(b) The random error, r', on the result, R, is given by R = 2 + 2 where v', and v, are the random errors on V', and Vt, respectively (1) Let V₁=26.00 mL, V₁ = 24.00 mL; v' = ±0.01 (3) mL, v = ±0.01(2) mL. What is the percentage random error, r'/R x 100%, on R? (2) What is r'/R x 100 if the conditions of each titration vary (e.g., different portions of the burette stem are used) so that V₁ = 26.00 mL, V₁ = 24.00 mL; v' = ±0.05 (2) mL, vt = ±0.04(8) mL?
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- dt The Gompertz growth model is commonly used to model tumor cell growth. Let v(t) be the tumor's volume, then du(t) = A e-atv(t) where λ and a are two appropriate constants. (a) Verify that the solution is given by v(t) = voe/a(1-e-at), where vo is the initial tumor volume. (b) This model takes into account the fact that when nutrients and oxygen are scarce at the tumor's core, its growth is impaired. Find the final predicted tumor volume (let too). (c) For a specific mouse tumor, it was experimentally found that λ = 2.5 days, a = 0.1 days with vo = 50 x 10³ mm³. Use any method available to make a plot of v(t) vs t. (d) Check the result obtained in Part b with the results from the graph from pat c.A volume of 250 ml of a 0.05 M solution of a reagent of formula weight (relative molecular mass) 40 was made up, the weighing being done by difference. The standard deviation of each weighing was 0.0001 g. 1 (a) What were the standard deviation and relative standard deviation of the weight of reagent used?9) Using error propagation formulas, find (i) the absolute uncertainty and (ii) the percent relative uncertainty for each of the following operations. (a) 6.1 (+0.3) – 3.6 (±0.2) = ? (b) 9.56 (+0.06)X 0.017 (+0.002) = ? (c) [6.9 (±0.3) – 3.9 (±0.2)] ÷ 9.32 (±0.04) = ? (d) 8.24 (+0.06)X {[6.9 (±0.3) X 10-3] + [4.2 (±0.2) X 10-3]} = ?
- A volumetric calcium analysis on triplicate samples of the blood serum of a patient believed to be suffering from a hyperparathyroid condition produced the following data: mmol Ca/L = 3.55, 3.65, 3.14. What is the 95% confidence interval for the mean of the data, assuming(a) No prior information about the precision of the analysis?(b) s → σ = 0.056 mmol Ca/L?(a) Explain the difference between systematic and random errors. State whether the errors in (b)–(e) are random or systematic. (b) A 25-mL transfer pipet consistently delivers 25.031 + 0.009 mL when drained from the mark. (c) A 10-mL buret consistently delivers 1.98 6 0.01 mL when drained from exactly 0 to exactly 2 mL and consistently delivers 2.03 6 0.02 mL when drained from 2 to 4 mL. (d) A 10-mL buret delivered 1.983 9 g of water when drained from exactly 0.00 to 2.00 mL. The next time I delivered water from the 0.00 to the 2.00 mL mark, the delivered mass was 1.990 0 g. (e) Four consecutive 20.0-mL injections of a solution into a chromatograph were made (as in Figure 0-6) and the area of a particular peak was 4 383, 4 410, 4 401, and 4 390 units. (f) A clean funnel that had been in the lab since last semester had a mass of 15.432 9 g. When filled with a solid precipitate and dried thoroughly in the oven at 1108C, the mass was 15.845 6 g. The calculated mass of precipitate was…In a survey of 1000 large corporations, 250 said that, given a choice between a job candidate who smokes and an equally qualified nonsmoker, the nonsmoker would get the job (USA Today).(a) Let p represent the proportion of all corporations preferring a nonsmoking candidate. Find a point estimate for p.(b) Find a 0.95 confidence interval for p.(c) As a news writer, how would you report the survey results regarding the proportion of corporations that hire the equally qualified nonsmoker? What is the margin of error based on a 95% confidence interval?
- Analysis of several plant-food preparations for potassium ion yielded the following data: Sample Percent K+1 6.02, 6.04, 5.88, 6.06, 5.822 5.29, 5.13, 5.14, 5.28, 5.20 The preparations were randomly drawn from the same population.(a) Find the mean and standard deviation s , variance , andCV for each sample.(a) For use in an iodine titration, you prepare a solution from 0.222 2 (+0.000 2) g of KIO3 [FM 214.001 0 (+0.000 9)] in 50.00 (+0.05) mL. Find the molarity and its uncertainty with an appropriate number of significant figures. (b) Would your answer be affected significantly if the reagent were only 99.9% pure?Q3. A cellulose coating that weighs at least 3.00 mg is often applied to the exterior of vitamin C tablets in order to delay the release of active ingredients. A random sampling of 100 vitamin tablets revealed that 6 vitamin tablets failed to meet the required weight of the cellulose coating. (а) Calculate the relative standard deviation (in %). (b) Determine the number of tablets should be taken into consideration to ensure a relative standard deviation of 15 %.
- (3) In a titration, the % analyte is computed from the following equation: Vol (titrant) x M (titrant) x MW (analyte) % analyte = x 100 Weight (sample) Calculate the absolute error in the % analyte from the following data. Vol (titrant)= 38.04 t 0.02 ml M (titrant) MW (analyte) = 74.116 t 0.005 mg/mmol Wt (sample) = 800.0 ± 0.2 mg = 0.1137 ± 0.0003 mmol/ml %3!3-3 Types of Error; 3-4 Propagation of Uncertainty from Random Error (30 min) If A = 3.475 (+0.002), B = 87.336 (±0.001), C = 10.004 5 (±0.000 5), D = 11.8 (+0.2), and E = 5.10 (±0.03), report the answers of the following calculations with both the absolute uncertainty and the percent relative uncertainty. a) (A - B) XE c) b) (C+D)/(AXE) d) [(A+B+C) x (B-C-E)] / [DXE] (10-D)/(E/1000) Answer w/ absolute uncertainty: -428 (13) or -427.7 (±2.5) Answer w/% relative uncertainty: -428 (±0.6%) or -427.7 (±0.5⁹%) b) Answer w/ absolute uncertainty: 1.23 (±0.01) or 1.230 (+0.013) Answer w/ % relative uncertainty: 1.23 (±1%) or 1.230 (+1.1%) Answer w/ absolute uncertainty: 3 (±1) x 10-10 or 3.1 (±1.4) × 10-10 Answer w/ % relative uncertainty: 3 (±50%) x 10-10 or 3.1 (±46%) × 10-10 Answer w/ absolute uncertainty: 121 (±2) or 121.0 (+1.4) Answer w/ % relative uncertainty: 121 (±2%) or 121.0 (±1.8%)Rewrite the number 3.123 56 (+0.167 89%) in the forms (a) number (6absolute uncertainty) and (b) number (+percent relative uncertainty) with an appropriate number of digits.