1. Density Measurement, Calibration of a Thermometer and a Pipette Accuracy and Precision in Measurements

2. Objectives To measure the density of an unknown solid To calibrate your alcohol thermometer To calibrate your volumetric pipette To gain an appreciation for precision and accuracy in temperature, volume and mass measurements in this lab

3. Reporting Figures in Science Scientists agree to a standard way of reporting measured quantities in which the number of reported digits reflect the precision in the measurement More digits more precision, fewer digits less precision Numbers are usually written so that the uncertainty is indicated by the last reported digit.

4. Counting Significant Numbers in the Lab, Precision The rule is that every digit in the number reported except the last one is certain. So if the mass is reported as 45.872 g we are certain about 45.87 but the 2 is estimated.

5. Mass in the Lab Instruments generally have a precision in their measurement. For example the scales in the lab measure the mass to 0.0001g they are digital so that is that. So the scale cannot measure something that has a mass of 0.00000001g say.

6. Temperature When we use a regular thermometer to measure temperature – how precisely can we measure the temperature?

7. Temperature With a typical thermometer, the best we can do is to estimate the temperature to within maybe a tenth of a degree Celcius or Farenheit, so we can specify the degree with certainty but the tenth we are not certain about. 60.6 o C or 21.3F

8. Alcohol Thermometers In your locker you most likely have an alcohol thermometer Unlike a mercury-in-glass thermometer, the contents of an alcohol thermometer are less toxic and will evaporate away fairly quickly The liquid used can be pure ethanol, toluene, kerosene or isoamyl acetate, depending on the manufacturer and the working temperature range. The liquids are all transparent, so a red or blue dye is added yours is suppose to measure to 110 o C Less Costly Less Accurate at high temperatures!

9. Resistance Temperature Detector Temperature sensors are An RTD is often made of a thin film of Pt – the thin-film’s resistance depends on temperature. Knowing the resistance as a function of temperature means it can be used as a thermometer. Needs software that knows the resistance vs. temperature characteristic for your temperature sensor Pay attention to the type of sensor you use and make sure you use the correct program with it Precision of 0.01 o C Accuracy of 0.15 o C at 0 o C

10. Volume The most accurate way to measure volume in the lab is using either a pipette or a burette burettes read the volume to 0.1mL, so the best we can do is report the volume to a hundredth of a mL.

11. Significant Figures in Calculations When we use measured quantities in calculations, the results of the calculations must reflect the precision of the measure quantities. We should not lose or gain precision

12. In multiplication we keep the precision of the lowest precision number 5.02 x 89.663 x 0.10 = 45.0118 = 45 (3 sig figs) (5 sig figs) (2 sig figs) (2 sig figs) In Division we follow the same rule 5.892 / 6.10 = 0.96590 = 0.966 (4 sig figs) (3 sig figs) (3 sig figs) When reducing the number of significant figures how do we round? Significant Figures Multiplication/Division

13. Rounding When we round to the correct number of figures we round down if the last digit is 4 or less round up is 5 or more – 1.01 x 0.12 x 53.5 / 96 = 0.067556 – = 0.068 (since 0.12 and 96 are two sig figs) – 9.4 x 10 = 94 = 90 (10 1 sig. fig) – 0.096 x 1000 = 100 (100 1 sig. fig)

14. Addition and Subtraction In addition and subtraction carry the fewest decimal places 5.74 (2 decimal places) 0.823 (3 decimal places) + 22.651 (3 decimal places) 29.214 = 29.21 (2 decimal places)

15. Calculations Involving Multiplication/Division and Addition/Subtraction Same as division/multiplication (lowest sig figs of any number in the equation) 3.489 x (5.67 – 2.3) 3.489 x (3.37) 11.758 = 12 (2 sig figs same as 2.3) Round to the appropriate sig. figs at the end!

16. Sampling (random) Errors whenever we attempt to measure a certain quantity we will find that the observed result is not always the same If we histogram the measured answer versus how many times we get the answer we get a distribution like this one This occurs either because the measured quantity varies in nature (like the height of adult males) Or because of random errors that affect the measurement of the result (marble to roll down an incline)

17. When reporting a value, we need to report the mean value along with information about the distribution of measured values Sampling (Random) Errors σ

18. The standard deviation σ is a measure of random error The smaller σ is the more precise the result is For a given set of results σ can be calculated using the formula where the sum is over your data values Sampling (Random) Errors

19. Accuracy vs. Precision

20. Measuring the density of an ‘unknown’ This method works only for solids, insoluble in water and more dense than water Take an unknown and record its number Weigh a Volumetric flask m 1 =m flask Add your unknown to the flask Reweigh the flask and its contents m 2 =m flask +m unk Add water up to neck of flask – remove any trapped air by gently tapping the flask or using a stirring rod Use a dropper to fill the volumetric up to the meniscus Remove any water adhered to neck of the flask above the meniscus Reweigh the flask m 3 =m flask +m unk +m water

21. Calculation To calculate the density of the unknown we need the mass of the unknown m unk and volume of the unknown V unk. Assuming that d water = 0.998203 g/mL, (true at 20.0 o C), and V tot = volume of volumetric flask (50.00mL)  50 mL = V water +V unk  V water = m water /d water  M water = m 3 -m 2  V water = (m 3 -m 2 )/(0.998203 g/mL)  V unk = 50.00 mL – V water  d unk = (m 2 -m 1 )/V unk Note we know V to 3-4 sig figs and mass to 6 sig. figs so we know d to 3-4 sig figs.

22. Thermometer Calibration By varying the temperate of water over the range from freezing to boiling, create a table of thermometer readings T r and sensor reading T s Assuming that the sensor reading may have a small systematic error over the range of the experiment – correct using the formula Plot T R vs T actual and make a linear fit, displaying the equation of the line – this is your calibration curve