Video Transcript
The table below shows the results
of titrating 0.02 decimeters cubed of barium hydroxide against 0.2 molar of
hydrochloric acid. Using the results in the table and
discounting any anomalies, determine the concentration of barium hydroxide. Give your answer to two decimal
places.
Looking at the data, we can see
that titration one and titration three required very similar volumes of hydrochloric
acid. Titration two, however, required
over 10 milliliters more of hydrochloric acid. This data is inconsistent with the
other two trials and should be discounted as an anomaly. We can then take the volume of HCL
solution added in titration one and titration three and find the average volume of
HCL. Performing the calculation gives us
an average volume of 61.5 milliliters.
Next, we can write a balanced
chemical equation between barium hydroxide and hydrochloric acid. We can see that the reaction of
barium hydroxide, a base, with hydrochloric acid, the acid, produces barium chloride
— a salt — and water. Be careful and ensure that the
chemical equation is balanced by adding appropriate coefficients before continuing
on with the rest of the problem.
Next, recall the key equation for
solving titration problems: 𝑛 equals 𝑐𝑣, where 𝑛 represents the amount in moles,
𝑐 is the concentration in moles per liter, and 𝑣 is the volume in liters.
We can make a table to match the
values given in the question with the variables of our key equation. We will also record the molar ratio
of the acid and base. This titration required 0.02
decimeters cubed of barium hydroxide. Recall that one decimeter cubed is
the same as one liter. We can then add our volume to the
table with the unit liters instead of decimeters cubed. The barium hydroxide solution was
titrated against a 0.2-molar solution of hydrochloric acid. We can add this concentration to
our table in the appropriate box, recognizing that molar and moles per liter are
equivalent units.
We also know the average volume of
hydrochloric acid used in the experiment. The volume is in milliliters but
must be converted into liters in order for the liters and the concentration unit to
cancel when solving. Recognize that 1000 milliliters are
equivalent to one liter. We can multiply the 61.5
milliliters by one liter per 1000 milliliters. The unit milliliters will cancel,
giving us a volume of 0.0615 liters. Ultimately, we would like to solve
for the concentration of barium hydroxide.
Now that the given values have been
filled into the table, we are ready to solve the problem. We can substitute our hydrochloric
acid concentration and volume into the key equation to determine the number of moles
of hydrochloric acid to be 0.0123 moles. Now that we know the number of
moles of acid used, we can determine the number of moles of base used in the
titration.
Looking at our balanced chemical
equation, we can see that the molar ratio of barium hydroxide to hydrochloric acid
is one to two. As the molar ratio is not one to
one, we will need to perform a calculation to convert moles of hydrochloric acid
into moles of barium hydroxide. We begin this process with the
moles of hydrochloric acid. We then multiply this value by the
molar ratio written as a fraction with moles of hydrochloric acid in the denominator
so that the units cancel out. We perform the calculation and
determine the number of moles of barium hydroxide to be 0.00615 moles.
Next, we can rearrange our key
equation to solve for the concentration of barium hydroxide. We can substitute our barium
hydroxide amount and volume and determine the concentration of barium hydroxide to
be 0.3075 molar. But the question asks us for an
answer rounded to two decimal places. Rounding our answer appropriately
gives us a final concentration of 0.31 molar.
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