Video Transcript
A student needs to use the mass
balance apparatus shown below to measure out a certain number of moles of a
substance. Using a calculator, the student
determines that they need to weigh out 12.108225 grams of the substance. Why is this amount not a suitable
value to measure using the mass balance apparatus?
Well, the first thing we need to do
is look at the mass balance apparatus. From the display, we can see it
measures in grams. The student is looking out to weigh
a mass in grams, which helps, but that’s not quite enough. The balance gives a value to a
maximum of four decimal places. A gram mass balance accurate to
four decimal places will be accurate to the nearest 0.0001 grams, one ten
thousandths of a gram. But the mass the student calculated
is to six decimal places. This is 100 times more precise than
the balance is capable of.
The balance would be able to read
the mass of 12.1082 grams. And if the student added a little
bit more, it would be able to read 12.1083 grams. But the number produced by the
student’s calculator is much more precise than the mass measurements this mass
balance is capable of. So, this amount is not a suitable
value to measure using the mass balance apparatus because the mass balance apparatus
only measures to four decimal places.
What mass should the student try to
weigh out instead? The number from the calculator was
to six decimal places, but the balance only reads to four. So, to make sure we get as close to
the calculated value as possible, we want to round that number to four decimal
places. You may think you could just chop
off the last two digits, but sometimes that won’t be as good as rounding. We know the first three decimal
digits are one, zero, eight. And the digit in the fifth decimal
place is a two. So, we round down. So, our final answer is 12.1082
grams.
