Calculating Uncertainty x value x absolute uncertainty of
Calculating Uncertainty x = value δx = absolute uncertainty of the value x+δx 21. 8+ 0. 1 °C
Fractional and Percentage uncertainties Don’t get confused with % error!!!
Each calculation has own rules… • Averaging trials • Addition/Subtraction • Raising to a power • Multiplication/Division with uncertainty • Multiplication/Division with constant or value without uncertainty
Averaging trials (up to 8) to find xavg + δ xavg Uncertainty of average = (range of trials) (# of trials)
You time how long it takes for a 1. 0 g of sodium metal to completely react in 200 cm 3 of water. The data is stated in the table below. What average value should be stated for this experiment? Trial Number 1 Time ± 23 2 sec 2 3 4 25 22 21
Addition/Subtraction • Absolute Uncertainty on final value = sum of absolute uncertainties An initial temperature reading of a water bath is taken at 80± 0. 5ºC and another reading after 2 minutes when the temperature is 70± 0. 5ºC. What is the change in X = 80 -70 = 10ºC temperature? δ x = 0. 5+0. 5 = 1ºC 10 + 1ºC
Raising to a power • Percent uncertainty on final value = multiply percent uncertainty by the power You are measuring the volume of a cube. You measure each side to be 5± 0. 5 cm-- what would its 3 = 125 X = 5 volume be? cm 3 125 + 40 cm 3 Now to 1 sig fig= ± 40
Multiplication/Division with uncertainty • Percent Uncertainty on final value = sum of percent uncertainties You cut a piece of paper to be a square so that you can make an origami crane. You measure a square 20± 0. 1 cm by 20± 0. 1 cm. What is the X = 20 x 20 = 400 area of this square? 400 + 4 cm 2 2 cm First: find the percent uncertainty of each. Now: the sum = 1% Convert to absolute: 0. 01 x 400
Multiplication/Division of value without uncertainty • Same percent uncertainty on final value Imogene Pass is measured as 13, 114 ± 2 ft. What is the pass in meters if 1 foot = 0. 3048 m? 3, 997. 2 + 0. 6 m X = 13114 x 0. 3048 = 3, 997. 2 m First: find the percent uncertainty of original. Convert to absolute of new value: 0. 0001525 x
Now get out your Molar Mass of Butane lab… 1. What mass of butane was released into the graduated cylinder? … n o i t btrac u s / n o dditi 21. 0 + 0. 1 g – 21. 3 + 0. 1 g 0. 3 = + 0. 2 g Unless you had a balance that measured to 0. 01 g
2. Convert the temperature and volume into more appropriate units. 100 m. L to dm 3 ~20. 0ºC to K 3 dm 0. 100 ± 0. 5/1000 = ± 0. 0005 dm 3 293. 0± 0. 1 K
3. With reference to chart, what is the pressure of water vapour at the relevant temperature? ~19 mm Hg
4. What is the pressure due to butane in the collected volume? Ptotal = Pcollected + Pwater vapour 768. 1 = Pcollected + 19 749. 1 mm. Hg = Pcollected
5. Convert the pressure to appropriate units. 0. 9856 749. 1 mm. Hg / 760 = atm x 100 k. Pa = 98. 56± 0. 01 k. Pa
6. How many moles of butane are in the collected sample of gas? PV = n. RT = ± 0. 01 n o i s i v i 0. 00405 mol d / t n n o i i a t t a r c e i l c p n i t u l mu percent f o m Su
6. How many moles of butane are in the collected sample of gas? PV = n. RT = n o i s i v i 0. 00405 mol d e / i t n n o i i a t t a r c e i l c p n i mult percent u f o m Su 0. 0054 x 0. 00405 = 0. 00002 ± 0. 00002 0. 00405
7. Based on your data, what is the molar mass of butane? g/mol = 0. 3/0. 00405 = 74. 1 n o i s i v i d / t n n o i i a t t a r c e i l c p n g/mol i t u l mu percent f o m u S 0. 672 x 74. 1 = 74. 1 ± 50 g/mo
8. What is the accepted value of butane (C 4 H 10)? 58. 14 g/mol
9. Calculate the % difference between your experimental value and the accepted. (AKA the percentage error) ? h g i h e so m y h W b r o r r e e h t t igh
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