The average of (0 + 1.6/2) = 0.8; therefore,
pKa = 0.8
pKa = 0.8
You got the correct pka value, but you need to take the anti log of that value to get Ka.
Answer is 0.158
pH = pKa + log([A-]/[HA])
Where pH is the desired pH (in this case, pH=1.6), pKa is the negative logarithm of the acid dissociation constant, [A-] is the concentration of methyl violet in its basic form, and [HA] is the concentration in its acidic form.
Since we know the pH and want to find the pKa, we can rearrange the equation:
pKa = pH - log([A-]/[HA])
Now, let's substitute the given values into the equation:
pH = 1.6
To determine the [A-]/[HA] ratio, we need to consider the range of pH provided (pH=0 to pH=1.6).
When pH=0, the concentration of [HA] is equal to [A-], so the ratio is 1.
When pH=1.6, the concentration of [HA] is 10 times higher than [A-], so the ratio is 1/10.
Now we have all the values to calculate the pKa:
pKa = 1.6 - log(1/10)
Simplifying the equation:
pKa = 1.6 + log(10)
Taking the logarithm of 10 is 1:
pKa = 1.6 + 1
Therefore, the pKa value of methyl violet is 2.6.
We can convert the pKa to the Ka value using the equation:
Ka = 10^(-pKa)
Substituting the pKa value we found:
Ka = 10^(-2.6)
Calculating:
Ka ≈ 2.5 x 10^(-3)
Therefore, the Ka value of methyl violet is approximately 2.5 x 10^(-3).