### Video Transcript

An experiment is performed to
determine the amount of hydrogen gas released in a reaction. Hydrogen gas is released by
reacting hydrochloric acid with zinc metal according to the given equation. Zn solid plus 2HCl aqueous react to
form ZnCl₂ aqueous plus H₂ gas. All the zinc metal was consumed,
and hydrogen gas was collected by displacement of water in an inverted bottle. The following data is obtained. What is the amount of zinc used, in
moles? A) 2.0 times 10 to the minus three
mole. B) 9.8 times 10 to the minus three
mole. C) 2.3 times 10 to the minus two
mole. D) 3.0 times 10 to the minus two
mole. Or E) 4.3 times 10 to the minus one
mole.

In the experiment that’s described
in this question, zinc metal and hydrochloric acid or HCl are reacted. And then the gas that’s produced as
a result of this reaction, hydrogen gas, is collected in a different container over
water. In this part of the question, we’re
simply tasked with finding the amount of zinc that’s used in moles. The mass of zinc that was used in
the experiment is the first entry in the data table. It’s 0.13 grams. In the problem, we’re told that all
of the zinc metal was consumed. So to find the amount of zinc that
was used in the experiment, we simply have to convert the mass of zinc that was used
to the amount of zinc used in moles.

The amount of a substance in moles
is equal to its mass divided by the molar mass, which we can find using the periodic
table. The mass of zinc given in the
problem is 0.13 grams. And the molar mass of zinc is 65
grams per mole. This math looks quite tricky to do
in our heads. But 65 is divisible by 13, which
gives us five. In other words, 13 divided by 65
will be equal to one-fifth. All of our answer choices are
expressed in the scientific notation. So we want to be able to convert
this fraction to a decimal. If you don’t know what one-fifth
is, express just a decimal off the top of your head. We could multiply both the top and
bottom of this fraction by two to give us two-tenths.

Two-tenths expresses the decimal is
0.2. So 13 divided by 65 is 0.2. But we want to know what 0.13
divided by 65 is. Well, we can get from 13 to 0.13 by
either dividing by 100 or moving the decimal place to the left twice. So we should be able to do the same
thing to our answer to make everything equal, which will give us 0.002 moles. All of our answer choices are
expressed in scientific notation. So our last step is converting to
scientific notation. This gives us 2.0 times 10 to the
minus three mole, which matches answer choice A. So the amount of zinc used in moles
is 2.0 times 10 to the minus three.