[CH3NH3+]/[CH3NH2] = [CH3NH3+] / [CH3NH2]
= 3.98 × 10^(-6) M / 4.31 × 10^(-8) M
= 92.4
Therefore, the ratio [CH3NH3+]/[CH3NH2] needed to prepare the buffer solution with a pH of 8.60 is 92.4.
To prepare a buffer solution with a desired pH, we need to find the ratio of [CH3NH3+] (methylammonium ion concentration) to [CH3NH2] (methylamine concentration) in the buffer solution.
First, let's understand the chemistry involved. Methylamine (CH3NH2) is a weak base, and when it reacts with water, it can accept a proton (H+) to form the methylammonium ion (CH3NH3+). The equilibrium equation for this reaction is:
CH3NH2 + H2O ⇌ CH3NH3+ + OH-
The equilibrium constant for this reaction is known as the base dissociation constant (Kb). For methylamine, Kb is given as 3.7e-4.
Kb = [CH3NH3+][OH-] / [CH3NH2]
Now, let's determine the concentration of hydroxide ion (OH-) in the solution at pH 8.60. In a solution with a pH of 8.60, the concentration of hydroxide ion can be calculated using the equation:
pOH = 14 - pH
pOH = 14 - 8.60 = 5.40
Now, we can find the concentration of hydroxide ion (OH-) using the equation:
[OH-] = 10^(-pOH)
[OH-] = 10^(-5.40)
Next, we can use the equilibrium constant expression (Kb) to calculate the ratio of [CH3NH3+] to [CH3NH2]. Rearranging the equation:
Kb = [CH3NH3+][OH-] / [CH3NH2]
Since hydroxide ion (OH-) is formed in equimolar amounts with the methylammonium ion (CH3NH3+), we can simplify the equation:
Kb = [CH3NH3+]^2 / [CH3NH2]
Now, let's substitute the values and solve for [CH3NH3+]/[CH3NH2]:
3.7e-4 = ([CH3NH3+]^2) / [CH3NH2]
[CH3NH3+]^2 = 3.7e-4 * [CH3NH2]
[CH3NH3+] = √(3.7e-4 * [CH3NH2])
Finally, calculate the ratio of [CH3NH3+] to [CH3NH2] by dividing [CH3NH3+] by [CH3NH2].