A salicyclic acid (MW= 138.123 g/mol) solution has a pH of 2.43. When 100 ml of this solution was evaporated 0.22g of dry salicylic acid was recovered. What is the Ka of salicylic acid?
mols SA = grams/molar mass = about 0.0015 but that's approximate.
M = mols/L = 0.0015/0.1 = about 0.015 approximaately.
pH = 2.43, pH = -log(H^-) so (H^+) = about 0.004 and that's approximate.
..........SA ==> H^+ + A^-
I........0.015...0.....0
C.........-x.....x......x
E......0.015-x....x.....x
Ka = (H^+)(A^-)/(HA)
Substitute from the E line (you know x from the above information) and solve for Ka.
what is x?
I solved the pH part before starting work on the second part. It's approximately 0.004M as I posted.
To find the Ka of salicylic acid, we need to make use of the equation for the acid dissociation constant (Ka), which is the ratio of the concentration of the dissociated acid (H+) and the unionized acid (SA). The equation can be written as:
Ka = [H+][SA] / [SAH]
In this case, we have the mass of the dry salicylic acid (0.22g) that was recovered after evaporation, and we can convert it to moles using the molar mass of salicylic acid (MW = 138.123 g/mol). The number of moles can be calculated as:
moles of salicylic acid (SA) = mass / MW = 0.22g / 138.123 g/mol
Next, we need to determine the concentration. Since the initial volume of the solution was 100 ml, we need to convert it to liters:
volume = 100 ml = 0.1 L
The concentration of the salicylic acid (SA) in the solution can be calculated as:
concentration = moles of salicylic acid / volume
Now that we have the concentration of the salicylic acid (SA), we can use the pH of the solution to find the concentration of the hydronium ion ([H+]). The pH can be converted to [H+] using the equation:
pH = -log[H+]
[H+] = 10^(-pH)
The concentration of the hydronium ion ([H+]) is equal to the concentration of the dissociated acid (H+). Therefore, [H+] = [H+].
Finally, we can substitute the values into the equation for Ka:
Ka = [H+][SA] / [SAH]
Since [H+] = [H+] (simplifying) and [SA] = concentration of salicylic acid, the equation becomes:
Ka = [H+] / [SAH]
Now, we have all the necessary data to calculate the Ka value.