Video Transcript
20 grams of NaAlH4 reacts with 10
grams of LiCl to produce 8.3 grams of LiAlH4: NaAlH4 plus LiCl react to produce
LiAlH4 plus NaCl, where the molar mass of sodium is 23 grams per mole, chlorine 35.5
grams per mole, aluminium 27 grams per mole, hydrogen one gram per mole, and lithium
seven grams per mole. What is the percentage yield for
this reaction to the nearest whole number?
NaAlH4 is sodium aluminium
hydride. It is also called sodium
alanate. It has a similar composition to
LiAlH4. So, it’s called lithium aluminum
hydride or lithium alanate. LiCl is lithium chloride, and NaCl
is sodium chloride; it is more commonly known as salt. The question asks us to find the
percentage yield. The percentage yield is calculated
by dividing the actual yield by the theoretical yield and multiplying by 100
percent, where the actual yield is the amount of product that is obtained from
carrying out a chemical reaction, and the theoretical yield is the maximum amount of
product that can be formed from the given amounts of reactants.
We’re told in the question that 8.3
grams of lithium alanate is produced. Since this is the amount of product
obtained, it is the actual yield. But to calculate the percentage
yield, we also need the theoretical yield. Our first step in calculating the
theoretical yield is to calculate the number of moles of starting materials that
react. We have been given the masses of
the starting materials in the question. We can use this equation to
calculate how many moles those masses are equivalent to. The equation tells us that you can
calculate the number of moles of a substance by dividing its mass by its molar
mass.
The starting materials can be found
on the left side of the reaction equation. So, they are sodium alanate and
lithium chloride. To calculate the number of moles of
sodium alanate, we divide its mass, which we’re told in the question is 20 grams, by
its molar mass. We can calculate the molar mass of
sodium alanate using the molar masses given in the question. Sodium has a molar mass of 23 grams
per mole. There is only one equivalent in
sodium alanate. So, we multiply this by one.
We then add the molar mass of
aluminum, which is 27 grams per mole, multiplied by the number of equivalents, which
again is one. We then add the molar mass of
hydrogen, which is one gram per mole, multiplied by the number of equivalents of
hydrogen in sodium alanate, which is four. If we perform this calculation, we
get 54 grams per mole. So, the molar mass of sodium
alanate is 54 grams per mole. If we perform this calculation, we
get a value of 0.370 moles.
We now need to do the same for the
other starting material, lithium chloride. We’re told in the question that the
mass of lithium chloride is 10 grams, but we need to calculate its molar mass using
the molar masses given in the question. We need to multiply the molar mass
of lithium, which is seven grams per mole, by the number of equivalents of lithium
and lithium chloride, which is one. We then need to add the molar mass
of chlorine, which is 35.5 grams per mole, multiply it by the number of equivalents
of chlorine, which is also one. If we perform this calculation, we
get a value of 42.5 grams per mole. So, the molar mass of lithium
chloride is 42.5 grams per mole. If we perform this calculation, we
get a value of 0.235 moles.
We have now calculated the number
of moles of starting materials, but not all of these moles of starting materials
will necessarily react. And we need to calculate the number
of moles of starting materials that can react. We can see from the reaction
equation that there’s a one-to-one molar ratio between sodium alanate and lithium
chloride. This means that the number of moles
of sodium alanate and the number of moles of lithium chloride that react are the
same, but the number of moles of sodium alanate and lithium chloride in the reaction
mixture is not the same. There are more moles of sodium
alanate than there are of lithium chloride. Therefore, sodium alanate is in
excess.
The number of moles of sodium
alanate that can react is limited by the lithium chloride. We call lithium chloride the
limiting reagent. The limiting reagent is defined as
the reactant that is first to be completely used up during a chemical reaction. So, a maximum of 0.235 moles of
lithium chloride will react. And since there’s a one-to-one
ratio between lithium chloride and sodium alanate, a maximum of 0.235 moles of
sodium alanate will react too. We have now calculated the number
of moles of starting materials that can react.
The next step is to calculate the
maximum number of moles of product, which is lithium alanate, that can be
produced. We have already seen that there’s a
one-to-one molar ratio between sodium alanate and lithium chloride. But there is also a one-to-one
molar ratio between sodium alanate and lithium alanate and lithium chloride and
lithium alanate. So, one mole of sodium alanate
reacts with one mole of lithium chloride to produce one mole of lithium alanate and
also one mole of sodium chloride. So, there is a one-to-one-to-one
ratio between the number of moles represented by the letter n of sodium alanate,
lithium chloride, and lithium alanate.
We have already calculated that
0.235 moles of lithium chloride and 0.235 moles of sodium alanate will react. As the molar ratio is the same for
the reactants and the key product, we can determine that 0.235 moles of product will
be produced. So, we’ve now calculated the
maximum number of moles of product, which is 0.235 moles of lithium alanate that can
be produced.
Our next step is to convert the
number of moles of product to grams. This will give us the theoretical
yield. To do this, we can again use the
equation that the number of moles is equivalent to the mass divided by the molar
mass. But since we want to convert to
grams, we need to make the mass the subject. We can do this by multiplying both
sides of the equation by the molar mass. The molar mass terms on the
right-hand side of the equation will cancel, leaving us with the mass equals the
number of moles multiplied by the molar mass.
We have already calculated the
number of moles of lithium alanate to be 0.235. We need to multiply this by its
molar mass, which we can calculate using the molar masses given in the question. We need to multiply the molar mass
of lithium, which is seven grams per mole, by the number of equivalents of lithium
in lithium alanate, which is one.
We then need to do the same for
aluminum and hydrogen and add all of the values up. If we perform this calculation, we
get a value of 38 grams per mole. So, the molar mass of lithium
alanate is 38 grams per mole. If we perform this calculation, we
get a value of 8.93 grams. Therefore, the theoretical yield of
the product lithium alanate is 8.93 grams.
We can now calculate the percentage
yield. If we perform this calculation, we
get a value of 92.945 percent. So, the percentage yield for this
reaction is 92.945 percent. But the question asks for the
percentage yield to be given to the nearest whole number. 92.945 to the nearest whole number
is 93. So, the answer to the question
“What is the percentage yield for this reaction to the nearest whole number?” is 93
percent.
