# Question Video: Calculating the Concentration of H⁺ Ions Given the Acid Dissociation Constant and Degree of Dissociation Chemistry

A weak acid with a dissociation constant of 1.54 × 10⁻⁵ mol/L is found to be 1.26% dissociated. What is the concentration of H⁺ ions? Give your answer to 2 decimal places.

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### Video Transcript

A weak acid with a dissociation constant of 1.54 times 10 to the negative fifth moles per liter is found to be 1.26 percent dissociated. What is the concentration of H plus ions? Give your answer to two decimal places.

A weak acid, represented in this generic equation as HA, is an acid that only partially dissociates in aqueous solution to produce H+ and A− ions. The strength of the acid can be quantified by its acid dissociation constant. An acid dissociation constant is the equilibrium constant for the dissociation of an acid in water. It can be calculated by dividing the equilibrium concentrations of H+ and A− by the equilibrium concentration of the acid. As acid strength increases, more of the acid molecules will dissociate into H+ and A− ions and the equilibrium constant will be larger.

In this question, we’ve been given the acid dissociation constant of the weak acid. We’ve also been told what percentage of the acid dissociates. This value is the degree of dissociation. The degree of dissociation and acid dissociation constant 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 all times the initial concentration of the acid.

For weak acids, where only a very small percentage of the acid molecules dissociate, one minus the degree of dissociation can be approximated to one. So, Ostwald’s dilution law can be approximated to 𝐾 𝑎 equals 𝛼 squared times 𝑐 naught. Since we’ve been given the acid dissociation constant and degree of dissociation, we can use Ostwald’s dilution law to calculate the initial concentration of the weak acid. We’ve been given the degree of dissociation as a percentage, but before we can substitute it into the equation, we need to convert the percentage into decimal form by dividing by 100 percent.

Now, we can substitute the 𝐾 𝑎 and 𝛼 into Ostwald’s dilution law. The degree of dissociation squared is 1.5876 times 10 to the negative fourth. Rearranging to solve for 𝑐 naught, we find that the initial concentration of the acid is 0.0970 moles per liter. To answer the question, we need to solve for the concentration of H+ ions at equilibrium. One mole of acid produces one mole of H+ ions and one mole of A minus ions. This means that the concentrations of H+ and A− in the solution will be equal. So, we can rewrite the 𝐾 𝑎 expression as 𝐾 𝑎 equals the concentration of H+ times the concentration of H+ divided by the concentration of HA. This can further be simplified to 𝐾 𝑎 equals the concentration of H+ squared divided by the concentration of HA.

Earlier, we calculated the initial concentration of the acid, but what about the equilibrium concentration? For a weak acid like this one, where only a small percentage of the molecules dissociate, we can say that the initial concentration of the acid is approximately equal to the equilibrium concentration of the acid.

With this in mind, we can substitute the acid dissociation constant and acid concentration into the equation. Multiplying both sides of the equation by the acid concentration gives us 1.4938 times 10 to the negative six moles squared per liters squared equals the concentration of H+ ions squared. Square rooting both sides of the equation gives us the concentration of H+ ions, 1.2222 times 10 to the negative third moles per liter. Rounding our answer to two decimal places, we have determined that the concentration of H+ is 1.22 times 10 to the negative third moles per liter.