Video Transcript
Scientists are attempting to
determine the identity of element X in a compound with the chemical formula
X2CO3. They combine 1.19 grams of the
unidentified carbonate with water to produce a 250.0-cubic-centimeter solution. They put 25.00 cubic centimeters of
this solution into a conical flask. They subsequently titrate this
conical flask solution with 0.1-molar hydrochloric acid. The following table shows the
result of their titration experiment. What is the most likely identity of
the unidentified element in the compound with the chemical formula X2CO3? The molar mass of sodium is 23
grams per mole. Lithium is seven grams per
mole. Potassium is 39 grams per mole. Magnesium is 24 grams per mole. Aluminum is 27 grams per mole. Carbon is 12 grams per mole. And oxygen is 16 grams per
mole. (A) Lithium, (B) potassium, (C)
sodium, (D) magnesium, (E) aluminum.
In this question, we must figure
out the name of the unidentified element X in the compound with the chemical formula
X2CO3. We are told that a titration
experiment is carried out by adding hydrochloric acid solution to an aqueous
solution of the carbonate compound. Before we begin our problem-solving
process, let’s clear some space to work.
The type of titration that is being
carried out by the scientists is an acid–base titration. In an acid–base titration, a
neutralization reaction is used to help determine the amount or concentration of a
substance. In this problem, a carbonate base
is reacted with hydrochloric acid. When a metal carbonate reacts with
an acid, a salt, carbon dioxide, and water are produced. Since the charge of a carbonate
anion is two minus, the charge of each X ion in the neutral carbonate compound must
be one plus. Therefore, X ions will combine with
chloride ions in a one-to-one ratio to form the salt. Therefore, to balance the chemical
equation, we will need to use a coefficient of two in front of the acid and the
salt.
Initially, 1.19 grams of the
carbonate compound is dissolved in water to make 250.0 cubic centimeters of
solution. The scientists then measure out
only 25.00 cubic centimeters of the solution into a conical flask. So how much carbonate compound is
in this smaller solution? By setting up a proportion, we can
see that if the volume of the solution decreases by a factor of 10, then the mass of
the dissolved compound also decreases by a factor of 10. So there is only 0.119 grams of the
carbonate compound in the conical flask. Since we know the scientists are
going to add the hydrochloric acid to the conical flask, then only 0.119 grams of
the carbonate compound will react. We know that the concentration of
the hydrochloric acid solution is 0.1 molar, or 0.1 moles per liter.
In the data table, we can see that
in two titration trials, or titers, 22.40 cubic centimeters of hydrochloric acid was
needed to neutralize all of the base in the conical flask. It’s important to remember that one
cubic centimeter is equivalent to one milliliter. So now, we know that the volume of
the acid used in the experiment was 22.40 milliliters. However, since molar concentration
is expressed in units of moles per liter, let’s convert the volume of the acid from
milliliters to liters. To perform the conversion, we must
divide by 1000, which gives us 0.02240 liters.
Now, let’s clear some space to
begin performing our calculations. First, let’s determine the amount
of moles of acid that reacted using the following equation. We should multiply the
concentration of the acid, which is 0.1 moles per liter, by the volume of the acid,
which is 0.02240 liters. The result is 0.00224 moles of
acid. Now we need to convert moles of
acid to moles of base by using the molar ratio from the balanced equation. We can see from the equation that
one mole of the carbonate compound reacts with two moles of hydrochloric acid. Therefore, we need to divide the
number of moles of acid by two.
Now, we can use the number of moles
of base and the mass of the base to determine its molar mass. Let’s make use of the following
equation. We need to divide the mass of the
base, which is 0.119 grams, by the number of moles of base, which is 0.00112
moles. We get 106.25 grams per mole. We can set up an equation to solve
for the molar mass of just X. Let’s bring the molar masses that
we’re given in the problem back up onto the screen. After substituting the values for
the molar masses of carbon and oxygen, we get the following equation. After rearranging and simplifying
the equation, we can now solve for X. We find that the molar mass of X is
23.125 grams per mole. We can see that the element that
has a molar mass closest to the value we calculated is sodium.
In conclusion, the most likely
identity of the element X in the compound X2CO3 is sodium, or answer choice (C).
