IB Chemistry IB Chemistry Chapter 11, Measurement & Chapter 11, Measurement & Data ProcessingData ProcessingMr. PruettMr. Pruett

Understand scientific notation

To convert a number into scientific notation; move the decimal point so only 1 non-zero digit

is to the left of the decimal point. if you move the decimal point to the left, the

power of 10 will be positive. if you move the decimal point to the right, the

power of 10 will be negative.3,600 = 3.6 x 103

0.000 075 2 = 7.52 x 10-5

5,732,873.912 = ?0.124 04 = ?

Understand scientific notation

To convert a number out of scientific notation; if the power of 10 is positive move the decimal

point to the right the power number of places if the power of 10 is negative move the

decimal point to the left the power number of places.

8.1 x 10-5 = 0.0000811.2 x 108 = 1200000009.342 780 23 x 104 = ?3.704 x 10-6 = ?

Practice Problems Handout

Measurement & Data ProcessingMeasurement & Data Processing

11.1.1 Errors or Uncertainties (aka. Random errors or random uncertainties) are what cause your final results to be inaccurate (meaning that your results are higher or lower than the true value)

There are 2 types of errors or uncertainties Random uncertainties Systematic errors

Random Uncertainties Makes the measured value either

smaller or larger than the true value. Chance alone determines if it is smaller or larger.

Examples – Reading the scale of any instrument such as a balance or pH meter or taking a reading which changes with time.

Not due to mistakes and can not be avoided.

Systematic Errors

Makes the measured value always smaller or larger than the true value. A systematic error causes a BIAS in an experimental measurement in one direction. ACCURACY (or validity) is the measurement of systematic error. Accuracy is a measure of how well an experiment measures what it is trying to measure.

Systematic Errors, Cont.

Examples – non-zero reading on a meter (zero error), incorrectly calibrated scale, reaction time of the experimenter. Using old reagents that have degraded over time. Use example Fig. 11.5 (page 307).

Evaluating Systemic Errors

Percent error Percent error = (Exp. – Actual)

(Actual)

Assessment Statement 11.1.2Assessment Statement 11.1.2Distinguish between precision Distinguish between precision and accuracyand accuracy

Precise – When a series of measurement Precise – When a series of measurement is repeated and the values obtained are is repeated and the values obtained are close together. close together.

If the same student was able to obtain the If the same student was able to obtain the same results then the procedure is same results then the procedure is REPEATABLE.REPEATABLE.

Assessment Statement 11.1.2Assessment Statement 11.1.2Distinguish between precision and Distinguish between precision and accuracyaccuracy

If the same experiment is carried out If the same experiment is carried out by many students the method or by many students the method or procedure is REPRODUCIBLE.procedure is REPRODUCIBLE.

ACCURATE – Results that are close to ACCURATE – Results that are close to the true value. See Fig. 11.7 & 11.8.the true value. See Fig. 11.7 & 11.8.

11.1.3 Describe how the effects 11.1.3 Describe how the effects of random uncertainties may be of random uncertainties may be reduced.reduced.

Random errors can be reduced by Random errors can be reduced by carrying out repeated measurements.carrying out repeated measurements.

11.1.4 State random uncertainty as an 11.1.4 State random uncertainty as an uncertainty range (+/-)uncertainty range (+/-)

Random uncertainties are reported as Random uncertainties are reported as an uncertainty range. Ex. A value an uncertainty range. Ex. A value reported as 5.2 +/- 0.5 cm , means the reported as 5.2 +/- 0.5 cm , means the actual length is between 4.7 and 5.7 actual length is between 4.7 and 5.7 cm.cm.

Generally, a reading can be measured Generally, a reading can be measured by one half the smallest division (least by one half the smallest division (least count).count).

A least count is the smallest division A least count is the smallest division on the scale of a apparatus.on the scale of a apparatus.

11.1.5 State the results of 11.1.5 State the results of calculations to the appropriate calculations to the appropriate number of significant figures.number of significant figures. The total number of digits in a number.The total number of digits in a number. SEE TABLE 11.4SEE TABLE 11.4 There is a basic distinction between There is a basic distinction between

measurement and counting. Counting is measurement and counting. Counting is exact. Measurement is more of an estimate exact. Measurement is more of an estimate depending on scale.depending on scale.

11.2.1 State uncertainties as 11.2.1 State uncertainties as absolute and % uncertainties.absolute and % uncertainties.

Estimated uncertainties should be Estimated uncertainties should be indicated for all measurements.indicated for all measurements. From the smallest division of a scale.From the smallest division of a scale. From the last sig fig in a digital From the last sig fig in a digital

measurement.measurement. From data provided by the manufacture. From data provided by the manufacture.

Absolute uncertainty is usually Absolute uncertainty is usually expressed in the same units as the expressed in the same units as the reading. Ex. 25.4 +/- 0.1 sreading. Ex. 25.4 +/- 0.1 s

11.2.1 State uncertainties as 11.2.1 State uncertainties as absolute and % uncertainties.absolute and % uncertainties. The mathematical symbol for absolute The mathematical symbol for absolute

uncertainty is uncertainty is δδx were x represents the x were x represents the measurement. Ex. 25.4 +/- .1s where x is measurement. Ex. 25.4 +/- .1s where x is 25.4 and 25.4 and δδx = .1x = .1

Absolute uncertainty is often converted to Absolute uncertainty is often converted to PERCENT UNCERTAINTY.PERCENT UNCERTAINTY. Ex. 25.4 s +/- 0.4% (Ex. 25.4 s +/- 0.4% (0.1 s0.1 s x100=0.4%) x100=0.4%)

25.4 s25.4 s

Uncertainties are recorded in one sig fig.Uncertainties are recorded in one sig fig. The last sig fig should be same place as The last sig fig should be same place as

uncertainty.uncertainty.

11.2.2 Determine the 11.2.2 Determine the uncertainties in resultsuncertainties in results

1) When adding or subtracting 1) When adding or subtracting uncertainty values, add the absolute uncertainty values, add the absolute uncertainties.uncertainties. Initial temp = 34.50 C (+/-0.05C)Initial temp = 34.50 C (+/-0.05C) Final temp = 45.21 C (+/- 0.05C)Final temp = 45.21 C (+/- 0.05C) 45.21 – 34.50= 10.71 C (+/- 0.05 + 0.05 45.21 – 34.50= 10.71 C (+/- 0.05 + 0.05

= 0.1 C), 10.71 +/- 0.1 C= 0.1 C), 10.71 +/- 0.1 C

11.2.2 Determine the 11.2.2 Determine the uncertainties in resultsuncertainties in results 2) When X or ÷, add the percent 2) When X or ÷, add the percent

uncertainties. uncertainties. Ex. Mass= 9.24 +/- 0.05 g and volume Ex. Mass= 9.24 +/- 0.05 g and volume

equals 14.1 cc +/- 0.05 cc. equals 14.1 cc +/- 0.05 cc. Ex. Perform calculation; D= m/vEx. Perform calculation; D= m/v Ex. 9.24 g/ 14.1 cc = 0.655 g/ccEx. 9.24 g/ 14.1 cc = 0.655 g/cc

Convert absolute uncertainty to %Convert absolute uncertainty to % Add the percentsAdd the percents Convert total back to percent uncertainty. Convert total back to percent uncertainty.

11.2.2 Determine the 11.2.2 Determine the uncertainties in resultsuncertainties in results

Ex. Mass=0.05/9.24 X 100 = 0.54%Ex. Mass=0.05/9.24 X 100 = 0.54% Ex. Volume=0.05/14.1 x 100=0.35%Ex. Volume=0.05/14.1 x 100=0.35%

0.54% + 0.35%=0.89%, = 0.655 g/cc (+/- 0.54% + 0.35%=0.89%, = 0.655 g/cc (+/- 0.89%)0.89%)

0.655 x 0.89/100=0.0058295, density = 0.655 x 0.89/100=0.0058295, density = 0.655 +/- 0.006 g/cc. 0.655 +/- 0.006 g/cc.

11.2.2 Determine the 11.2.2 Determine the uncertainties in resultsuncertainties in results

3) When X or ÷ by a whole number, X or ÷ 3) When X or ÷ by a whole number, X or ÷ the uncertainty by that number.the uncertainty by that number.

Ex. (4.95 +/- 0.05) x 10 = 49.5 +/- 0.5Ex. (4.95 +/- 0.05) x 10 = 49.5 +/- 0.5

4) Powers: When raising to the 4) Powers: When raising to the nnth power, th power, multiply the % uncertainty by multiply the % uncertainty by nn. When . When lowering the nth root, ÷ the percent lowering the nth root, ÷ the percent uncertainty by uncertainty by nn. .

11.2.2 Determine the 11.2.2 Determine the uncertainties in resultsuncertainties in results

Ex. (4.3+/- 0.5 cm)Ex. (4.3+/- 0.5 cm)33 = = 4.34.333 +/- ( +/- (0.50.5) X 3 =) X 3 = 4.34.3 79.5 cm79.5 cm33 (+/- 0.349%) (+/- 0.349%) 79.5 cm79.5 cm33 +/- 0.3 cm +/- 0.3 cm33

11.3.1 Sketch graphs to represent 11.3.1 Sketch graphs to represent dependences and interpret graph dependences and interpret graph behavior.behavior.

Dependent variable (manipulated) – shown Dependent variable (manipulated) – shown on y-axis.on y-axis.

Independent variable (responding) – shown Independent variable (responding) – shown on the x-axis.on the x-axis.

Know a linear and hyperbolic graph Know a linear and hyperbolic graph (inverse relationship graph or logarithmic)(inverse relationship graph or logarithmic)

11.3.2 Construct graphs from 11.3.2 Construct graphs from experimental Dataexperimental Data

Be able to plot data on proper scale. Be able to plot data on proper scale. Use proper unitsUse proper units Label each axisLabel each axis Plot the points accuratelyPlot the points accurately Draw a straight line, line of best fit or a Draw a straight line, line of best fit or a

curve of best fit.curve of best fit. Add title and Key if necessary.Add title and Key if necessary. Any outliers must be identified.Any outliers must be identified.

11.3.3 Draw best-fit lines 11.3.3 Draw best-fit lines through data points on graphthrough data points on graph

THE LINE OF BEST FIT – The best fit THE LINE OF BEST FIT – The best fit line that averages the distance line that averages the distance between the data points. between the data points.

There should be roughly the same There should be roughly the same number of data points on one side of number of data points on one side of the data line as the other. the data line as the other.

ANOMALOUS – Data that clearly does ANOMALOUS – Data that clearly does not fit the trend.not fit the trend.

11.3.4 Determine the values of 11.3.4 Determine the values of physical quantities from graphs.physical quantities from graphs.

Be able to determine the gradient and Be able to determine the gradient and the intercept.the intercept.

Intercept – Where the line crosses the Intercept – Where the line crosses the y-intercept.y-intercept.

Gradient – The gradient of a straight-Gradient – The gradient of a straight-line graph is the increase in the y-axis line graph is the increase in the y-axis value divided by the increase in the x-value divided by the increase in the x-axis value.axis value.

11.3.4 Determine the values of 11.3.4 Determine the values of physical quantities from graphs.physical quantities from graphs.

Interpolation – A technique where a graph is Interpolation – A technique where a graph is used to determine data points between used to determine data points between taken measurements.taken measurements.

Extrapolation – A technique used to find Extrapolation – A technique used to find values outside the range for which values outside the range for which measurements were made. measurements were made.

Area under the graph - For most graphs in Area under the graph - For most graphs in chemistry the area under the graph does chemistry the area under the graph does not represent a useful physical quantity. not represent a useful physical quantity.