Intro Flashcards
Sig Fig basic rules
-Start counting with the first non-zero digit
-Zeros between numbers are significant
-Zeros to the right of a number with a decimal are significant
-Zeros to the right of a number that has no decimal are not significant
-An integer has an infinite number of significant figures
Addition/subtraction of sig figs
The number of decimal places in the answer should be the same as the term with the fewest number of decimal places
Common logarithms sig figs
Number of digits after the decimal in a common logarithm has the same number of SF as the original number
Multiplication/division of sig figs
Number of significant figures in answer should be same as the term with the fewest number of significant figures
Population standard deviation
Square root of the Sum of (values - mean)^2 divided by number of values
Sample standard deviation
-used for smaller sample sets
-Square root of the Sum of (values - mean)^2 divided by (number of values - 1)
Average deviation
-estimate of uncertainty
-(Absolute value of sum of values - mean) divided by number of values
% average deviation
Average deviation / average value x 100%
Accuracy
-the correctness of a measurement/determination
-The closer a result is to te true value, the more accurate
Error
measure of accuracy
Precision
- reproducibility of a set of measurements
-The closer the several results are to each other, the more precise they are regardless of accuracy
Deviation
measure of precision
Rejection of measured values
-Rule 1: if a cause is known for an error (spillage or dirt), discard the result
-Rule 2: if there are three or fewer results in a set, do not discard any results except by Rule 1
-Rule 3: apply the Q test
Rejection quotient, Q
-the ratio of difference between the questionable value and its closest neighbor (the gap) to the range (the difference between the largest and the smallest value)
-If calculate Q exceeds the values of rejection quotients listed in the top row, the questionable value can be rejected with 90% confidence that the rejection will improve the accuracy of the result
Systemic errors
-errors that occur in repeated determinations with the same sign and approximately the same magnitude
-due to intrinsic flaw in the procedure or an instrument used in the experiment
-Two or more different methods of analysis applied to the same determination will reveal systematic errors
-example: if scale not properly calibrated, then weight will consistently read slightly higher/lower than true value
Random error
-errors that occur with random magnitude and random sign
-Unavoidable because there is always some uncertainty in every physical measurement (due to limitations of the instrument or human)
-example: when weighing on scale, position changes slightly every time
-example: when reading volume of flask, you read from different angle every time
Absolute error (Sx)
discrepancy between an experimentally measured result and the true value is called absolute error
Relative error (Sx/x)
-the absolute error expressed as a fraction of the average measured value
-Relative error = absolute value of absolute error divided by average measured value (true value)
Propogation of errors
-Often a quantity (z) is not measured directly but computed from measured values (x and y) of one or more variables using a known equation
-It is important to know experimental errors in measured values (x and y) and how they propagate through computation to produce resulting error of computed value (z)
-Max error of z, (Sz) = (Sy) + (Sx)
-Relative error = (Sz) / z
Propogation of errors when computed value (z) is found through multiplication/division
-Relative error of z = sum of relative errors of x and y
-Not possible to calculate absolute error when desired value is obtained by multiplication or division
-Can be converted to absolute value through multiplying relative error by measured value
Progation of errors when logarithm is used
-If z = a lnx, then
-Sz = a Sx/x
Errors thata ffect number of sig figs
-Since deviation is an uncertain number by nature, it is common practice to report only one uncertain digit in an error estimate
-Ex. if calculated deviation is 0.017, it should be reported as 0.02
-And since uncertain digit is in the second decimal place, the average value should also be reported to only the two decimal places (1.236 would be reported as 1.24)
-Deviation dictates the number of decimal places in the average value
-Do not write digits of error beyond the first uncertain one
-Number of sig figs does not depend on input of addition/subtraction of error input but rather number of decimal places of uncertainty number
Electronic analytical balance
-Maximum error of the balance is +/- 0.0001 g (fine) and +/- 0.001 g (coarse)
-a coarse range from
0 to 160 grams where readability is 1 milligram (0.001 g), and a fine range from 0 to 60
grams where readability is 0.1 mg (0.0001 g)
Steps to weigh object on analytical balance
-Check balance is level (spirit bubble should be centered in a circle). Do not move balance as it may become unleveled
-Clean the balance of spills from previous weighings with brush
-Place the object in the center of the pan and close the sliding doors to eliminate any air currents that may perturb the measurement
-Ensure that the object to be weighed is at room temperature (warm object causes upward movement of the nearby air, buoying the object to be weight)
-Place the liquid in a closed container and ensure that the outside of the container is dry (prevents inconsistent readings due to evaporation and protects the instrument from moisture)
-An open container of liquid should never be weighed on an analytical balance
-Place solid samples in a weigh boat or in a small container before weighing
-Remove the weigh boat to add or remove materials, never do so with the weigh boat on the balance, as the spilled materials will contaminate the balance
-Never overload the balance (>160 g) or you may damage the fragile parts within. Use a top-loading balance for heavier objects
Ideal gas law
PV = nRT
Dalton’s law of partial pressures
-P(total) = Pa + Pb
-Pa = n(a)RT/V
-Pb = n(b)RT/V
Poor precision and poor accuracy
-poor technique
-values will be spread out and not close to true value
Good precision but poor accuracy
-due to systematic error
-values are close together but not close to true value
Good precision and good accuracy
-good technique
-values are close together and close to true value
Poor precision but good accuracy
-lucky
-values are spread out but some are still close to true value
