### Video Transcript

A scientist is given the chemical
formula and relative formula mass of two unknown compounds, as shown below: chemical
formula XY2, M r equals 64; chemical formula XY3, M r equals 80. If the atomic mass of element X is
twice that of element Y, which of the following are elements X and Y? The relative atomic mass of sulfur
is 32, oxygen is 16, nickel is 59, silicon is 28, carbon is 12, magnesium is 24,
neon is 20, argon is 40, lithium is seven, and nitrogen is 14. (A) X equals Ni; Y equals Si. (B) X equals S; Y equals O. (C) X equals Li; Y equals N. (D) X equals Ne; Y equals Ar. Or (E) X equals C; Y equals Mg.

To answer this question, we need to
determine the identity of elements X and Y by comparing their relative atomic mass
to the relative atomic masses given. But in the question, we aren’t
provided with the relative atomic mass of X and Y. But we are provided the relative
formula mass, also called the relative molecular mass, of two compounds that contain
only elements X and Y. The relative formula or molecular
mass is a ratio of the average mass of one molecule or formula unit to one twelfth
of the mass of a carbon-12 atom. The relative formula mass of a
molecule or formula unit can be calculated by summing the relative atomic masses of
the constituent atoms.

For example, a molecule of carbon
dioxide contains one carbon atom and two oxygen atoms. The relative atomic mass of carbon
is 12, and the relative atomic mass of oxygen is 16. So the relative molecular mass of
carbon dioxide will be equal to 12 plus two times 16. We multiply 16 by two because there
are two atoms of oxygen in the chemical formula. So the relative molecular mass of
carbon dioxide is 44. Let’s apply this understanding to
the first unknown compound. As we don’t know the relative
atomic mass of X and Y, let’s define these as the variables X and Y for
simplicity.

We know that the relative formula
mass of XY2 will be equal to the relative atomic mass of X plus two times the
relative atomic mass of Y. We also know that the relative
formula mass of this compound is 64. This gives us the equation 64
equals X plus two Y. We are also told that the atomic
mass of element X is twice that of element Y. So we can set up a second
equation. The relative atomic mass of X
equals two times the relative atomic mass of Y. Since we now have a relationship
for the value of X, we can substitute this into the first equation. This gives us 64 equals two Y plus
two Y. We can combine like terms then
divide both sides of the equation by four. This gives us a value of 16 for
Y. We can then substitute this value
into the second equation, giving us X equals two times 16, or X equals 32.

Now that we know that the relative
atomic mass of X is 32 and the relative atomic mass of Y is 16, we can compare these
values to the values given in the question. We can see that a relative atomic
mass of 32 corresponds to the element sulfur and a relative atomic mass of 16
corresponds to the element oxygen. Therefore, element X must be sulfur
and element Y must be oxygen. So from the relative formula mass
and chemical formulas of two unknown compounds, we have determined that the elements
X and Y are X equals S and Y equals O, answer choice (B).