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Chem 360 Check List - Data Analysis
Reference: Taylor, J. R. 2nd Ed., (Oxford University Press): Mill Valley, CA,1997 An Introduction to Error Analysis; University Science Books, Listed below are These are all addressed in Taylor, and many are contained inside the front and back covers. You are responsible for correctly applying these concepts in your Chem 360 lab data analysis concepts that a B.S. chemist should know about. work and reports. Y Error vs. blunder ou may want to use this list as a check list as you read Taylor. Definition vs. measurement uncertainty Experimental discrimination Interpolation of scale readings Systematic vs. random error Report best value ± uncertainty Round uncertainty to 1 significant digit Matching last significant figure with order of magnitude of uncertainty Significant discrepancy vs. insignificant discrepancy Accepted value vs. true value Checking proportionality with graph or ratio Error bars on graph Relative or fractional uncertainty Significant digits Estimating uncertainties in direct measurements repeated measurements - rounding off, arithmetic operations Propagation of uncertainty in q(x,y,...) Role of quadrature in propagation of error for normal (Gaussian) errors^ resolution of measuring devices - general formula (3.47) Propagation through several experimental steps Mean x Standard deviation σ, rms deviation, variance σ (^2) (5 or more measurements required) ± Standard deviation of mean (SDOM)σ and 68% confidence σx = σx / N
Distribution functions: f(x) dx - probability of finding x in dx
" a^ b^ f^ ( x ) dx^ for probability of finding x between a,b
x = "#^ # $ f ( x ) dx
" (^) x^2 = !
"#^ #^ $^ ( x^ " x^ )^2 f^ ( x ) dx
Normalized Gaussian distribution fx,σ(x) =
!
( " 12 # ) exp($( x^ $^ x^ )^2 /^2 "^2 ) ± 1.96 Confidence and reasonable outcomes Rejecting dataσ and 95% confidence - need for criteria Chauvenet's criterion Chi squared criterion, χ 2 Linear least square regression minimize χ (^2) = [yi - (A + Bx - line of maximum likelihoodi)] (^2) /σy (^2) in normal distribution Least square equations for A, B, Extrapolation dangers σy^2 , σA^2 , σB^2
Does the data listed below verify this relation betwe graphical or ratio argument to support your answer. You may wish to include estimated uncertainties into your argument. en VHydrogen and gMg? Use a
VHydrogen 12.7 (ml) 0.0101gMg 14.0 15.2 16.5 0.01100.01210.01 29 17.8 19.0 0.01400. (Taylor, Sec. 2.6)
Physical Measurements Elementary Propagation Data Analysis Assignment 2 (50 pts) Apply the general uncertainty propagation equation (Taylor, 3.47, p.75) to the measurement situations lis Answer the following questions on 8.5x11 inch paper (i.e.,ted below to develop specific explicit uncertainty expressions. NOT IN YOUR LAB NOTEBBOK! Example: Absorbance ). = molar absorbtivity x path length x molarity A = a x b x M Uncertainty in A ≡ δA, etc. δA = (^) ^ ^ ^ ^ ∂ ∂Aa^ ^2 bM δa2 +^ ^ ^ ∂ ∂Ab^ ^2 aM δb2 +^ ^ ^ ∂∂MA^ ^2 ab δM^2 ^ ^ ^ 1/
= ( b^2 M^2 δa^2 + a^2 M^2 δb2 +a^2 b^2 δM^2 )^ 1/
Do All: vrms = 3 RT M , R constant
P = (^) VRT-b - (^) Va 2 , R, a, b constants E = !
8^ n 2 mah^22 , n, h constants qr = 2 I kT σ h 2 , k, σ, h constant qtr = (^) ^ ^2 π^ m kT h 2 ^ ^ 3/2 V , k, h constant
- Use your spreadsheet to answer some questions a) What are the requirements of δE (if any) to produce an uncertainty of 10 - let's play what if - Daltons in the molecular weight of the 50,000 Dalton protein (keeping all other parameters constant). 10 Daltons in the 50,000 Da uncertainty in time,^ b) If the^ δE is limited to .5% (.5% of 20 keV, 100. eV), can we achieve a δt? lton protein? If so, what is the greatest allowable value of the^ δm of
Physical Measurements Data Analysis Assignment 3 Example Here's an example we'll go over in class Estimate the propagated uncertainty for an experiment from an old Chem 150 Lab- we've used this in the past: Manual (Determination the Molecular Weight of a Volatile Liquid) by reconstructing on paper a plausible experiment (lab handout provided). Assume that you use an analytical balance, graduated cylinder, barometer, and ordinary thermometer. I'll remind you of the procedure. A suggested spreadsheet layout we'll discuss:
Propagation of Error Molecular Weight Determination R= 0.
Parameter Value Error V-Converted^ (l E - rror Converted atm)/(mol-K) Mass(g) Temp(°C) Pressure(mmHg) (^) 600.00.3294.0 0.010.50.5 (^) 0.7895367.20.32 (^) 0.00070.010. Volume(mL) 265.0 (^) MW= 0.5 (^) 0.265046. 0.0005g/mol
Mass Temp^ Term^ ±Error^ 0.010.5 (Partials)^2 20737.25520.01575303^ Term Value 2.073725520.00393826^ =^ Err^2Par* (g/mol)^2(g/mol)^2 tial^ Pressure Volume 0.00070.0005 3407.0296430238.4468 0.001474650.00755961 (g/mol)^2(g/mol)^
Overall Error = (±) Sum=^ 2.086698031.44454077^ (g/mol)^2g/mol ± 1 g/mol
