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Uncertainties Salters A2

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Salters B There is guidance as to what the error is acknowledged to be if it is not stated on the apparatus It is generally taken to be the smallest unit on the scale being used eg if a balance weighs to 0.01g the error uncertainty is taken as +/- 0.01g

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**Uncertainty Variation – Why?**

Example: Electronic set top balance Reading is 2.05g What range of values could it actually be?

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**Deciding on precision – Volumetric glassware**

Graduated pipette Maximum volume/cm3 Temperature for true volume Standard CLASS: Class B has twice the tolerance of class A Tolerance / ± xcm3 Flask

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**Volumetric equipment – class B**

Flasks: Capacity/ cm3 Accuracy limit / ± cm3 5, 10 0.05 15 0.06 20,25 0.08 50 0.12 100, 250 0.20 500 0.50 Standards: DIN, ISO and BS) BS1792:1982(93)

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**Volumetric equipment – class B**

Bulb pipettes: Capacity/ cm3 Accuracy limit / ± cm3 1 0.016 2 0.02 5 0.03 10 0.04 25 0.06 50 0.10 Standards: One Mark Bulb pipettes: DIN, ISO, BS)(ISO648)

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**Volumetric equipment – class B**

Graduated pipettes: Capacity/ cm3 Accuracy limit / ± cm3 1 0.012 5 0.06 10 0.10 25 0.20 Standards: Graduated pipettes:(USP, DIN, ISO, BS)(ISO835

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**Volumetric equipment – class B**

Burette Capacity/ cm3 Accuracy limit / ± cm3 10 0.040 25 0.06 50 0.10 100 0.26

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**Volumetric equipment – Calculated example**

The uncertainty associated with a grade B 25 cm3 pipette is 0.06 cm3 or 0.24% . This is calculated as follows:

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Volumetric equipment For a 250 cm3 volumetric flask the uncertainty is 0.20 cm3.

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Measuring Cylinder For volume measurements, the precision of a 25 cm3 measuring cylinder is 0.1 cm3: Eg for 20cm3 of a solution:

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**Mass For mass measurements, the precision of a 2d.p. balance is 0.01g:**

e.g. for 1.27g of iodine:

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**Making a solution Total % uncertainty = % U of mass or**

% U of volume (measuring cylinder or pipette) + % U of volumetric flask

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**Example 1 250 cm3 of 0.2M iron (III) chloride solution Mass**

Volume (volumetric flask) Total

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**Example 2 250 cm3 of 0.2M HCl Volume Volume (flask) Total**

(10 cm3 measuring cylinder Volume (flask) Total

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Comment: The overall percentage uncertainty in measuring a volume of reagent for dilution is higher because three pieces of equipment were used (even if one was the same, it was used twice), and this piece of equipment had a lower precision than for the dilution of the solid reagent. In general, the more equipment that is used, the greater the %U for that procedure.

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Titrations For titration measurements, the uncertainty in each reading is: The % U in the titre is:

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Comment: Clearly, if the initial burette reading is 0.0 cm3, then it is unreasonable to include this in the calculation since it would return an infinite error. To overcome this, use 2 x %U in final burette reading. It is the same reasoning that tells you that the uncertainty in measuring a piece of paper with a mm-precision ruler is ± at either end, ie 2 x precision.

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Comment: The burette itself has an inherent error over the whole volume range (0.10cm3 for a 50 cm3 burette). This could be included in the overall error by adding the %U due to this:

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Multiple additions Multiple additions from a burette when it is not refilled can be treated as though the burette had been refilled. Adding to the reaction mixture from several burettes containing different substances: %U from each burette must be calculated and the values added together

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Standard Curves When creating a standard curve, the % U of each measurement and for the colorimeter must be added together to obtain the overall % U for the curve. This may produce a high overall %U but remember, this is the MAXIMUM possible %U

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**Example: Standard Curve**

Salicylic acid/mol dm-3 Volume FeCl3/cm3 Volume Salicylic acid/cm3 Volume Water/cm3 10 0.004 2 8 0.008 4 6 0.012 0.016 0.020 Volumes added using 3 burettes. Salicylic acid dilutions used 50cm3 volumetric flasks and 1cm3 pipettes

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**Uncertainty in standard curve**

Dilution of salicylic acid: 50cm3 ± 0.12cm3 volumetric flask Transfer of salicylic acid: 1.0cm3 ± 0.012cm3 pipette Note, 5 volumes of 1cm3 were used in the whole curve

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**Uncertainty in standard curve**

INITIAL burette reading – salycilic acid FINAL burette reading – salycilic acid

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**Uncertainty in standard curve**

INITIAL burette reading – Iron (III) Chloride FINAL burette reading –Iron (III) Chloride Note, 6 volumes of 10cm3 were used

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**Uncertainty in standard curve**

INITIAL burette reading - water FINAL burette reading – water

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**Uncertainty in standard curve**

Colorimeter Total % Uncertainty = ( )% = 69% (2sf is enough)

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**Example 2: Gas Syringe Precision of gas syringe – 1cm3.**

Find the uncertainties for all other measurements, eg balance, making solutions and the measurement of your independent variable (e.g.time) add to the %U of the gas syringe. For the single curve resulting from one value of your variable, add together all of your %U to give you the overall %U for that experiment.

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Example 2: Gas Syringe If a gas syringe method is used to measure a rate of reaction at different substrate concentrations or other condition, then the error for your reaction rate curve should, theoretically be the sum of all %U from the individual curves from which the initial rate (gradient) was taken. The %U from the smallest values, closest to the origin, are likely to be the highest, and so it is not unreasonable to add together the largest individual uncertainties from each individual curve in order to approximate an overall maxiumum %U in the derived reaction rate curve if that is your intent. However, this calculation is not really necessary of you are looking for the order of a reaction, since the shape of the resulting curve is all you need.

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**Improvements to technique**

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**Precision for burettes and graduated pipettes**

The bottom of the concave meniscus must be precisely on a calibration mark. To make reading of the meniscus position easier we can use piece of paper with a horizontal black stripe, about an inch and half wide. If the paper is held half an inch behind a burette with the stripe about a half an inch below the meniscus, the solution surface seems to be black and is much easier to see.

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