IB Chemistry Chapter 11, Measurement & Data Processing Mr. 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 = 0.000081 1.2 x 108 = 120000000 9.342 780 23 x 104 = ? 3.704 x 10-6 = ? Practice Problems Handout

Measurement & 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. The term error has the everyday meaning of a mistake. Random uncertainties are not due to mistakes and cannot 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. If an experiment is accurate or valid then the systematic error is very small.

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 11.1.2 Distinguish between precision and accuracy Precise – When a series of measurement is repeated and the values obtained are close together. If the same student was able to obtain the same results then the procedure is REPEATABLE.

Assessment Statement 11.1.2 Distinguish between precision and accuracy If the same experiment is carried out by many students the method or procedure is REPRODUCIBLE. ACCURATE – Results that are close to the true value. See Fig. 11.7 & 11.8.

11.1.3 Describe how the effects of random uncertainties may be reduced. Random errors can be reduced by carrying out repeated measurements.

11.1.4 State random uncertainty as an uncertainty range (+/-) Random uncertainties are reported as an uncertainty range. Ex. A value reported as 5.2 +/- 0.5 cm , means the actual length is between 4.7 and 5.7 cm. Generally, a reading can be measured by one half the smallest division (least count). A least count is the smallest division on the scale of a apparatus.

11.1.5 State the results of calculations to the appropriate number of significant figures. The total number of digits in a number. SEE TABLE 11.4 There is a basic distinction between measurement and counting. Counting is exact. Measurement is more of an estimate depending on scale.

11.2.1 State uncertainties as absolute and % uncertainties. Estimated uncertainties should be indicated for all measurements. From the smallest division of a scale. From the last sig fig in a digital measurement. From data provided by the manufacture. Absolute uncertainty is usually expressed in the same units as the reading. Ex. 25.4 +/- 0.1 s

11.2.1 State uncertainties as absolute and % uncertainties. The mathematical symbol for absolute uncertainty is δx were x represents the measurement. Ex. 25.4 +/- .1s where x is 25.4 and δx = .1 Absolute uncertainty is often converted to PERCENT UNCERTAINTY. Ex. 25.4 s +/- 0.4% (0.1 s x100=0.4%) 25.4 s Uncertainties are recorded in one sig fig. The last sig fig should be same place as uncertainty.

11.2.2 Determine the uncertainties in results 1) When adding or subtracting uncertainty values, add the absolute uncertainties. Initial temp = 34.50 C (+/-0.05C) Final temp = 45.21 C (+/- 0.05C) 45.21 – 34.50= 10.71 C (+/- 0.05 + 0.05 = 0.1 C), 10.71 +/- 0.1 C

11.2.2 Determine the uncertainties in results 2) When X or ÷, add the percent uncertainties. Ex. Mass= 9.24 +/- 0.05 g and volume equals 14.1 cc +/- 0.05 cc. Ex. Perform calculation; D= m/v Ex. 9.24 g/ 14.1 cc = 0.655 g/cc Convert absolute uncertainty to % Add the percents Convert total back to percent uncertainty.

11.2.2 Determine the uncertainties in results Ex. Mass=0.05/9.24 X 100 = 0.54% Ex. Volume=0.05/14.1 x 100=0.35% 0.54% + 0.35%=0.89%, = 0.655 g/cc (+/- 0.89%) 0.655 x 0.89/100=0.0058295, density = 0.655 +/- 0.006 g/cc.

11.2.2 Determine the uncertainties in results 3) When X or ÷ by a whole number, X or ÷ the uncertainty by that number. Ex. (4.95 +/- 0.05) x 10 = 49.5 +/- 0.5 4) Powers: When raising to the nth power, multiply the % uncertainty by n. When lowering the nth root, ÷ the percent uncertainty by n.

11.2.2 Determine the uncertainties in results Ex. (4.3+/- 0.5 cm)3 = 4.33 +/- (0.5) X 3 = 4.3 79.5 cm3 (+/- 0.349%) 79.5 cm3 +/- 0.3 cm3

11.3.1 Sketch graphs to represent dependences and interpret graph behavior. Dependent variable (manipulated) – shown on y-axis. Independent variable (responding) – shown on the x-axis. Know a linear and hyperbolic graph (inverse relationship graph or logarithmic)

11.3.2 Construct graphs from experimental Data Be able to plot data on proper scale. Use proper units Label each axis Plot the points accurately Draw a straight line, line of best fit or a curve of best fit. Add title and Key if necessary. Any outliers must be identified.

11.3.3 Draw best-fit lines through data points on graph THE LINE OF BEST FIT – The best fit line that averages the distance between the data points. There should be roughly the same number of data points on one side of the data line as the other. ANOMALOUS – Data that clearly does not fit the trend.

11.3.4 Determine the values of physical quantities from graphs. Be able to determine the gradient and the intercept. Intercept – Where the line crosses the y-intercept. Gradient – The gradient of a straight-line graph is the increase in the y-axis value divided by the increase in the x-axis value.

11.3.4 Determine the values of physical quantities from graphs. Interpolation – A technique where a graph is used to determine data points between taken measurements. Extrapolation – A technique used to find values outside the range for which measurements were made. Area under the graph - For most graphs in chemistry the area under the graph does not represent a useful physical quantity.