Answer:
3.24
Explanation:
The dissociation equation for the carboxylic acid can be represented as follows:
RCOOH —-> RCOO- + H+
We can use an ICE table to get the value of the concentration of the hydrogen ion. ICE stands for initial, change and equilibrium.
RCOOH RCOO- H+
Initial 0.2 0.0. 0.0
Change -x +x. +x
Equilibrium 0.2-x. x. x
We can now find the value of x as follows:
Ka = [RCOO-][H+]/[RCOOH]
(1.66* 10^-6) = (x * x)/(0.2-x)
(1.66 * 10^-6) (0.2-x) = x^2
x^2 = (3.32* 10^-7) - (1.66*10^-6)x
x^2 + (1.66 * 10^-6)x - (3.32* 10^-7) = 0
Solving the quadratic equation to get x:
x = 0.0005753650094369094 or - 0.0005753650094369094
As concentration cannot be negative, we discard the negative answer
Hence [H+] = 0.0005753650094369094
By definition, pH = -log[H+]
pH = -log(0.0005753650094369094)
pH = 3.24
