Formic acid, HCOOH, is a common weak acid that is found primarily in wood ants. If 0.02 moles of HCOOH is dissolved into one liter of water at 25 degrees Celsius, what is the concentration of H3O+ if 𝐾 𝑎 of HCOOH is 1.8 times 10 to the negative four? Give your answer to one decimal place.
Formic acid, also known as methanoic acid, is a carboxylic acid containing one carbon atom. By drawing the displayed formula for formic acid, we can clearly see the carboxylic acid functional group within this molecule. It contains a carbon atom doubly bonded to an oxygen atom and singly bonded to another oxygen atom, which is bonded to a hydrogen atom. As a weak acid, when formic acid molecules are placed into water, some of the formic acid molecules disassociate by reacting with the water molecules. Water molecules accept protons from the formic acid molecules and form the hydronium ion. Hydronium ions, sometimes referred to as hydroxonium ions, have the formula H3O+.
In each formic acid molecule, the oxygen-hydrogen bond in the carboxylic acid functional group has broken. After the proton has been donated to the water molecule, a carboxylate anion remains. Since the carboxylate anion is derived from formic acid in this case, it would be called the formate ion, sometimes called the methanoate ion. At 25 degrees Celsius, this reaction eventually reaches an equilibrium, for which we can write the acid dissociation constant.
The acid dissociation constant, or 𝐾 𝑎, expression for this particular reaction would be written as the concentration of H3O+ ions multiplied by the concentration of the formate ions divided by the concentration of the formic acid in the solution. The square brackets placed around each species in this expression denotes concentration units. The concentration of water is not included in this expression as it is very large compared to the other species in the mixture.
From the equation representing the dissociation process, we can see that one formic acid molecule always produces one formate ion and one hydronium ion. Therefore, at equilibrium, the quantity of formate ions released is exactly equal to the quantity of hydronium ions in the equilibrium mixture. We can therefore simplify the 𝐾 𝑎 expression so that it equals the concentration of hydronium ions squared divided by the concentration of the formic acid in the mixture. The 𝐾 𝑎 value for formic acid equals 1.8 times 10 to the negative four. This equates to the concentration of hydronium ion squared divided by the concentration of the formic acid.
Since we are dealing with a weak acid here, the actual amount of dissociation occurring is very, very small. We can therefore assume that the formic acid concentration in this expression will be equivalent to the formic acid concentration before any dissociation took place. In fact, to find this formic acid concentration in our problem, we simply need to take the number of moles of formic acid taken at the start and divide it by the volume of water it was placed in in liters.
Since we placed 0.02 moles of formic acid into one liter of water, the concentration of the formic acid is 0.02 divided by one. We now have a 𝐾 𝑎 expression which shows us that 1.8 times 10 to negative four is equal to the concentration of the hydronium ion squared divided by 0.02. If we multiply both sides of the expression by 0.02, we can get the concentration of hydronium ion squared on its own. The concentration of hydronium ion squared is therefore equal to 1.8 times 10 to negative four multiplied by 0.02. The concentration of hydronium ion squared is equal to 3.6 times 10 to the negative six.
To find the concentration of the hydronium ions to answer this question, we need to find the square root of 3.6 times 10 to negative six. Using a calculator, the numeric answer for this square root operation is approximately 1.8973 times 10 to the negative three. To comply with the question, we need to round our answer to one decimal place. Rounding to one decimal place, we get 1.9 times 10 to the negative three as the concentration of the hydronium ions in this solution. Since we are dealing with moles and liters for volume in this question, our concentration units will be moles per liter.
The correct answer to one decimal place for the concentration of hydronium ions in this formic acid solution is 1.9 times 10 to the negative three moles per liter.