Question Video: Calculating and Comparing the Concentration of Hydroxide from the Proton Concentration of an Aqueous Solution Chemistry

A solution at 25°C has an [OH⁻] of 1.26 × 10⁻⁸ mol/L. Is the solution acidic, basic, or neutral?

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Video Transcript

A solution at 25 degrees Celsius has an OH− concentration of 1.26 times 10 to the minus eight moles per liter. Is the solution acidic, basic, or neutral?

We probably associate OH−, or the hydroxide ion, with basic solutions. After all, bases like sodium hydroxide disassociate to form hydroxide ions in solution. However, hydroxide ions exist in most aqueous solutions, regardless of whether or not the solution is basic. This is because molecules of water can react which forms the hydroxide ion and the hydronium ion, H3O+.

What determines if a solution is acidic, basic, or neutral is the concentrations of the hydroxide and hydronium ions. If the concentrations of the hydronium and hydroxide ions are equal, the solution is neutral. If the concentration of hydronium ions is greater than the concentration of hydroxide ions, the solution is acidic. And the solution is basic if the concentration of hydroxide ions is greater than the concentration of hydronium ions.

So we can figure out if the solution is acidic, basic, or neutral by comparing the hydroxide concentration we were given in the problem to the concentration of hydronium. To solve for this, we’ll use this equilibrium reaction for the autoionization of water. The equilibrium constant for this reaction 𝐾 𝑤 has a value of 1.0 times 10 to the negative 14 at 25 degrees Celsius. The equilibrium expression for this reaction is the concentration of hydronium times the concentration of hydroxide. We leave the molecules of water out of the equilibrium expression because the concentration of water doesn’t change significantly over the course of the reaction. We can plug in the value for 𝐾 𝑤 and the value of the hydroxide ion concentration.

Let’s quickly rearrange this equation so that the concentration of hydronium is on the left. And then we can solve by dividing both sides by 1.26 times 10 to the minus eight. This gives us 7.9365 times 10 to the minus seven, which we can round to one decimal place. And of course, this concentration is in units of moles per liter. Now we can compare the concentrations of hydroxide and hydronium. The hydronium ion concentration is larger than the hydroxide ion concentration, which means the solution is acidic. A solution at 25 degrees Celsius that has a hydroxide concentration of 1.26 times 10 to the minus eight moles per liter is acidic.

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