Uncertainties

Uncertainties

By Angela Toh

Multiple Choice

$$\left(2.34\pm0.02\right)+\left(1.25\pm0.03\right)=$$  

Use significant rules.

• $$3.59\pm0.05$$  

• $$3.59\pm0.02$$  

• $$3.59\pm0.03$$  

• $$3.59\pm0.06$$  

Multiple Choice

$$\left(1.209\pm0.001\right)+\left(0.34\pm0.02\right)=$$  

Use Significant Figures rules.

• $$1.55\pm0.02$$  

• $$1.54\pm0.02$$  

• $$1.549\pm0.021$$  

• $$1.549\pm0.012$$  

Multiple Choice

$$\left(100\pm10\right)+\left(25\pm5\right)=$$  

Use Significant rules

• $$125\pm15$$  

• $$125\pm10$$  

• $$125\pm5$$  

• $$125\pm50$$  

Multiple Choice

$$\left(3.425\pm0.003\right)+\left(7.1\pm0.9\right)=$$  

Use Significant Figures rules.

• $$10.5\pm0.9$$  

• $$10.6\pm0.9$$  

• $$10.53\pm0.90$$  

• $$10.525\pm0.901$$  

Multiple Choice

$$\left(100\pm20\right)-\left(30\pm7\right)=$$  

Use Significant rules.

• $$70\pm27$$  

• $$70\pm13$$  

• $$70\pm7$$  

• $$70\pm20$$  

Multiple Choice

In an experiment, a radio-controlled car takes 2.50 ± 0.05 s to travel 40.0 ± 0.1 m.

What is the car’s average speed and the uncertainty in this value?

• 16 ± 1m s^-1

• 16.0 ± 0.2 m s^-1

• 16.0 ± 0.4 m s^-1

• 16.00 ± 0.36 m s^-1

Multiple Choice

• A

• B

• C

• D

Multiple Select

The initial and final volume readings of a burette in a titration are shown in the diagram. Select the initial reading and the final reading with its appropriate uncertainty.

• Initial Reading: 46.60 + 0.05 cm³

• Initial Reading: 3.40 + 0.01 cm³

• Final Reading: 20.44 + 0.01 cm³

• Final Reading: 29.55 + 0.01 cm³

Multiple Choice

A thermometer can be read to an accuracy of ±0.5 °C. This thermometer is used to measure a temperature rise from 40 °C to 100 °C.

What is the percentage uncertainty in the measurement of the temperature rise?

• 0.5 %

• 0.8 %

• 1 %

• 2 %

Multiple Choice

A micrometer screw gauge is used to measure the diameter of a small uniform steel sphere. The micrometer reading is 5.00mm ± 0.01mm.

What will be the percentage uncertainty in a calculation of the volume of the sphere, using these values?

• 0.2 %

• 0.4 %

• 0.6 %

• 1 %

Multiple Choice

The first length measured in a laboratory experiment is 2.5 + 0.1 m and the second length 3.4 + 0.1 m. What is the uncertainty of the sum of the lengths?

• 0.1 m

• 0.2 m

• 0.3 m

• 0.4 m

Multiple Choice

A quantity x is to be determined from the equation

x = P $$-$$  Q.

P is measured as 1.27 ± 0.02 m and Q is measured as 0.83 ± 0.01 m.

What is the percentage uncertainty in x to one significant figure?

• 0.4 %

• 2 %

• 3 %

• 7 %

Multiple Choice

In an experiment, a radio-controlled car takes 2.50 ± 0.05 s to travel 40.0 ± 0.1 m.

What is the car’s average speed and the uncertainty in this value?

• 16 ± 1m s^-1

• 16.0 ± 0.2 m s^-1

• 16.0 ± 0.4 m s^-1

• 16.00 ± 0.36 m s^-1

Multiple Choice

In an experiment to determine the acceleration of free fall g, the period of oscillation T and length l of a simple pendulum were measured. The uncertainty in the measurement of l is estimated to be 4%, and the uncertainty in the measurement of T is estimated to be 1%.  The value of g is determined using the formula $$g=\frac{4\pi^2l}{T^2}$$   What is the uncertainty in the calculated value for g?

• 2 %

• 3 %

• 5 %

• 6 %

Multiple Choice

The power loss P in a resistor is usually calculated using the formula $$P=\frac{V^2}{R}$$   The percentage uncertainty in the potential difference V is 3 % and the percentage uncertainty in the resistance R is 2 %. What is the percentage uncertainty in P?

• 4 %

• 7 %

• 8 %

• 11 %

Multiple Choice

The resistance R of a resistor is determined by measuring the potential difference V across it and the current I in it. The value of R is then calculated using the equation $$R=\frac{V}{I}$$  . The values measured are V = 1.00 ± 0.05 V and I = 0.50 ± 0.01 A. What is the % uncertainty in the value of R?

• 2. %

• 3 %

• 7 %

• 10 %

Multiple Choice

An experiment is carried out to measure the resistance of a wire.

The current in the wire is (1.0 ± 0.2) A and the potential difference across the wire is (8.0 ± 0.4) V.

What is the resistance of the wire and its uncertainty?

• (8.0 ± 0.2) Ω

• (8.0 ± 0.6) Ω

• (8 ± 1) Ω

• (8 ± 2) Ω

Multiple Choice

A student determines the density ρ of steel by taking measurements from a steel wire. 

mass m = 6.2 ± 0.1 g 

length l = 25.0 ± 0.1cm 

diameter d = 2.00 ± 0.01mm 

He uses the equation $$\rho=\frac{4m}{\pi d^2l}$$  .

What is the percentage uncertainty (to 2 s.f. in this case) in his calculated value of density?

• 1.1 %

• 1.8 %

• 2.5 %

• 3.0 %

Fill in the Blanks

If four volume readings using burette are as listed below.

26.50 cm³        26.25 cm³        26.60 cm³        26.65 cm³

 

              Calculate the average volume (omit units in your answer).

Multiple Select

Which of these titres are concordant?

• 12.7cm³

• 12.3cm³

• 12.4cm³

• 12.0cm³

Multiple Select

Which of the following titrations can be used to find the average titre value

• 1

• 2

• 3

Multiple Choice

A student carries out a titration three times and obtains the following volumes: 3.0±0.1cm³, 3.2±0.1cm³ and 3.2±0.1cm³. What is the average volume?

• 3.1±0.1 cm³

• 3.13±0.1 cm³

• 3.1±0.3 cm³

• 3.13±0.3 cm³

Multiple Choice

Volumes of titre are measured using burettes, with each burette reading having an uncertainty of ±0.05 cm³.

The percentage error in measuring the 25.00 cm³ of the acid is

• ±0.05%

• ±0.10%

• ±0.20%

• ±0.40%

Open Ended

In an experiment to determine the enthalpy of neutralisation of sodium hydroxide by hydrochloric acid, the initial temperature was (19.2 ± 0.2) ^oC, and the final temperature (26.4 ± 0.2) ^oC. Record the temperature rise in a proper manner suitable for lab report writing.

Multiple Choice

Four students have done a calorimetric experiment to determine the enthalpy change of a reaction in aqueous solution, for which the literature value is 38.73 kJ mol^-1. The values found by the students (in kJ mol^-1) were:

              I.            35.1 ± 0.3                                      II.          36.5 ± 0.5

              III.         33.2 ± 0.1                                      IV.         34.7 ± 0.2

Which value is MOST PRECISE?

• I

• II

• III

• IV

Multiple Choice

Four students have done a calorimetric experiment to determine the enthalpy change of a reaction in aqueous solution, for which the literature value is 38.73 kJ mol^-1. The values found by the students (in kJ mol^-1) were:

              I.            35.1 ± 0.3                                      II.          36.5 ± 0.5

              III.         33.2 ± 0.1                                      IV.         34.7 ± 0.2

Which value is MOST ACCURATE?

• I

• II

• III

• IV

Multiple Choice

Four students have done a calorimetric experiment to determine the enthalpy change of a reaction in aqueous solution, for which the literature value is 38.73 kJ mol^-1. The values found by the students (in kJ mol^-1) were:

              I.            35.1 ± 0.3                                      II.          36.5 ± 0.5

              III.         33.2 ± 0.1                                      IV.         34.7 ± 0.2

What do you think the major problem is?

• Random error

• Systematic error

• Both are equally important

• It is not possible to tell from the data given.

Multiple Choice

If you were to repeat the experiment which of the following is most likely to be the improvement that would most improve the result?

• Using a more precise thermometer.

• Not assuming that the specific heat of the solution equalled that of water.

• Using pipettes rather than measuring cylinders.

• Improving the insulation of the calorimeter.

Open Ended

Calculate the value and uncertainty of X, where

X  =  A (B – C)

Given the values:       

A = 123.0 ± 0.5;

B = 12.7 ± 0.2;

C = 4.3 ± 0.1