Errors and Uncertainty

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435.5g

Question 1

Perform the indicated operation and give the answer to the appropriate accuracy.

451g – 15.46g

436g 435.54g

4.4 x 102g

Wrong Answer!455.54 = 436 (when adding the final result should be reported to be the same number of decimal places as the number with the least number of decimal places. i.e. 451)

Question 2

Repeated measurements of a quantity can reduce the effects of

both random and systematic errors.

neither systematic nor random errors.

random errorssystematic errors.

Wrong Answer!

Question 3

A student recorded the volume of a gas as 0.0014020dm3. How many significant figures are there in this value?

7 6

45

Wrong Answer!Zeros to the right of the decimal point and between non-zero numbers are significant.

Question 4

A thermometer with an accuracy of 0.20C was used to record an initial temperature of 20.20C and a final temperature of 29.80C. The temperature was

9.6 0.40C 9.6 0.20C

9.6 0.10C100C

Wrong Answer!When adding or subtracting measurements, the absolute uncertainties are added.

Question 5

Which experimental technique reduces the systematic error in the investigation?

Using a magnifying glass to enlarge the meniscus in a burette.

Using a larger amounts of an indicator during a titration.

Adjusting an electronic balance to remove its zero error before weighing a chemical.

Repeating a titration a number of times and calculating an average titre.

Wrong Answer!A zero error is a systematic error.

Question 6The volume V, pressure P and temperature T and number

of moles of an ideal gas are related by the ideal gas equation PV = nRT.

If the relationship between pressure and volume at constant temperature of a fixed amount of gas is investigated experimentally, which one of the following plots would produce a linear graph?

P against V P against 1/V

No plot can produce a straight line

1/P against 1/V

Wrong Answer!

Question 7An object of mass 2.000kg is placed on four different balances (A, B, C and D) and

for each balance the reading is recorded five times. The table shows the values obtained with the averages.

Which balance has the smallest systematic error but is imprecise?

Balance 1 2 3 4 5 Average/kg

2.000 2.000 2.002 2.001 2.002 2.001

2.012 2.013 2.012 2.014 2.014 2.013

1.993 1.987 2.002 2.000 1.983 1.993

2.011 1.999 2.001 1.989 1.995 1.999

Wrong Answer!A small systematic error occurs when all the readings are consistently higher or lower than true values. Imprecise readings implies there is a spread of readings about the true value. The spread for balance C is more than balance A.

Question 8

What is the following measurement with the possible random uncertainty shown as a percentage instead of an absolute error:

6.25cm3 0.005cm3?

6.25cm3 0.4% 6.25cm3 0.8%

6.25cm3 0.08%6.25cm3 0.04%

Wrong Answer!

0.005100 0.0769% 0.08%

6.25

Question 9

An experiment to determine the molar mass of solid hydrated iron(II)sulfate, FeSO4.5H2O gave a result of 258 gmol-1.

What is the experimental error?

0.07% 7%

77%0.7%

Wrong Answer!

Literature - Experimental value (278 258)Perecntage error = 100% 7%

Literature value 278

Question 10When comparing systematic errors and random uncertainties during an

investigation, the following pairs of properties of errors in an experimental measurement may be considered:

I. Error can possibly be removed.

II. Error cannot possibly be removed.

III. Error is of constant sign and size.

IV.Error is of varying sign and size.

V. Error will be reduced by averaging repeated measurements.

VI.Errorwill not be reduced by averaging repeated measurements.

Which properties apply to random uncertainties?

I, II, III I, IV, VI

II, III, VII, IV, V

Wrong Answer!Systematic error : I, III, VI

Random uncertainties : II, IV, V

Question 11

What are the greatest and smallest possible values for the following length: 34.3 cm?

34.6cm and 34.0cn 34.35cm and 34.25cm

35.3cm and 33.3cm34.2cm and 34.4cm

Wrong Answer!There is an implied random uncertainty of +/- 0.05cm

Question 12The diagram shows a set of experimental data points, x,

determined when one experimental measurement

was repeated four times. The centre of the

diagram represents the ideal value calculated

from theory. What statement is correct about

These measurements?

The measurements involve high accuracy and low precision.

The measurements involve high accuracy and high precision.

The measurements involve low accuracy and

high precision.

The measurements involve low accuracy and low precision.

x xx x

Wrong Answer!Low in accuracy as they are far from the centre; but high in precision as they are closer together.

Question 13

Perform the following density calculation to the correct number of significant figures:

0.333 gcm-3 0.3333 gcm-3

0.33 gcm-30.3 gcm-3

33.00cm

1.00g

Wrong Answer!There are 3 signifiant figures, equal to the number of significant digits in each number.

Question 14

What is the percentage random uncertainty in a mass of pure water measured to the nearest microgram (µg) in a kilogram (kg)?

10-4 10-6

10-1210-7

Wrong Answer!1 µg = 10-6 g = 10-6 x 10-3 kg = 10-9 kg ;

Percentage random uncertainty

= (10-9 kg / 1 kg) x 100%

= 10-7 %

Question 15An IB chemistry student records a series of precise

measurements from which the student calculates the enthalpy of combustion of a hydrocarbon as 327.66kJmol-1 . The student estimates that the result is accurate to 3%.

Which of the following gives the student’s result expressed to the appropriate number of significant figures?

300 kJmol-1 328 kJmol-1

327.7 kJmol-1330 kJmol-1

Wrong Answer!Value of error

= 327.66 kJmol-1x0.03

= 9.83kJmol-1

= 10kJmol-1

(rounded to the same tens place as the error)

Congratulations!