Video Transcript
Students find that 15.30
milliliters of aqueous sodium hydroxide solution neutralizes 20.00 milliliters of a
hydrochloric acid solution. The aqueous sodium hydroxide
solution has a concentration of 0.095 moles per liter. What is the unidentified
concentration of the aqueous hydrochloric acid solution? Give your answer to three decimal
places. (A) 0.073 moles per liter, (B)
0.146 moles per liter, (C) 0.037 moles per liter, (D) 0.938 moles per liter, (E)
0.469 moles per liter.
In this question, we must determine
the concentration of an aqueous hydrochloric acid solution from experimental
data. First, we need to write a balanced
chemical equation for the neutralization reaction of sodium hydroxide with
hydrochloric acid.
A neutralization reaction involving
strong acids and bases follows the general pattern shown here. So in the balanced chemical
equation, hydrochloric acid and sodium hydroxide solutions react to produce aqueous
sodium chloride and water. We are told in the problem that
15.30 milliliters of sodium hydroxide base neutralizes 20.00 milliliters of
hydrochloric acid. We also know that the concentration
of the sodium hydroxide solution is 0.095 moles per liter.
Determining the concentration of
the hydrochloric acid solution will involve three steps. First, we need to calculate the
number of moles of base that reacted. Then we need to convert moles of
base to moles of acid using the molar ratio from the balanced chemical equation. Finally, in step three, we will
calculate the molar concentration of the acid.
The units of molar concentration
are moles per liter. So before starting step one, we
should convert our volume measurements from milliliters to liters. To make the conversion from
milliliters to liters, we should divide each measurement by 1000. Let’s take a moment to record these
values in our chart.
To calculate the number of moles of
sodium hydroxide base, let’s make use of the following equation. Let’s multiply the concentration of
the base, which is 0.095 moles per liter, by the volume of the base, which is
0.01530 liters.
Now that we have the number of
moles of base, we need to use the molar ratio from the balanced equation to find the
number of moles of acid that reacted. The molar ratio of hydrochloric
acid to sodium hydroxide in the reaction is one to one. Therefore, the number of moles of
acid that reacted is the same as the number of moles of base. For now, let’s wait to round our
answer until the last step of the calculation.
Next, let’s use the number of moles
of acid and the volume of the acid to calculate the molarity, or molar
concentration, of the acid. We should divide the number of
moles of acid by the volume in liters of acid. Now that we’ve determined the molar
concentration of the hydrochloric acid solution, we must round our answer to three
decimal places. The result is 0.073 moles per
liter.
In conclusion, the concentration of
the aqueous hydrochloric acid solution is 0.073 moles per liter, or answer choice
(A).
