Question Video: Calculating 𝐾_𝐚 given the Concentration and the Percentage of Dissociation of an Acid Chemistry

Video Transcript

A 0.3 molar solution of benzoic acid was found to be 1.47 percent dissociated. What is the value of 𝐾 𝐚 to two decimal places for this acid? Assume one minus 𝛼 is approximately equal to one.

Benzoic acid is a weak acid. When it is dissolved in water, only a portion of the molecules will dissociate into benzoate ions and hydrogen ions. We are told that 1.47 percent of the acid was found to be dissociated. This means that if we dissolved 100 moles of benzoic acid in water, at equilibrium 1.47 moles will have dissociated into ions, while the remaining 98.53 moles are undissociated. The proportion of the substance that is dissociated is called the degree of dissociation. It is usually represented by the symbol 𝛼 and is typically given as a decimal. We were given the percentage of dissociation. We can convert the percentage of dissociation to a decimal by dividing by 100 percent. So the degree of dissociation of the benzoic acid given in the question is 0.0147.

We want to use the degree of dissociation to calculate the value of 𝐾 𝐚. 𝐾 𝐚 is the acid dissociation constant, an equilibrium constant for the dissociation of an acid in water. The acid dissociation constant and the degree of dissociation can be related using Oswald’s dilution law. In this expression, 𝑐 naught represents the initial concentration of the acid. The question tells us that the concentration is 0.3 molar. We know the degree of dissociation and the concentration. So we could put those values into the expression and solve for 𝐾 𝐚. But the question tells us to assume that one minus 𝛼 is approximately equal to one.

If the denominator of the expression is approximately equal to one, we can rewrite the expression as 𝐾 𝐚 is approximately equal to 𝛼 squared times 𝑐 naught. We can substitute the degree of dissociation and concentration into the expression and perform the calculation to determine the acid dissociation constant. Rounding our answer to two decimal places, we have determined that the value of 𝐾 𝐚 for benzoic acid is 6.48 times 10 to the negative fifth molar or moles per liter.