Was the density you determined accurate, taking into account the total instrument uncertainty?
I got 0.778 g/ml
the theoretical value is 0.789 g/ml
the instrumental uncertainty was 0.2%
How do I know if its accurate ??
please help
(.789-.778)/.778=1.4 percent error.
does that mean is accurate?
It means your answer (experimental result) is 1.4% above the accepted value. To call this 'accurate' based on a %Error calculation would be unwise unless there is a published accepted %Error 'range' for the experiment instruments used to collect the raw data. That is, your answer would be published as (Experimental Density) ± 1.4%(Experimental Density) = 0.778 g/ml ± 1.4%(0.778)g/ml giving an experimental range of [0.778 – (1.4% of 0.778)] to [0.778 + (1.4% of 0.778)] => [(0.778 – 0.011)g/ml to (0.778 + 0.011)g/ml] => [0.767g/ml to 0.789g/ml] for your experimental results. Now, this is based on your instructor (or note in the procedures section of your experiment) giving an ‘accepted’ %Error. You would then be able to determine the ‘expected’ range of reliability of the lab data collected based on an accepted value and accepted %Error. For example, let’s say you are given a 2% Error as an accepted %Error. Then your answer of 0.778g/ml would be ‘accurate’ with respect to the published %Error. That is, Density = Accepted Density ± 2% of accepted density = 0.789g/ml ± 2%(0.789g/ml) = (0.789 ± 0.016)g/ml => [(0.773g/ml) to (0.805g/ml)]. Since your experimental results falls within the range based on accepted value variation of data, then your answer can be said to be accurate. However, if the instructor/reference manual says the accepted %error is, say 1%, then this would give an accepted range of (0.789 ± 0.008)g/ml => [(0.781)g/ml to (0.797)g/ml]. Your answer of 0.778g/ml would NOT be accurate b/c it was not within the ‘accepted’ range of %Error for the instrument used to obtain your data. %Error is generally the ‘Accuracy’ factor as it indicates variation of data about an accepted value, but the accepted value and the standard %Error for the instrument used needs to be given.
woow thank you so much
To determine whether the density you determined is accurate, you can consider the total instrument uncertainty and compare it with the difference between your measured value and the theoretical value.
First, let's calculate the instrumental uncertainty. You mentioned that it was 0.2%, which means it is 0.2/100 = 0.002.
Next, find the absolute difference between your measured density and the theoretical value:
Absolute difference = |Measured Density - Theoretical Density|
Absolute difference = |0.778 g/ml - 0.789 g/ml|
Absolute difference = 0.011 g/ml
Now, compare the absolute difference with the instrumental uncertainty. If the absolute difference falls within the instrumental uncertainty range, it would indicate that your measured density is accurate considering the instrument's limitations.
In this case, the absolute difference is 0.011 g/ml, and the instrumental uncertainty is 0.002. Since 0.011 g/ml is greater than 0.002, your measured value does not fall within the instrument's uncertainty range.
Thus, based on the comparison, we can conclude that your measured density of 0.778 g/ml is not accurate, taking into account the total instrument uncertainty.