Video Transcript
A magnesium halide salt has the
formula MgX2. A 0.593-gram sample of MgX2 was
dissolved in 100 milliliters of deionized water, followed by the addition of excess
NaOH. The precipitate of MgOH2 was
filtered, washed, and dried. The precipitate was found to have a
mass of 0.187 grams. What is the identity of X? (A) I, (B) F, (C) Br, (D) Cl.
In this question, we’re being asked
to find the identity of X which will be the halogen that’s responsible for the
halide ion in the ionic salt MgX2. The halogen present as the halide
ion in MgX2 could be iodine, fluorine, bromine, or chlorine. With this in mind, the actual
formula of MgX2 could be MgI2, MgF2, MgBr2, or MgCl2. Firstly, we need to look at the
reaction that occurs between the magnesium halide salt and NaOH, which is sodium
hydroxide. Both are dissolved in water, so
these are aqueous solutions. We are told in this question that
one of the products is MgOH2. This is magnesium hydroxide, which
is an insoluble precipitate. The other product of this reaction
will be a combination of the sodium ions and the halide ions from the two reactants
concerned. Sodium halides are soluble, so this
product is an aqueous solution.
We now need to balance this
equation. We can see from the formula for
magnesium hydroxide that one mole of magnesium hydroxide contains two moles of
hydroxide ions. This makes sense as the magnesium
ion is present as a two plus ion and the hydroxide ions are one minus ions. The charges must balance up, so we
need two hydroxide ions for every magnesium two plus ion. We therefore need two moles of
sodium hydroxide. This will provide two moles of
sodium ions and two moles of hydroxide ions on the left side of our equation, which
will balance with the hydroxide ions on the right side. We therefore need to form two moles
of NaX, our sodium halide, which will contain two moles of sodium ions. Two moles of NaX also contains two
moles of X−, or halide ions, which balance with the two moles of halide ions in the
magnesium halide salt we started with.
This equation is now balanced, and
we can use it with the quantitative data provided in the question. We know in this question that the
mass of magnesium hydroxide precipitate collected was 0.187 grams. Since we know the precise
composition of magnesium hydroxide from its formula, we can find the molar mass of
magnesium hydroxide. This equates to 58.3 grams per
mole. The moles of magnesium hydroxide
produced can then be found by taking its mass in grams and dividing it by the molar
mass in grams per mole. The moles of magnesium hydroxide is
therefore 0.0032.
We can link the moles of magnesium
hydroxide formed to the moles of magnesium halide salt in the analyte using the mole
ratio in the balanced equation. One mole of magnesium hydroxide
originates from one mole of magnesium halide salt. There must therefore have been
0.0032 moles of the magnesium halide salt in the sample. Since the 0.0032 moles of magnesium
halide salt was found in 0.593 grams of sample, we can use this information to find
the molar mass.
Since we now have the moles and the
mass for the magnesium halide salt, we can use this information to find the molar
mass of the magnesium halide salt itself. The molar mass of MgX2 is the mass
of the sample divided by the number of moles that it contains. The molar mass of MgX2 is therefore
185.3 grams per mole. Using the atomic mass from
magnesium, we can find the atomic mass for the element X in this magnesium halide
salt. By subtracting the atomic mass for
magnesium from the molar mass of the magnesium halide salt, we have the mass of
twice the halogen present. Twice the atomic mass of the
halogen present equates to 161. The atomic mass of the halogen X is
therefore 161 divided by two, which equals 80.5.
We need to bear in mind that this
will not be the precise atomic mass of our halogen X, as it’s derived from
experimental data where there are errors. The only halogen with an atomic
mass close to 80.5 is bromine. The atomic mass of bromine is
79.9. The correct answer is therefore
bromine.
