Video Transcript
In calorimetry, the transfer of
energy during a chemical reaction can be calculated using the equation 𝑞 equals 𝑚
times 𝑐 times Δ𝑇. How can this equation be rearranged
to make 𝑐 the subject? (A) 𝑐 equals 𝑚 times Δ𝑇 divided
by 𝑞. (B) 𝑐 equals 𝑞 times 𝑚 divided
by Δ𝑇. (C) 𝑐 equals 𝑚 divided by 𝑞
times Δ𝑇. (D) 𝑐 equals 𝑞 divided by 𝑚
times Δ𝑇. (E) 𝑐 equals 𝑞 times Δ𝑇 divided
by 𝑚.
Calorimetry is the study of heat
transfer during physical and chemical changes. During calorimetry experiments, we
can’t measure the heat that’s transferred directly. But we can measure the change in
temperature. We can use equations like the one
shown to relate the observed change in temperature to the heat transferred.
In this equation, 𝑞, 𝑚, 𝑐, and
Δ𝑇 are all variables. 𝑞 represents the heat
transferred. 𝑚 is the mass. 𝑐 is the specific heat capacity, a
quantity that indicates the amount of energy required to raise the temperature of
one gram of a substance by one degree Celsius. And Δ𝑇 is the change in
temperature.
In the equation as written, heat is
the subject. The subject is the isolated term in
a mathematical formula. It is the variable that is being
solved for. To answer this question, we need to
make 𝑐 the subject. We can do this by rearranging the
formula. Before rearranging the formula, we
need to understand two rules.
The first rule is that we can
cancel or move a quantity or a variable if we perform the opposite operation. Addition and subtraction cancel
each other, as do multiplication and division. For example, let’s consider the
equation 𝑎 plus 𝑏 equals 𝑐, where we want 𝑎 to be the subject. Since 𝑏 is being added to 𝑎, we
can subtract 𝑏 from the left-hand side of the equation to cancel the term.
This leads us to our second
rule. Any operation performed on one side
of the equation must be performed on the other side as well. Since we subtracted 𝑏 from the
left-hand side of the equation, we have to subtract 𝑏 from the right-hand side of
the equation too.
Following both rules gives us the
equation 𝑎 equals 𝑐 minus 𝑏, a rearranged equation where 𝑎 is the subject. Now we can use our understanding to
rearrange the given equation to set 𝑐 as the subject. 𝑚 is being multiplied by 𝑐. So we need to divide both sides of
the equation by 𝑚 to cancel the 𝑚-terms on the right-hand side. 𝑐 is also being multiplied by
Δ𝑇. So we need to divide both sides of
the equation by Δ𝑇 as well. We’ve now set 𝑐 as the
subject. 𝑐 is equal to 𝑞 divided by 𝑚
times Δ𝑇.
The answer choice where this is
true is answer choice (D). Therefore, the rearranged equation
where 𝑐 is the subject is 𝑐 equals 𝑞 divided by 𝑚 times Δ𝑇, answer choice
(D).
