Pchem lab

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Apr 3, 2024

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Basic Measurements Assignment Week 1: Stopper Measurements Answers Must be typed in 12 pt. Times N ew Roman. Individual Calculations can be handwritten if legible. There is no revision opportunity for this assignment. Part A: Experimental Theory and Data Management (30 pts) Mass (g) σ m (g) % Uncertainty Volume (cm 3 ) σ V (cm 3 ) % Uncertainty Random errors are errors in the data that are unpredictable and unbiased. Systematic errors are errors caused by an error in the experimental setup that are often consistend and biased. If the values are precise but not accurate, there was likely some systematic error that skewed all of the values one way or another. If they are not precise, then there was probably random error(s)affecting some data. Accuracy is how close a measured or estimated value is to the accepted value. Precision is now consistent a data set is. It is about how close the individual measurements are to each other. The goal of this experiment was to take measurements, learn to manipulate the data to calculate new quantities, and using the error in the measurements to estimate error of the new quantities. Accuracy : %error is a measure of the accuracy error =ILiterature Experimental 1 x 100% Experimental precision : O is a measure of the precision o = I 1 S(X Y)2 => a => 104 58g =0 00289 0 002790 79cm3 I 3 7 cm3 4 790

Density (g/cm 3 ) σ p (g/cm 3 ) % Error % Uncertainty Stopper # Mass (g) σ m (g) Volume (cm 3 ) σ V (cm 3 ) Stopper # Density (g/cm 3 ) σ p (g/cm 3 ) % Error % Uncertainty The mass and density are both very precise. The standard deviation can be used as an indicator for precision with a small s.d. meaning more precision. The s.d. of mass was +/- 0. 0028g, so most values were within 0.0028g of the mean. The density has a little less precision with a s.d. of +/- 0.6 g/cm3, but this is still precise. The volume is the least precise with a s. d. of +/- 3.7 cm^3. The density we found was relatively accurate with a % error of only 5.1%. This means that the experimental density is only 5.1% different from the accepted density. A % error of 0% would mean total accuracy, so we are pretty accurate. The masses and densities for both stoppers are very precise with standard deviations of +/- 0. 0028 g for both and a s.d. of +/- 0. 084g/cm^3 and +/- 0.075 g/cm^3 for 1 and 2, respectively. The precision of the masses of stoppers 1 and 2 is the same as the common stopper because they all three have the same standard deviation of the mass. The density of the common stopper is slightly more precise with a s.d. of +/- 0.06 g/cm^3. The volumes for stoppers 1 and 2 are relatively precise but not as good as mass or density with a s.d. of +/- 0.84 cm^3 for 1 and +/- 0.58 cm^3 for 2. However, these are both still more precise than the common stopper with a s.d. of +/- 3.7 cm^3. The accuracy is related to the % error, so stopper 2 and the common stopper have very similar accuracies but stopper I was more accurate with a % error of only 2.2%.

Stopper # Density g/cm 3 There are no outliers in the data as per the rule of four. Next page -> = I 1 37 if 9ll 11 : 2 1 27 mean=1 38g/cm3 2 02 0 = 0 31g/cm3 20 31(4) = 1 24 , 80 1 38 11 24 3 1 48 if W10#5 : 0 14 mean= 1 32g/cm3 L 1 23 0 = = 0 43g/cm3 5 2 85 Questionable (not more than 40 , 50kept) D 1 00 T 1 22 g 1 30 9 1 37 if W10#10 : Mean= 1 . 44g1cm3 (-doesn't deviate 0 774 r = =0 25 g/cm3 by 40 , so kept) 18 Questionable 1 54 Il

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Th vertical error bars for the standard deviation of the mass are included but cannot be seen on this scale.

Slope Intercept Error in slope Error in Intercept R-squared Not Needed Standard Deviation of Y F-statistic Not Needed Not Needed Degrees of Freedom Density Correctly Reported as: ________________________ The density of an object is a matter of the material from which it is made. For example, I could have 12L of water or 1000L but the density is always the same because it is a function of the water itself. Although each of our masses and volumes were different, they calculated out to be the same density because we were using the same object.

° Part B: Sample Calculations Using Experimental Data (20 pts) Show your work with all individual steps for all of the calculations listed in this section. If these calculations were done on paper and uploaded as pictures, include the organized and labeled original handwritten work when submitting the hard copy of the worksheet. Common Stopper Calculations: a) The density average from a range of individual stopper densities would be more accurate because the % error is only 0.73% but the % error for the calculated is 5.1%. b) The calculated density is more precise because the standard deviation is +/- 0.06 g/cm^3 but the standard deviation for the density average from a range of individual stopper densities it is +/- 0.081 g/cm^3. c) In general theory, the better method would be the density averaged from a range of individual stopper densities. Although it was slightly less precise, it was not a significant difference when compared to the difference between the accuracies. It is significantly more accurate. Taking multiple measurements increases the reliability and accuracy of the densities. The dV/dh value contributed the most to the final error in the propagation. It had the highest value of 12.33 once the derivative was solved, so this would mean it pushes the value further from the mean, thus increasing the error. We can use the standard deviation for the absolute error of the mass because it is an extrinsic property and can be directly measured. The propagation step needs to be used for the absolute error of the density because it is an intrinsic property that needs to be calculated, so we cannot truly “measure” the density, it is an estimation based on the mass and volume measurements taken.

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Average Mass of the Common Stopper: ____________________ Average Small Diameter of the Common Stopper: _____________________ Average Large Diameter of the Common Stopper: _____________________ Average Slant Height of the Common Stopper: ________________________

Height of the Common Stopper: _________________________ h = (2 053) 2 - (6 521 5 675) 4 = 7 040 0 846 = on = =2 Dom 2 OCM 0 12 Cm = i2 + (2 7) (0 52 + n 515 7) + 5 7) : =79 02cm3 =79cm3 S : OV=Eh(otSs+2s h : =I 8 : v = Rh' (S2 + 25 + (2) = Eh(S + 2 Y = +2 π h(2S + s 1S" + 0 = T2 π (f2 + Ss + 3) = (2 π h(2S + 5) OVST (16 2 + 3 7) ov = 29 27cm3 =29cm3

Volume of the Common Stopper: ____________________ Density of the Common Stopper: _______________________ % Error: ________________ % Uncertainty: ______________

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Individual Stopper Calculations: For the Individual Stopper calculations, you may assume that σ m , σ s , σ S , σ h’ , and σ h are the same as they are for the Common Stopper. Height of Individual Stopper: _________________ Volume of Individual Stopper: __________________ Density of Individual Stopper: ____________________ % Error: ____________________ % Uncertainty: ____________________