Measurement & Data Processing

IB Chem

• Objective: demonstrate knowledge of

measurement & data processing.

• Warm up: Explain the difference between accuracy and precision.

Challenge…• Hemoglobin (C2952H4664O832S8Fe4) is the oxygen

carrier in blood. • Calculate its molar mass.

An average adult has about 5.0 liters of blood.

Every milliliter of blood has approximately 5.0 x 109 erythrocytes, or red blood cells, and every red blood cell has about 2 x 108 hemoglobin molecules.

• Calculate the mass of hemoglobin molecules in grams in an average adult.

Significant Figures

200.54 g

• The certain (known) digits and one estimated digit of each measurement are significant.

• Remember! Every time you make a measurement, you record all of the certain digits and one estimated digit.

Rules for Sig Figs1. Non-zeros are always significant.

2. Zeros between non-zeros are significant.

3. All final zeros to the right of the decimal are significant. (estimated value)

4. Placeholder zeros are NOT significant.– Zeros preceding significant digits.– Zeros following significant digits without

a decimal point.

5487 has 4

sig figs

5508 has 4 sig figs

67.80 has 4 sig figs

0.04567 has

4 sig figs

45,670 has 4 sig figs

Significant Figures

Adding and

Subtracting

Round to the

fewest number of

decimal places

given in problem.

Sample Problem:

17.20 (.01) 4.137 (.001)

+ 26.6 (.1) 47.937

Correct Answer: 47.9

Significant Figures

Sample Problem:

14.3 (3 sig figs)

1.0200 (5 sig figs)

x 0.005 (1 sig fig)

0.07293 Correct Answer:

0.07

Multiplying and

Dividing

Round to the fewest

number of significant

digits given in the

problem.

Significant Figures

In chemistry, we work with very large and very small numbers.

Number of particles in a mole =602200000000000000000000

Mass of an electron =0.000000000000000000000000000000911kg

We need a simple way to write these numbers!

Scientific Notation

1. Identify the significant digits

2. Write out the significant digits as a number greater than 1 but less than 10

3. Count the number of places you had to move the decimal to complete step 1

4. Write this number of decimal places as an exponent to 10

602200000000000000000000

There are 4 sig figs in this number

6.022 is < 1 and > 10

The decimal was moved 23 places

6.022 x 1023

When the decimal place is moved to the left, the exponent is positive.

Scientific Notation

Things you already know

• Significant figures

• Scientific notation

• Basic calculations

without a calculator

Types of Uncertainty/Error• Random:

Error introduced has an equal probability of being too high or too low 50/50 chance

Ex: Door open on analytical balance

• SystematicError introduced will always be too high or too low.

Ex: Air bubbles in thermometer

Using equipment• Analogue

+/- Half of the smallest division

• Digital+/- The smallest scale division

Uncertainty• Absolute

± half of thesmallest division

Always include units

35.0 ± 0.5 cm3

• Percent

Absolute uncertainty divided by the measurement x 100

0.5/35.0 *100 = 1.4%

Uncertainties in CalculationsAddition/Subtraction

Add absolute uncertainties

23.0 ± 0.1 cm3

+ 34.0 ± 0.5 cm3 57.0 ± 0.6 cm3

IB refers to

this as propagating

error

Uncertainties in CalculationsMultiplication/Division

1. Multiply or divide measured numbers

3.0 ± 0.1 cm3

x 4.0 ± 0.5 cm3 12

2. Convert absolute uncertainties into

percents

0.1/3.0 * 100 = 3% 0.5/4.0 * 100 = 10%

(remember to use multiplication/ division sig fig rules)

3. Add percents 12 cm3 ± 13%

4. Convert back to absolute

13% = 100 * x/12.0 12 ± 1.6 cm3

Percent errorA measure of how close the experimental

value is to the accepted/known value

Not to be confused with percent uncertainty…

(accepted value – experimental value) accepted value X 100

Equipment/technique uncertainty compared to literature values

• If % uncertainty > % error, the experimental value fitswithin the uncertainty range and is acceptable; thedifferences in the experimental and literature values isdue to random errors

• If % uncertainty < % error, the experimental valuedoes not fit within the uncertainty range and isunacceptable; the differences in the experimental andliterature values is due to systematic errors

Equipment/technique uncertainty compared to literature values

• Example: % uncertainty is 20 g +/- 5% < % error is 10%

This indicates the data should fall between 19 and 21 grams. The error of 10% falls outside of this. Meaning the accepted or literature values are outside of this range produced.

This must be due to systematic error and is UNACCEPTABLE!

Accuracy vs. Precision

Accuracy measures how close a measured value comes to a predetermined target value (the set volume on your pipettor).

Reproducibility (precision) measures how close repeated values are to one another. These concepts can be visualized using these cartoon (idealized) bulls-eye diagrams. Notice that accuracy and precision can vary independently, so they can be evaluated independently, as well.

not accurate precise

accuratenot precise

accurate precise

not accurate not precise

Accuracy vs. Precision

Test yourself on identifying if these examples are precise, accurate, neither, or a mix

Graphing• Always include:

– Title– Axis titles with units– A best fit line– Identification of outliers– Consistent scales – no uneven jumps

Always make the graph as large as possible…maximize axis usage and paper usage

Graphing video

Extrapolation & Interpolation• Extrapolation- Extending the graph to

determine an unknown value outside the range of measured values

• Interpolation- Determining an unknown value within the limits of the measured values

Challenge…• Hemoglobin (C2952H4664O832S8Fe4) is the oxygen

carrier in blood. • Calculate its molar mass.

An average adult has about 5.0 liters of blood.

Every milliliter of blood has approximately 5.0 x 109 erythrocytes, or red blood cells, and every red blood cell has about 2 x 108 hemoglobin molecules.

• Calculate the mass of hemoglobin molecules in grams in an average adult.

• Objective: demonstrate knowledge of

measurement & data processing.

• Warm up: Explain the difference between accuracy and precision.