# Question Video: Calculating the Degree of Dissociation of a Solution of Phenol Given the Acid Dissociation Constant Chemistry

To 1 decimal place, what is the degree of dissociation for a 0.25 M solution of phenol at 25°C? The dissociation constant 𝐾_𝑎 is 1.6 × 10⁻¹⁰ M.

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### Video Transcript

To one decimal place, what is the degree of dissociation for a 0.25-molar solution of phenol at 25 degrees Celsius? The dissociation constant 𝐾 𝑎 is 1.6 times 10 to the negative 10th molar.

The degree of dissociation, often represented by the symbol 𝛼, is the proportion of a substance that is dissociated. The degree of dissociation can be calculated by dividing the amount of the dissociated substance by the total amount of substance, where the amount can be given as the number of molecules or moles.

To answer this question, we need to determine the degree of dissociation for a solution of phenol. But the question does not provide us with the total amount of substance nor the amount of dissociated substance. So we cannot make use of this equation. The question does provide us with the acid dissociation constant for the solution of phenol at a given temperature. The acid dissociation constant is the equilibrium constant for the dissociation of an acid in water. Phenol is a weak acid that only partially dissociates when dissolved in water. As only a very small amount of phenol molecules will dissociate, the concentration of ions in solution at equilibrium will be very low, while the concentration of the acid will remain virtually unchanged.

The acid dissociation constant and the degree of dissociation can be related using Ostwald’s dilution law. Ostwald’s dilution law states that the acid dissociation constant is equal to the degree of dissociation squared divided by one minus the degree of dissociation times the initial concentration of the acid. For weak acids like phenol, where only a small percentage of the molecules dissociate, the degree of dissociation is very small. So, one minus the degree of dissociation is approximately equal to one. This means that for weak acids, Ostwald’s dilution law can be simplified to 𝐾 𝑎 is approximately equal to 𝛼 squared times 𝑐 naught. As we need to solve for the degree of dissociation, we can rearrange this equation to make 𝛼 the subject.

Now we are ready to solve the problem. We can substitute the acid dissociation constant and the concentration given in the question into the equation. Dividing 1.6 times 10 to the negative 10th molar by 0.25 molar gives us 6.4 times 10 to the negative 10th. Square rooting this value gives us the degree of dissociation, 2.5298 times 10 to the negative fifth. The question asks us to give our answer to one decimal place. Rounding appropriately, we have determined that the degree of dissociation for a 0.25-molar solution of phenol at 25 degrees Celsius is 2.5 times 10 to the negative fifth.