Chemistry Uncertainties, homework help

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SL & HL Questions on Uncertainties & errors in measurement and results 1. Explain why repeating a measurement and taking the average of five separate readings of data will decrease the random error but have no effect on the systematic error. 2. A balance has been wrongly calibrated so that it always records a reading that is 1.00 g too high. Explain how, without recalibrating it, the balance could be used to obtain: (a) an inaccurate and precise result for the mass of a piece of magnesium metal. (b) an accurate and precise result for the mass of a piece of magnesium metal. 3. A 100 cm3 measuring cylinder has an uncertainty of ± 1.00 cm3. A student used the measuring cylinder to measure 25.00 cm3 of a solution into a burette. The burette has an uncertainty of 0.05 cm3. Assuming no other errors what range of readings could the burette give for the accurate transfer of the 25.00 cm3 of solution. 4. A stop-watch states that it can record to ± 0.01 s. A student used this stop-watch to record measurements every 30 seconds for the volume of gas evolved in a particular reaction. She recorded her values of time with an uncertainty of ± 1 s. Explain why she gave the uncertainty as ± 1 s rather than ± 0.01 s. 5. 1.541 ± 0.001 g of hydrated oxalic acid crystals were dissolved in distilled water. The solution was placed in a 250.0 ± 0.5 cm3 volumetric flask and the total volume made up to the mark with distilled water. After thoroughly mixing the contents, 25.00 ± 0.04 cm 3 of this solution was pipetted into a conical flask. This required 24.90 ± 0.08 cm 3 of 0.100 ± 0.001 mol dm3 sodium hydroxide solution to be neutralised completely. The equation for the reaction is: (COOH)2(aq) + 2NaOH(aq) ↓ (COONa)2(aq) + 2H2O(l) (a) Calculate the percentage uncertainty associated with: (i) the mass of the oxalic acid. (ii) the solution in the volumetric flask. (iii) the volume in the pipette. (iv) the molarity of the sodium hydroxide solution. (v) the volume of sodium hydroxide solution used. (b) Calculate the total percentage uncertainty for this experiment. (c) Calculate the molar mass of the oxalic acid obtained from these experimental results to the correct number of significant figures and state the uncertainty. (d) The correct literature value for the molar mass of the acid is 126.06 g mol -1. Calculate the percentage error. (e) State any other assumptions which may have affected the accuracy of the result. © Dr Geoffrey Neuss, InThinking http://www.thinkib.net/chemistry 1
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Explanation & Answer

Kindly see attached file with the step by step solution of the 5 problems

Problem 1.
The random or statistical error is given by the formula:
𝑠=√

∑(𝑥 − 𝜇) 2
𝑛

Where x represents the result obtained in each of the samples, µ is their average value and n is
the number of data. As can be observed, as we increase the value of n (that is, the number of
measurements) by repeating the experiment, the random error decreases.
In contrast, the systematic error is given by the formula:
𝐸𝑠𝑦𝑠𝑡 =

𝑥 −𝜇
∗ 100
𝜇

Where once more, x is the real measurement and µ is the expected real value. As can be
observed, this error is no longer dependent on the number of measurements but only on the
difference between the experimental and the theoretical value. As a consequence, it will
remain constant even if we increase the number of repetitions done of a given experiment.

Problem 2.
a) An inaccurate but precise result would be obtained if we don’t consider the error done
during the calibration. In this sense, all the obtained results will present a systematic
error of +1g, but since the calibration does not affect the repeatability of the balance
the obtained masses would still be precise.
b) An accurate and precise result for the mass would be obtained if we take the
systemat...


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