# Question Video: Calculating the Concentration of OH⁻ Ions in a Solution of Pyridine Given Its 𝐾_b Chemistry

What is the concentration of OH⁻ ions in a 0.15 mol/L solution of pyridine? The 𝑘_b value for pyridine is 1.8 × 10⁻⁹ mol/L. Give your answer to 2 decimal places.

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### Video Transcript

What is the concentration of OH− ions in a 0.15 moles per liter solution of pyridine? The 𝑘 𝑏 value for pyridine is 1.8 times 10 to the negative nine moles per liter. Give your answer to two decimal places.

This question deals with the 𝑘 𝑏, or base dissociation constant. The base dissociation constant is the equilibrium constant for the reaction of a base with water. The general reaction for a base and water is shown. The species behaving as a base accepts a proton from water. This produces hydroxide ions in solution.

This question is asking us to find the concentration of hydroxide ions in this solution of pyridine. We can express the base dissociation constant as the equilibrium concentrations of the products multiplied together then divided by the equilibrium concentration of the base. At equilibrium, the concentration of the conjugate acid and hydroxide ions will be stoichiometrically equivalent. Because of this, we can simplify this expression. We can rewrite the 𝑘 𝑏 as equal to the concentration of hydroxide ions squared divided by the concentration of the base.

We are given the 𝑘 𝑏 value for the base, pyridine. We are also given the initial concentration of pyridine. This expression, however, is only representative of the reaction at equilibrium. The 𝑘 𝑏 value is very low, and thus this equilibrium reaction favors the reactants highly. Therefore, we can assume the initial and equilibrium concentrations of the base will be extremely similar. We can use the initial concentration in the expression when 𝑘 𝑏 is very small. So we can rearrange the expression to solve for the hydroxide ion concentration.

First, we can multiply both sides by the concentration of the base. We can rewrite the expression as concentration of the base times the 𝑘 𝑏 is equal to the hydroxide ion concentration squared. To solve for the hydroxide ion concentration, we can take the square root of both sides.

Now that we have an expression to solve for the hydroxide ion concentration, we can substitute the values given. We multiply the concentration of the base, 0.15 moles per liter, by the value of the 𝑘 𝑏 of pyridine, which is 1.8 times 10 to the negative nine moles per liter. We can then take the square root of the product, which we get to be 2.7 times 10 to the negative 10, with units of moles squared per liter squared. When we take the square root of the units, we get the unit of moles per liter. When we take the square root of 2.7 times 10 to the negative 10, we get the value of the hydroxide ion concentration in moles per liter.

The question tells us to give our answer to two decimal places. So we can round our numerical answer to 1.64 times 10 to the negative five. Therefore, the concentration of hydroxide ions in a 0.15 moles per liter solution of pyridine with a 𝑘 𝑏 value of 1.8 times 10 to the negative nine moles per liter is 1.64 times 10 to the negative five moles per liter.