Video Transcript
The concentration of a sample of
milk of magnesia, Mg(OH)2, was determined by titration with phosphoric acid,
H3PO4. 30 milliliters of milk of magnesia
required 54.8 milliliters of 0.5 molar phosphoric acid to neutralize it. The equation for this reaction is
shown. Two H3PO4 plus three Mg(OH)2 react
to form six H2O plus Mg3(PO4)2. What was the concentration of the
milk of magnesia?
This question is asking us to
calculate the concentration of a sample of milk of magnesia by using the results of
a titration experiment. A titration is a quantitative
analytical method used to determine the concentration of an analyte using a known
concentration of a second solution.
The titration experiment described
in this problem is an acid–base titration. During the experiment, phosphoric
acid, or H3PO4, is added to milk of magnesia, which contains the base, magnesium
hydroxide, or Mg(OH)2. A neutralization reaction takes
place, producing water and the salt magnesium phosphate. The molar ratio of acid to base is
two to three.
Let’s clear some space to record
the experimental data provided in the problem.
The concentration of phosphoric
acid in this experiment is 0.5 molar. The volume of phosphoric acid
needed to neutralize the milk of magnesia is 54.8 milliliters. The volume of the milk of magnesia
used in the experiment is 30 milliliters. And the goal of this problem is to
calculate the molar concentration of the milk of magnesia.
Solving this problem involves three
steps. First, we need to calculate the
number of moles of acid used. Then, we need to convert moles of
acid to moles of base using the molar ratio from the balanced equation. Finally, in step three, we will
calculate the molar concentration of the base. Before starting step one, we need
to convert the volume measurements from milliliters to liters by multiplying by one
liter per 1000 milliliters. Let’s add these values to our chart
and get started.
To find the number of moles of acid
used, we can use the following equation, in which the number of moles equals
molarity in moles per liter multiplied by volume in liters. We will multiply 0.5 moles per
liter by 0.0548 liters, which allows us to cancel the units liters. The result is 0.0274 moles of
H3PO4.
Now, we can use the molar ratio
from the balanced chemical equation to convert from moles of acid to moles of
base. We will multiply 0.0274 moles of
H3PO4 by three moles of Mg(OH)2 per two moles of H3PO4, which allows us to cancel
out the units moles of H3PO4. The result is 0.0411 moles of
Mg(OH)2.
Now that we know the number of
moles of base that reacted, we can calculate the molar concentration. To calculate the molar
concentration, or molarity, we should divide the number of moles of base by the
volume of the base. Therefore, we need to divide 0.0411
moles by 0.03 liters. The result is 1.37 moles per
liter. We can also represent the units
moles per liter with an uppercase M.
In conclusion, based on the results
of the titration experiment, the concentration of the milk of magnesia is 1.37
molar.
