Question #aa498
1 Answer
Here's how you can approach this problem.
Explanation:
FULL QUESTION
M–nitrophenol, a weak acid, can be used as an indicator because its base,
The pH of a 0.010M solution of the compound is 3.44. What would be the lowest pH at which a solution of the indicator would have a definite yellow colour?
I'll start by saying that your values could be a little off, because this concentration of m-nitrophenol would actually produce a pH of about 5.1 to 5.3.
I'll show you the concept behind this problem and you can double-check your values if you want.
So, what this problem wants you to do is recognize the fact that you're dealing with a weak acid that does not dissociate completely in aqueous solution.
When placed in aqueous solution, this acid will exist both as an acid, and a conjugate base, the ratio beyween these two forms ultimately being determined by the solution's pH.
The degree of dissociation for any weak acid depends on its acid dissociation constant,
#HIn_((aq)) + H_2O_((l)) rightleftharpoons H_3O_((aq))^(+) + In_((aq))^(-)#
The first thing that you need to do is determine the value of the acid dissociation constant. To do that, use the fact that the concentration of hydronium ions can be calculated using pH by
#[H_3O^(+)] = 10^(-pH)#
In your case, you have
#[H_3O^(+)] = 10^(-3.44) = 3.63 * 10^(-4)"M"#
You can work your way backward from this value to determine
#HIn_((aq)) + H_2O_((l)) rightleftharpoons H_3O_((aq))^(+) + In_((aq))^(-)#
I......0.010....................................0..................0
C.......(-x).....................................(+x)...............(+x)
E.....0.010-x.................................x...................x
You know that
#K_a = ([H_3O^(+)] * [In^(-)])/([HIn])#
#K_a = (3.63 * 10^(-4) * 3.63 * 10^(-4))/(0.010 - 3.63 * 10^(-4)) = 1.37 * 10^(-5)#
Now, a very useful tool to have when dealing with an acid is its
#pK_a = -log(K_a)#
In your case, you have
#pK_a = - log(1.37 * 10^(-5)) = 4.86#
The value of the
Since the acid's dissociation is an equilibrium reaction, think of what will happen if you decrease pH.
When you decrease pH, you actually increase the concentration of hydronium ions (or protons,
The concentration of the conjugate base will decrease as a result of this shift. The weak acid will be the dominant form and the solution will be colorless. This happens when pH is smaller than
On the other hand, is you increase the pH, i.e. decrease the concentration of the hydronium ions, the equilibrium will shift to the right.
More acid will be consumed and more conjugate base will be produced. If the pH is high enough, then the conjugate base will be the dominant form and the solution will be yellow.
At
So, in order for the solution to have a definite yellow color, you need the conjugate base form to dominate the solution. This means that the pH must be greater than
Now, the color change for m-nitrophenol takes place over a pH range of about
#pH_"sol" = 4.86 + 1 = color(green)(5.86)#
the solution would have a definite yellow color.
SIDE NOTE You could also use the Henderson-Hasselbalch equation to try and explain why this is the case
#pH_"sol" = pK_a + log((["conjugate base"])/(["weak acid"]))#
Once again, a pH smaller than
When pH is bigger than