Precision and accuracy of a solution

In summary, the conversation discusses the precision of a solution S=0.4±0.01/250ml and how to calculate it when doing a dilution. The solution for precision is F=5*S/100 and the relative uncertainty stays the same regardless of dilution factors. However, there may be additional sources of error from the inexact measurements of 5ml and 100ml used in the dilution. The resulting uncertainty would be 8*10^-5 ± 2*10^-6.
  • #1
cham
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Homework Statement


so let's say that we have a solution S=0.4±0.01/250ml
i want to do a dilution
so i pick 5ml and pour it into 100ml beaker
how should i calculate precision of the solution (mathematically or with some other equations)?

Homework Equations


so basically we have F=5*S/100

The Attempt at a Solution


for me 5*S/100=8*10^-5±2*10^-6
is this true because it doesn't seem right for me (about the pricision)?
 
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  • #2
The relative uncertainty stays the same, that is right.
You might get an additional uncertainty if the 5ml or the 100ml are not exact.
 
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  • #3
so
mfb said:
The relative uncertainty stays the same, that is right.
You might get an additional uncertainty if the 5ml or the 100ml are not exact.
so what you say is that no mater how many dilution we do the precision stays the same and it depends on the solution we're using.so it means ±0.01 for all diluted solutions we made,right?
 
  • #4
The relative uncertainty stays the same.
It is always 1/40. Roughly speaking, your solution might be 1/40 more concentrated than you thought, or 1/40 less. And that uncertainty does not change if your dilution factors afterwards are known exactly.
 
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  • #5
so let's assume that final result is true , so it would be 8*10^-5 ±1/40 and so for all resulting solutions
and that by using Δy/y
correct me if I'm wrong
thanks and sorry for my stubbornness
 
  • #6
I am afraid you can be sure neither 5 mL nor 100 mL are exact and they are additional sources of error.
 
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  • #7
cham said:
so let's assume that final result is true , so it would be 8*10^-5 ±1/40 and so for all resulting solutions
No, in this case it would be 8*10-5 +- 2*10-6 as the uncertainty is 1/40 of the value.

With the caveat that the 5ml and 100ml won't be exact, as mentioned.
 
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  • #9
thank you mfb and Borek for your help
much appreciated
 
  • #10
You can use @cham to tag users in the thread.
 
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Related to Precision and accuracy of a solution

What is the difference between precision and accuracy?

Precision refers to how close a series of measurements are to each other, while accuracy refers to how close a measurement is to the true or accepted value.

Why is it important to have a solution that is both precise and accurate?

Having a solution that is both precise and accurate ensures that the results are reliable and can be replicated. It also allows for better understanding and interpretation of the data.

How can precision and accuracy be improved?

Precision can be improved by reducing sources of error and increasing the number of measurements. Accuracy can be improved by using more precise instruments and techniques, and by ensuring that the instruments are properly calibrated.

What are some potential sources of error that can affect the precision and accuracy of a solution?

Sources of error can include human error, faulty equipment, environmental factors, and limitations of the measurement technique. It is important to identify and minimize these sources of error to improve the precision and accuracy of the solution.

How can the precision and accuracy of a solution be measured?

Precision can be measured by calculating the standard deviation or range of the measurements. Accuracy can be measured by comparing the results to a known or accepted value. Both precision and accuracy can also be evaluated through statistical analysis and confidence intervals.

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