### 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.