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Chapter 3: Q15P (page 62)

Find the absolute and percent relative uncertainty and express each answer with a reasonable number of significant figures.

a)6.2±0.2-4.1±0.1=?b)9.43±0.05×0.0160.001=?c)6.2±0.2-4.1±0.1÷9.43±0.05=?d)9.43±0.05×6.2±0.2×10-3+4.1±0.1×10-3

Short Answer

Expert verified

To calculate the absolute and percent relative uncertainty.

Step by step solution

01

To calculate absolute and percent relative uncertainty

Absoluteuncertainty=3.12(±0.05)a)6.2±0.2-4.1±0.1=2.1±0.2or±11%b)9.43±0.05×0.0160.001=0.151±0.09or±6%c)6.2±0.2-4.1±0.1÷9.43±0.05=0.223±0.024or±11%d)9.43±0.05×6.2±0.2×10-3+4.1±0.1×10-3=0.0971±0.0022or±2.2%

02

To calculate the percent relative uncertainty

Percent relative uncertainty with formula (e represents the ±value)

=e12+e22+e32

03

To obtain the absolute uncertainty

The following is the formula;

percentrelativeuncertainty/100×thevalueofa)2.1;b)0.151c)0.223d)0.0971

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Most popular questions from this chapter

Explain the difference between systematic and random error.

Write each answer with a reasonable number of figures. Find the absolute and percent relative uncertainty for each answer.

(a)[12.41(±0.09)÷4.16(±0.01)]×7.0682(±0.0004)=?

(b)[3.26(±0.10)×8.47(±0.05)]-0.18(±0.06)=?(c)6.843(±0.008)×104÷[2.09(±0.04)-1.63(±0.01)]=?(d)3.24±0.08=?(e)(3.24±0.08)4=?(f)log(3.24±0.08)=?(g)103.24±0.08=?

State whether the errors in (a)-(d) are random or systematic:

(a) A 25 - mL transfer pipet consistently delivers 25.031±0.009mL.

(b) A 10 - mL buret consistently delivers role="math" localid="1663303542431" 1.98±0.01mLwhen drained from exactly 0 to exactly 2mL and consistently delivers 2.03mL±0.02mL when drained from 2 to 4mL .

(c) A 10 - mL buret delivered 1.9839g of water when drained from exactly 0.00 to 2.00mL . The next time I delivered water from the 0.00 to the 2.00mL mark, the delivered mass was .

(d) Four consecutive 20.0 - μL injections of a solution into a chromatograph were made and the area of a particular peak was 4383 , 4410, 4401 , and 4390 units.

(a) Show that formulamassofNaCIis58.442±0.006g/mol(b) To prepare a solution of NaCI , you weigh out 2.634(60.002)g and dissolve it in a volumetric flask whose volume is 100.00(60.08)mL Express the molarity of the solution, along with its uncertainty, with an appropriate number of digits.

Vernier scale. The figure below shows a scale found on instruments such as a micrometer caliper used for accurately measuring dimensions of objects. The lower scale slides along the upper scale and is used to interpolate between the markings on the upper scale. In (a), the reading (at the left-hand 0 of the lower scale) is between 1.4and 1.5on the upper scale. To find the exact reading, observe which mark on the lower scale is aligned with a mark on the upper scale. Because theon the lower scale is aligned with the upper scale, the correct reading is 1.46. Write the correct readings in (b) and (c) and indicate how many significant figures are in each reading.
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