If we dispense 20 mL using a 10-mL Class A pipet, what is the total volume dispensed and what is the uncertainty in this volume? If the pH of a solution is 3.72 with an absolute uncertainty of ±0.03, what is the [H+] and its uncertainty? How might we accomplish this? The concentration and uncertainty for Cu2+ is 7.820 mg/L ± 0.047 mg/L. The dilution calculations for case (a) and case (b) are, \[\text{case (a): 1.0 M } \times \frac {1.000 \text { mL}} {1000.0 \text { mL}} = 0.0010 \text{ M} \nonumber\], \[\text{case (b): 1.0 M } \times \frac {20.00 \text { mL}} {1000.0 \text { mL}} \times \frac {25.00 \text{ mL}} {500.0 \text{mL}} = 0.0010 \text{ M} \nonumber\], Using tolerance values from Table 4.2.1, the relative uncertainty for case (a) is, \[u_R = \sqrt{\left( \frac {0.006} {1.000} \right)^2 + \left( \frac {0.3} {1000.0} \right)^2} = 0.006 \nonumber\], and for case (b) the relative uncertainty is, \[u_R = \sqrt{\left( \frac {0.03} {20.00} \right)^2 + \left( \frac {0.3} {1000} \right)^2 + \left( \frac {0.03} {25.00} \right)^2 + \left( \frac {0.2} {500.0} \right)^2} = 0.002 \nonumber\]. Suppose we dispense 20 mL of a reagent using the Class A 10-mL pipet whose calibration information is given in Table 4.2.8. uncertainty is 1/2 of the smallest measurable difference. Thus, we report the total charge as 18 C ± 1 C. Many chemical calculations involve a combination of adding and subtracting, and of multiply and dividing. I … (Part 2) Equilibrium Constant of Iron Thiocyanate, 01. Calculate the total mg of iron in the 250-mL flask. To estimate the uncertainty in CA, we first use Equation \ref{4.1} to determine the uncertainty for the numerator. For the equations in this section we represent the result with the symbol R, and we represent the measurements with the symbols A, B, and C. The corresponding uncertainties are uR, uA, uB, and uC. If the uncertainty in measuring Po and P is 15, what is the uncertainty in the absorbance? A propagation of uncertainty allows us to estimate the uncertainty in a result from the uncertainties in the measurements used to calculate that result. The absorbance and uncertainty is 0.40 ± 0.05 absorbance units. Verify the results of your mass percent iron calculation with your instructor. we clearly underestimate the total uncertainty. Verify that an uncertainty of ±0.0015 ppm–1 for kA is the correct result. Of these two terms, the uncertainty in the method’s sensitivity dominates the overall uncertainty. J. S. Fritz and G. H. Schenk, Quantitative Analytical Chemistry, 3rd ed., Allyn & Bacon, Boston, 1974, p. 560, Sign in|Report Abuse|Print Page|Powered By Google Sites, 02. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. It depends on the size of the volumetric flask. In other words, the volume contained in the 100-mL volumetric flask is 100.0 mL and the volume contained in the 250-mL volumetric flask is 250.0 mL. The spool’s initial weight is 74.2991 g and its final weight is 73.3216 g. You place the sample of wire in a 500-mL volumetric flask, dissolve it in 10 mL of HNO3, and dilute to volume. The concentration of iron in the 5.00-mL sample is the same as the concentration in the 250-mL flask. For more information contact us at info@libretexts.org or check out our status page at https://status.libretexts.org. Improving the signal’s uncertainty will not improve the overall uncertainty of the analysis. The absolute uncertainty in the mass of Cu wire is, \[u_\text{g Cu} = \sqrt{(0.0001)^2 + (0.0001)^2} = 0.00014 \text{ g} \nonumber\], The relative uncertainty in the concentration of Cu2+ is, \[\frac {u_\text{mg/L}} {7.820 \text{ mg/L}} = \sqrt{\left( \frac {0.00014} {0.9775} \right)^2 + \left( \frac {0.20} {500.0} \right)^2 + \left( \frac {0.006} {1.000} \right)^2 + \left( \frac {0.12} {250.0} \right)^2} = 0.00603 \nonumber\]. In other words, the volume contained in the 100-mL volumetric flask is 100.0 mL and the volume contained in the 250-mL volumetric flask is 250.0 mL. Since the relative uncertainty for case (b) is less than that for case (a), the two-step dilution provides the smallest overall uncertainty. Many other mathematical operations are common in analytical chemistry, including the use of powers, roots, and logarithms. if i remember correctly, a volumetric flask has one line marking the 100ml mark. Is Calculating Uncertainty Actually Useful? As shown in the following example, we can … The short answer is, yes. An uncertainty of 0.8% is a relative uncertainty in the concentration of 0.008; thus, letting u be the uncertainty in kA, \[0.008 = \sqrt{\left( \frac {0.028} {23.41} \right)^2 + \left( \frac {u} {0.186} \right)^2} \nonumber\], Squaring both sides of the equation gives, \[6.4 \times 10^{-5} = \left( \frac {0.028} {23.41} \right)^2 + \left( \frac {u} {0.186} \right)^2 \nonumber\]. First, complete the calculation using the manufacturer’s tolerance of 10.00 mL±0.02 mL, and then using the calibration data from Table 4.2.8. Absorbance, A, is defined as, \[A = - \log T = - \log \left( \frac {P} {P_\text{o}} \right) \nonumber\]. To prepare a standard solution of Cu2+ you obtain a piece of copper from a spool of wire. Missed the LibreFest? Which procedure will give better precision? Suppose you have a range for one measurement, such as a pipet’s tolerance, and standard deviations for the other measurements. So what is the total uncertainty? To complete the calculation we use Equation \ref{4.2} to estimate the relative uncertainty in CA. The other will pipette 9 ml of the dilution liquid into the sample solution. For example, if the result is given by the equation, \[u_R = \sqrt{u_A^2 + u_B^2 + u_C^2} \label{4.1}\]. The overall uncertainty in the final concentration—and, therefore, the best option for the dilution—depends on the uncertainty of the volumetric pipets and volumetric flasks. Rounding the volumes to four significant figures gives 20.00 mL ± 0.03 mL when we use the tolerance values, and 19.98 ± 0.01 mL when we use the calibration data. Let’s consider three examples of how we can use a propagation of uncertainty to help guide the development of an analytical method. Calculate the total mg of iron in this 100-mL flask. rectangular distribution, an estimate of the standard uncertainty (or standard deviation) can be calculated using1: () 3 uV α = i.e. First, we find the uncertainty for the ratio P/Po, which is the transmittance, T. \[\frac {u_{T}} {T} = \sqrt{\left( \frac {15} {3.80 \times 10^2} \right)^2 + \left( \frac {15} {1.50 \times 10^2} \right)^2 } = 0.1075 \nonumber\], Finally, from Table \(\PageIndex{1}\) the uncertainty in the absorbance is, \[u_A = 0.4343 \times \frac {u_{T}} {T} = (0.4343) \times (0.1075) = 4.669 \times 10^{-2} \nonumber\]. To estimate the uncertainty we use a mathematical technique known as the propagation of uncertainty. 1980, 52, 1158–1161]. All the iron in the 100-mL flask came from a 5.00-mL sample that was removed from the 250-mL volumetric flask.
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