Question Video: Calculating the pOH of Perchloric Acid Using the Molarity of Its Aqueous Solution

To 1 decimal place, what is the pOH of a 0.000259 M aqueous HClO₄ solution at 25°C? Assume that HClO₄ ionizes completely.

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Video Transcript

To one decimal place, what is the pOH of a 0.000259 molar aqueous HClO₄ solution at 25 degrees Celsius? Assume HClO₄ ionizes completely.

The pOH of a solution is defined as the negative log of the concentration of OH⁻, or hydroxide. But we’re only given the concentration of HClO₄, which is an acid. In any aqueous solution, water can react with itself in a process known a self-ionization or autoionization. In this equilibrium reaction, water reacts to form H₃O⁺, or hydronium, and OH⁻, or hydroxide.

The equilibrium expression for this reaction is the concentration of hydronium times the concentration of hydroxide divided by the concentration of water squared. However, the concentration of water doesn’t change significantly, so we don’t actually need to include it in this equilibrium expression. The value of the equilibrium constant for this reaction, which we call K w, has a value of 1.02 times 10 to the minus 14 at 25 degrees Celsius.

If we rearrange this equation by dividing both sides by the concentration of hydronium, we’ll have an expression for the concentration of hydroxide, which we need to find the pOH. Now, we need to find the concentration of hydronium. When HClO₄ is put into water, it ionizes to form hydronium H₃O⁺ and ClO₄⁻. We’re told in the problem that HClO₄ ionizes completely. Since HClO₄ in H₃O⁺ have a one to one stoichiometric ratio, the concentrations of HClO₄ and H₃O⁺ must be equal.

Now, we have everything we need to find the concentration of hydroxide. If we plug everything in, we’ll find that the concentration of hydroxide is 3.9382 times 10 to the minus 11 molar. Now, we can find the pOH by taking the negative log of this concentration of hydroxide. Now, if we plug everything in, we’ll see that the pOH is 10.405. So, rounded to one decimal place, the pOH of our HClO₄ solution is 10.4.

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