Question

Can anyone explain how to solve this?


Suppose you conduct a laboratory experiment to measure the boiling point of methanol and your measurements showed the boiling point of methanol to be 62.4oC. However, the actual boiling point of methanol, which can be looked up in reference tables, is 64.9oC. What is the percent error of your measurement?

A. 0.80%

B. 1.08%

C. 3.85%

D. 4.01%

E. 7.50%

Answer 1

\(\sf\Large error=\dfrac{Approximate~value-Exact~value}{Exact~value}*100%\)

Answer 2

Thank you! But I don't know where to substitute the values... :(

Answer 3

The approximate value is what you think
The exact value is what the reference says.
\(\sf\Large error=\dfrac{62.4-64.9}{64.9}*100\%\)

Answer 4

You need to convert these to absolute temperatures first in order to have an accurate representation of your real percent error. You should not use relative temperature values.

An example showcasing why using Celsius temperatures is wrong:

Real value: 1ºC
Measured value: 0ºC

\[error=\frac{0-1}{1}\cdot 100 =100\% \]
Clearly this is wrong, and is a good example to why you should convert these to absolute temperature values first — not doing so will give you the wrong answer.

Answer 5

@Xishem He's asking for the error in his measurement in ºC. I don't think he has to convert it to kelvin first.
\(\sf\Large error=\dfrac{62.4-64.9}{64.9}*100\%~~~~~~~~~~~~~~~=3.85\%\)

In absolute temperature:

\(\sf\Large error=\dfrac{335.55K-338.05K}{338.05K}*100\%~~=0.74\%\)

Answer 6

WARNING: To the OP, this is mostly ranting — thomaster is correct for this question (even though the question may be wrong).

@thomaster Based on the answers given, I would agree with you — but in that case, I'd argue that the correct answer isn't given.

When you are saying you have some percent error from another value, it is implied that it is an absolute value. Percent errors have no meaningful context in relative scales.

In other words, if you say you have a 10% error in a measurement in temperature, you are suggesting that the collected value is +/-10% from the actual value. And if you are suggesting your temperature is +/-10% from the actual value, then you are therefore suggesting that the average kinetic energy per molecule is +/-10% from the actual (absolute) value.

The fact of the matter is, when you are measuring temperature, you ARE measuring this average kinetic energy per molecule (and it's being converted to some temperature scale through some physical model that describes it) — which allows you to indirectly measure the temperature in Celsius.

Obviously, when you get to the real definition of temperature, Celsius has no part in it and can't give you any valuable information (by itself) about the physical quantities behind temperature.

Either way, I digress. I don't feel that the question is correct, but there's nothing that can be done about it here.

Answer 7

Yea you are right about this but i don't think the unit (in this case ºC) is important to the question.
He's just asked to calculate the error between an approximate number and the reference number. The question could also be distance meters, or time in seconds. It would be the same error %.

Answer 8

Yeah, it should be noted that I totally see where you are coming from when you say that the question is asking for the error in measurement in ºC.

Important part about length is that almost every system of length measurement is absolute. As far as time goes, not sure that it's comparable to temperature in that time is a relative measurement to begin with. There is no "0" time.

It's all semantics anyway.

Answer 9

It really comes down to differentiating between the numerical values and the actual meaning behind those values, and what percent temperature difference REALLY means.

Answer 10

So should I convert the values to absolute temperatures?

Answer 11

No that's not necessary for your question.

Answer 12

Thanks a lot! :) So C is the correct answer right?