Video Transcript
A vanadium compound has the
molecular formula V 𝑥 O 3, where 𝑥 is a whole number. If the percentage by mass of V in V
𝑥 O 3 is 68 percent, what is the value of 𝑥? The molar mass of oxygen is 16
grams per mole and vanadium, 51 grams per mole.
To calculate the percentage by
mass, if we assume that we’re calculating the percentage by mass of element A
present in substance B, then we need to divide the mass of element A by the mass of
substance B and multiply it by 100 percent. More specifically for this example,
element A will be V, vanadium, and substance B will be V 𝑥 O 3, vanadium oxide. So to find the percent by mass of
vanadium in vanadium oxide, we need to divide the mass of vanadium, making sure to
include the subscript value, which in this case is 𝑥, by the mass of vanadium oxide
and multiply by 100 percent.
We have been given the percentage
by mass of vanadium in vanadium oxide in the question. It is 68 percent. To find the mass of vanadium, we
can use the molar mass. The molar mass of vanadium is 51
grams per mole, so one mole of vanadium is 51 grams. Therefore, 𝑥 moles of vanadium
will be 𝑥 times 51 grams. To find the mass of vanadium oxide,
we need to use the molar masses of oxygen and vanadium. We have already established that 𝑥
moles of vanadium is 𝑥 times 51 grams. The molar mass of oxygen is 16
grams per mole, so one mole of oxygen is 16 grams.
We have three equivalents in the
molecular formula of vanadium oxide, so we need to multiply three by 16 grams. Adding 𝑥 times 51 grams and three
times 16 grams will give us the mass of one mole of vanadium oxide. We then need to multiply this by
100 percent. Since we’re trying to find the
value of 𝑥, we need to make 𝑥 the subject. But first, let’s simplify this a
bit. We can divide both sides of the
equation by 100 percent to give us 0.68 equals 𝑥 times 51 grams divided by 𝑥 times
51 grams plus 48 grams.
If we multiply both sides of the
equation by 𝑥 times 51 grams plus 48 grams and then multiply the contents of the
parentheses by 0.68, then we get 34.68𝑥 grams plus 32.64 grams equals 51𝑥
grams. We need to make 𝑥 the subject. So we need to subtract 34.68𝑥
grams from both sides of the equation. So 32.64 grams equals 16.32𝑥
grams. If we divide both sides of the
equation by 16.32 grams, we find that 𝑥 equals two. So the answer to the question “If
the percentage by mass of vanadium in vanadium oxide is 68 percent, what is the
value of 𝑥?” is two.
