Experiment Error(英语)

Experimental Error
Significant Figures: 142.7 (4 sig. figs)
It is the minimum number of digits needed to write a given value in scientific notation without loss of accuracy.
142.7 (4 sig. figs)
1.427 x 102
9.25 x 104 (3 sig. figs)
9.250 x 104 (4 sig. figs)
9.2500 x 104 (5 sig. figs)
Zeros are significant when they occur
1)in the middle of the number;
2)at the end of the number on the rhs of a decimal pt.
106, 0.0106, 0.01060
Estimates:
Absorbance: 0.234 ± 1: 0.235 to 0.233
Transmittance: 58.3 ± 2
Significant figures in arithmetic
1.362 x 10-4 5.345
+3.111 x 10-4 + 6.728
---------------- -----------
4.473 x 10-4 12.073
In addition and subtraction the number of the significant figures in the answer may exceed or be less than that in the original data.
In multiplication and division the number of the significant figures is limited to the number of digits contained in the number with the fewest significant figures.
34.60 ÷ 2.46287 = 14.05
4.3179 x 1012 * 3.6 x 10-19 = 1.6 x 10-6
Logarithms n = 10a means that log n = a (the number n is the antilogarithm of a)
339 = 3.39 x 102
log 339 = 2. 530 | 2: characteristic 530: mantissa
The number of digits in the mantissa should equal the number of total significant figures
Consequently, when we convert a logarithm to an antilogarithm, the number of sig. figs in the antilogarithm should equal the number of digits in the mantissa. antilog ( - 3.42 ) = 10 -3.42 = 3.8 x 10-4
Significant figures and graphs
Calibration curve for a 50-mL buret
Types of Error
Every measurement has some uncertainty⇒experimental error Systematic (determinate) error: arises from a flaw in equipment or the design of the experiment
Random (indeterminate) error: arises from the effects of uncontrolled (and maybe uncontrollable) variables in the measurement. It can be positive or negative and always present! (electric noise, human readings…)
Precision : describes the reproducibility of the results
Accuracy : describes how close a measured value is to the “true value”.
Absolute Uncertainty : expresses the margin of uncertainty associated with a measurement. Buret: ± 0.02 mL
Relative Uncertainty : compares the size of the absolute uncertainty to the size of its associated measurement.
{absolute uncertainty ÷ magnitude of measurement}
12.35 ± 0.02 002.035
.1202.0=
Percent Relative Uncertainty : Relative Uncertainty x 100
Propagation of Uncertainty In the product x • x
Uncertainty in Molecular Mass
In the Periodic Table of the textbook we read that the atomic mass of O is 15.999 4 ± 0.000 3 g/mol. The uncertainty is not the result of random error but it comes predominantly from the isotopic variation in samples of oxygen from different sources.
From one source: O = 15.999 1 From another source: O = 15.999 7
So, atomic mass of O for this particular group: 15.999 1 to 15.999 7
If the “true” mass is 15.999 7 then the mass of O 2 = 2 x 15.999 7 = 31.999 4 g/mol
If the “true” mass is 15.999 1 then the mass of O 2 = 2 x 15.999 1 = 31.998 2 g/mol
The mass of oxygen is 31.999 8 ± 0.000 6 g/mol (acceptable value by all!)
Uncertainty of n atoms = n x (uncertainty of one atom ) It is not given by 22003.0003.0+±
Find the molecular mass of C 2H 4:
2C: 2(12.010 7 ± 0.000 8) = 24.021 4 ± 0.001 6 4H: 4(1.007 94 ± 0.000 07) = 4.031 76 ± 0.000 28
2C + 4H = 28.053 16 ± ?
And ±? = 0016.000028.00016.022=+± because the uncertainties in the masses of C and H are independent of each other.
2C + 4H = 28.053 16 ± 0.001 6 = 28.053 ± 0.002 g/mol。