A 0.010 M solution of a weak monoprotic acid is 3.0% dissociated. What is the equilibrium constant, Ka, for this acid?
HA = H^+ + A^-
Ka = (H^+)(A^-)/(HA)
initial:
HA = 0.01
H^+ = 0
A^- = 0
change:
H^+ = x
A^- = x
HA = 0.01 - x
equilibrium:
x = 0.01 x 0.03 = ??
Substitute and solve for Ka.
To find the equilibrium constant (Ka) for a weak monoprotic acid that is partially dissociated, we need to use the equation for percent dissociation:
%Dissociation = (Amount dissociated / Initial concentration) × 100
Given that the acid is 3.0% dissociated, it means that 3.0% of the initial concentration has dissociated into its ions.
Let's assume the initial concentration of the acid is [HA], and the amount dissociated is [A-].
%Dissociation = ([A-] / [HA]) × 100
3.0% = ([A-] / [HA]) × 100
Now, since the acid is monoprotic, the moles of HA that dissociate will equal the moles of A- formed.
Since the initial concentration of HA is given as 0.010 M, we can convert 3.0% to decimal form (0.030) and substitute the values into the equation:
0.030 = ([A-] / 0.010) × 100
Simplifying the equation, we get:
0.030 = 10 × [A-]
Dividing both sides of the equation by 10:
0.003 = [A-]
Now, we know the concentration of the dissociated species [A-]. However, since the solution contains a weak acid, it will still have a significant amount of undissociated species [HA].
To find the equilibrium constant Ka, we can write the equilibrium expression for the dissociation reaction:
HA ⇌ H+ + A-
Ka = [H+][A-] / [HA]
Given that [A-] = 0.003 and [HA] = 0.010, we can substitute these values into the equation to calculate Ka:
Ka = (0.003)(0.003) / 0.010
Ka = 0.000009 / 0.010
Ka = 0.0009
Therefore, the equilibrium constant (Ka) for this weak monoprotic acid is 0.0009.
To find the equilibrium constant (Ka) for a weak acid, you need to use the concentration of the acid and the percent dissociation.
The percent dissociation of the acid is given as 3.0%. This means that 3.0% of the initial concentration of the acid has dissociated into H+ ions and its conjugate base.
First, let's convert the percent dissociation to decimal form. The percent dissociation of 3.0% can be written as 0.030.
The concentration of the acid, [HA], can be calculated as follows:
[HA] = Initial concentration - Dissociated concentration
[HA] = 0.010 M - (0.030 * 0.010 M)
[HA] = 0.010 M - 0.0003 M
[HA] = 0.0097 M
Now, let's calculate the concentration of H+ ions in the solution. Since the acid is monoprotic, the concentration of H+ ions will be equal to the percent dissociation:
[H+] = 0.030 * 0.010 M
[H+] = 0.0003 M
Using the equilibrium equation for the dissociation of the acid:
HA ⇌ H+ + A-
The equilibrium constant (Ka) can be expressed as the ratio of the concentration of the products to the concentration of the reactants:
Ka = [H+][A-] / [HA]
Substituting the given values:
Ka = (0.0003 M) / (0.0097 M)
Calculating this value:
Ka ≈ 0.0309
Therefore, the equilibrium constant (Ka) for this acid is approximately 0.0309.