Video: Calculating pOH of Vinegar Using the Concentration of Hydronium Ion

At 25°C, the hydronium ion concentration of vinegar is approximately 4.0 × 10⁻³ M. To 1 decimal place, what is the corresponding value of the pOH?

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Video Transcript

At 25 degrees Celsius, the hydronium ion concentration of vinegar is approximately 4.0 times 10 to the minus three molar. To one decimal place, what is the corresponding value of the POH?

This problem wants us to find the POH of vinegar, which is defined as the negative log of the concentration of hydroxide. But the problem only gives us the concentration of hydronium. To solve this problem, we’re going to make use of the fact that, in any aqueous solution, water can react with itself in a process known as self-ionization or autoionization.

In this equilibrium reaction, water reacts to form the hydronium ion and the hydroxide ion. 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. Since the concentration of water doesn’t significantly change, we don’t have to include it in our equilibrium expression. The equilibrium constant for this reaction, which we call Kw, has a value of 1.0 times 10 to the minus 14 at 25 degrees Celsius.

Since the problem gives us the concentration of hydronium, we have everything we need to solve for the concentration of hydroxide. The first thing I’ve done here is just switched the sides of the equation. So ultimately, we’ll end up with the concentration of hydroxide on the left.

Now we can divide both sides by the concentration of the hydronium ion to obtain an expression for hydroxide. Plugging in both the value of Kw and the concentration of hydronium, we’ll find that the concentration of hydroxide is 2.50 times 10 to the minus 12 molar. Now we can find the POH by taking the negative log of this concentration that we just found. Plugging that in, we’ll find that the POH is 11.602. So rounded to one decimal place, the POH of vinegar is 11.6.

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