Video Transcript
An aqueous solution at 25 degrees Celsius has an H+ concentration of two times 10 to the negative nine molar. What is the value of OH− concentration to the nearest whole number?
In this problem, we’ve been given a concentration for hydrogen ions, and we’ve been asked to solve for the concentration of hydroxide ions. To solve this problem, we need to understand the relationship between these two chemical species. Molecules of water can react with each other, forming the hydronium ion and the hydroxide ion. For simplicity, this equation is often represented with one molecule of water instead of two and a hydrogen ion instead of a hydronium ion. However, hydrogen ions don’t exist by themselves in solution for very long as they react easily with water to form the hydronium ion. We’ll see this expression as an equilibrium reaction, which means we can write an equilibrium expression for it.
The equilibrium expression is equal to the concentration of hydrogen ions times the concentration of hydroxide ions. The equilibrium constant for this reaction is called 𝐾 𝑤. 𝐾 𝑤 has a value of one times 10 to the negative 14 at 25 degrees Celsius. If we divide both sides of the 𝐾 𝑤 expression by the concentration of the hydrogen ions, we’ll end up with an equation that we can use to solve for the concentration of hydroxide ions. We can plug in the value for 𝐾 𝑤 and the value for the concentration of hydrogen ions, which was given in the problem. This gives us five times 10 to the negative six.
Since this quantity is the concentration of the hydroxide ion, it has units of molar. We can see the value of the concentration for the hydroxide ion is greater than the concentration of the hydrogen ions in the solution. A solution is acidic, basic, or neutral depending on the concentrations of both the hydrogen and hydroxide ions. As we said, the hydroxide ion concentration is greater than the hydrogen ion concentration, so this solution is basic. But this problem only asked that we determine the concentration of hydroxide, which is five times 10 to the negative six molar.
