MACS 302 Exam 1 Concentration/Dimensional Analysis

Molarity (M)

moles solute/liters solution

Molality (m)

moles solute (g)/mass solvent (kg)

Molecular Weight

the sum of atomic masses of all atoms in a molecule

𝐻2O = (2×1.008) + 15.999 = 18.015 amu
amu or Da = g/mol

Parts Per Thousand

(g of solute x / g of solution) * 10³

1 g/ kg

1 g/ 1 L

Parts Per Million (ppm)

(g of solute / g of solution) x 10^6

Accuracy

how close a measurement is to the true or accepted value

systematic

Precision

how close the measurements are to each other

random error

standard deviation

Systematic (determinate) Error

correctable, repeatable

instrumental/environmental/observational

uncalibrated equipment, bubble in buret

Random (indeterminate) Error

uncorrectable, always present

limits in physical measurement/natural variation

electrical noise, reading scale bars/buret

Gross Error

human error, one time mistake

can lead to systematic error

Implicit Uncertainty

uses significant figures

all certain digits and first uncertain digit

Explicit Uncertainty

uses error bars

can be reported in stdev (+ N), std error, or confidence interval

Gaussian or Normal Distribution

continuous probability distribution

defined by mean and stdev (precision)

• mean is at zero

• w/in 1 stdev is 34.1%, 2 stdev is 13.6%

Case 1

comparing measurement (x₁) to accepted value (u)

Case 2b

Comparing two measurements

not poolable

f-calc>f-table

Case 2a

Comparing two measurements

poolable

f-calc<f-table

In all cases, T-calc > T-table

measurements are statistically different at the confidence level

Confidence level

% probability that true mean (u) lies within the interval

F-test

comparing stdev of two measurements to each other

always put the bigger stdev on top

Absolute Error

magnitude of the difference between a measured value and the true, actual value

absolute value of (Measured Value - True Value)

Relative Error

ratio of the absolute error of a measurement to the actual or accepted value, indicating the precision of a measurement relative to its size