trimblechemistry.wikispaces.com · Web viewPut the following numbers into scientific notation and write down the number of significant digits in each: a. 0.225 b. 2.5 c. 44,163 d.

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UNIT 1TOPIC 11: MEASUREMENT AND DATA PROCESSING

Assessment Statements Objective11.1 Uncertainties and Error in Measurements

Describe and give examples of random uncertainties and systematic errors. 2 Distinguish between precision and accuracy. 2 Describe how the effects of random uncertainties may be reduced. 2 State random uncertainty as an uncertainty range (±). 1

State the results of calculations to the appropriate number of significant figures. 1

11.2 Uncertainties in calculated results

State uncertainties as absolute and percentage uncertainties. 1 Determine the uncertainties in results. 3

11.3 Graphical techniques

Sketch graphs to represent dependences and interpret graph behaviour. 3

Construct graphs from experimental data. 3

Draw best-fit lines through data points on a graph. 1 Determine the values of physical quantities from graphs. 3

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Uncertainty in Measurements

o Different measuring devices have

Estimating Uncertainty

o To estimate a measuring devices uncertainty

Indicating uncertainty in a measurement

o Indicate using + after the recorded measurement

o Example:

Significant figures - Counting

o Counting Significant Figures – Atlantic Pacific Method

• Decimal point absent (Atlantic) – begin on right side of number

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• Decimal point present (Pacific) - begin on left side of number

• Exact numbers –

Examples: Counting Sig. Figs

234 cm

67000 cm

45000 cm

560. cm

0.5630 cm

1.0034 cm

0.00467 cm

Scientific Notation

o Used to

o Standard Form

Base –

Exponent –

Negative Exponent –

Positive Exponent –

Examples: Scientific Notation

124300 =

0.00362 =

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1300000 =

1.23E-5 =

5.61 x 10^6 =

Calculators and Scientific Notation

o Calculators handle scientific notation by only inputting the exponent,

enter the base as you would a regular number,

o Display –

Experimental errors

Random errors - Precision

• Random errors - Precision

• A random error makes the measured value

• Reduce random errors-

Systematic errors

• Systematic error -

• Errors due to

• Makes the measured value

• An experiment may involve

Categories of systematic errors

• Personal errors -

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• Instrumental Errors –

• Method Errors -

Determination of error

o Accuracy

o Precision

Precision vs. accuracy

Evaluating accuracy and precision in data

o When evaluating whether data is accurate or precise you could look at

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• Single Data Point –

• Set of Data Points -

Uncertainties in calculated results

Significant figures in mathematical operations

o Addition/Subtraction –

o Multiplication/Division –

o Mixed operations –

Example of Sig. Figs in Calculations

33.5 cm + 7.88 cm + 0.977 cm =

23000 km + 8.7 km =

67.23 cm x 9.22 cm =

200 cm x 3.333 cm =

Percentage uncertainties and propagation of errors

Percent Uncertainties and errors

o Fractional Uncertainty

o Absolute Uncertainty – • Example:

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o Percent Uncertainty

Percent Uncertainties and errors

o Percent Error

Error propagation

o Error propagation is a way of

o All chemical equipment has

Ex. 10.00mL pipettes

50.00mL burettes

Thermometer -

Rule: 1 Addition and Subtraction

o If you add or subtract two numbers

o Example 22.34 + 0.02 mL - 1.06 + 0.02 mL =

Rule 2: Multiplication and Division

o Make

o Convert

o Add

o Multiply

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o Apply

Example: Multiplication and Division

o Find the density of a substance using the following data:

g = 1.22 + 0.01 g

V = 21.28 + 0.04 mL

Example: multiplying and dividing

1. Density =

2. Converting Uncertainties to Percent Uncertainties

Mass:

Vol:

Example: multiplying and dividing

3. Adding percent uncertainties

4. Multiply Percent Uncertainty by Calculated Value

5. Report Value with Propagated Error

Rule 3: Whole number

• Multiplying or dividing by a whole number –

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Example:

4.95 ± 0.05 x 10

Rule 4: Powers

o Powers -

Example:

(4.3 ± .5 cm)3

Rule 5: Formulas

o Formulas - Follow the order of operations:

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1. Determine the number of significant figures in each of the following numbers.a. 175,000b. 0.0125c. 76,000d. 0.4600e. 0.00000000525f. 900g. 900.h. 10,100i. 0.07007

2. Round off each of the following numbers to three significant figuresa. 15.9994 b. 1.0080c. 0.6654 d. 4885e. 87,550 f. 0.027225

3. Put the following numbers into scientific notation and write down the number of significant digits in each:a. 0.225 b. 2.5c. 44,163 d. 20,190e. 0.00000000000991 f. 7,000

4. How many significant figures are in each of the following numbers?a. 225.0 b. 1000.0c. 0.0003210 d. 0.0067e. 1,000,000. f. 2.00001

CDO IB Chemistry SL Problem Set 1-1

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1. Perform the indicated arithmetic operations, and round the results to the appropriate number of significant digits.

a. 77.981 x 2.33 = b. 4 x 0.0665 = c. 17.34 + 4.900 + 23.1 = d. 9.80 – 4.762 = e. 3.9 X 6.05 X 420 = f. 14.1 / 5 = g. 1001 + 16.23 = h. 424.5 + 2.8461 = i. 9.9 – 9.54 = j. 7.3778 – 0.000265 = k. 8.561 x 109 – 6.21 x 1010= l. (24.358)(6.4) = m. 48.6(0.6959) = n. 23081 / 0.8981 = o. (6.082 x 1023)(5.0 x 10-3) = p. (9.9x104) + (1.273 x 102) =

2. In the diagram at right, 4 targets are shown. If the goal is to hit the centre of the bulls-eye,

a. Which show a precise aim?b. Which show an accurate aim?

3. a) Calculate the average and the uncertainty for each set of data:

AVERAGE UNCERTAINTYSET A: 15.32, 15.37, 15.33, 15.38, 15.35SET B: 16.30, 16.19; 16.24 16.29, 16.23

b) The "true" value that we were attempting to measure was: 16.26 Which set of data is most precise? _______ Which was most accurate? _______

4. In an experiment, you are measuring the mass of water by difference. You use only one balance, but ask 2 friends to help you make measurements. Your data looks like this:

You Friend A Friend B Avg. with UncertaintyEmpty Beaker 207.2 g 207.1 g 207.3 gBeaker + 50mL water

257.3 g 257.0 g 257.5 g

50 mL water alone


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Complete the table. Might random error be present? What is causing it? If so, how would you correct for it? Might systematic error be present? What is causing it? How would you find out?

1. Adding and subtracting values:

a) 1.00 + 0.05 g of Copper is added to 10.00 g+ 0.05 g of Iron. What is the mass of the two, together?

b) The starting volume on a buret is 40.00 + 0.02 mL. The final volume on the buret is 32.60 + .02 mL. What volume of liquid was removed from the buret?

c) The weighing boat weighs 2.45 + 0.01 g. The total weight, after adding Calcium Carbonate to the weighing boat is 4.62 + 0.01 g. What is the mass of the calcium carbonate?

2. Multiplying and dividing when both values have uncertainty a) Molarity: Calculate the molarity when 2.0 + .1 moles of NaCl is dissolved in

0.100 + 0.001 L of water. ( Molarity = moles / L )b) Density: Calculate the density of an object with mass 25.0 + .2 g and volume

50.0 + .5 mL (Denisty = mass/volume)c) Density: Calculate the density of a rectangular object with mass 32.0 + .2 g,

length 1.25 + .05 cm, width 2.25 + .05 cm and height 3.35 + .05 cm.

3. Other Rules:a) 13.62 + 0.02 cm x 100b) Find the volume of a rectangle measuring

l: 2.5 + 0.1cm w:4.2 + 0.1cm h:1.1 + 0.1 cm c) (3.6 + 0.5 cm)3


trimblechemistry.wikispaces.com · Web viewPut the following numbers into scientific notation and write down the number of significant digits in each: a. 0.225 b. 2.5 c. 44,163 d.

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