To two decimal places, what is the pH of 0.000071 molar Ba(OH)₂ at 25 degrees Celsius? Assume Ba(OH)₂ ionizes completely.
We want to find the pH of the solution which is defined as the negative log of the concentration of H₃O⁺. But, we’re only given the concentration of Ba(OH)₂ which will ionize to produce OH⁻, which is a base. In any aqueous solution, water can react with itself in a process known as self-ionization or autoionization.
In this equilibrium reaction, water forms hydronium, or H₃O⁺, and hydroxide, OH⁻. The equilibrium expression for this reaction is equal to the concentration of hydronium times the concentration of hydroxide divided by the concentration of water squared. The equilibrium constant for this expression, which we call K𝑤, has a value of 1.0 times 10 to the minus 14 at 25 degrees Celsius.
Since the concentration of water doesn’t change significantly, we can remove it from this expression. We can use this equilibrium expression to create an equation that we can use to solve for the concentration of hydronium, so that we can find the pH. We can do this by dividing both sides by the concentration of hydroxide. Now, what we need to find the concentration of hydronium is the concentration of hydroxide.
The problem tells us that Ba(OH)₂ ionizes completely. And according to our balanced chemical equation, every one mole of Ba(OH)₂ ionizes to form two moles of OH⁻. So, the concentration of hydroxide will be twice the concentration of Ba(OH)₂. If we plug the concentration of the Ba(OH)₂ in, we’ll find that the concentration of hydroxide is 0.000142 molar.
Now, we can find the concentration of hydronium. We can plug in the value for K𝑤 and the value for the concentration of [hydroxide]. Which gives us a concentration of hydronium of 7.0423 times 10 to the minus 11 molar. Now, we can find the pH by taking the negative log of this concentration. This gives us 10.1523. So, rounding to two decimal places, we get 10.15 for the pH of our Ba(OH)₂ solution.