1. The Numerical Side of Chemistry
Chapter 2
The Numerical Side of Chemistry

2. 2.2 Numbers in Chemistry – Uncertainty and Significant Figures
What is wrong with the logic shown below?

3. 2.2 Numbers in Chemistry – Uncertainty and Significant Figures
Associated with any measured value
The value of 2.5 cm is an estimate of where the line crosses the ruler. What might someone else estimate?

4. 2.2 Numbers in Chemistry – Uncertainty and Significant Figures
The uncertainty lies in the last digit written of the number…

5. 2.2 Numbers in Chemistry – Uncertainty and Significant Figures
What is the uncertainty of the ruler shown here? Measurement= 2.50cm

6. 2.2 Numbers in Chemistry – Uncertainty and Significant Figures
What is the range of the correct measurement value?

7. 2.4 Scientific Notation
Scientific notation – Accepted practice to unambiguously indicate uncertainty
Written as a number (A), multiplied by 10 raised to an exponent (x)

8. Understanding scientific notation…
To change back to decimal (standard) notation…
Exponent is a whole number that tells how far to move the decimal point
When exponent is positive…
When exponent is negative…

9. Convert the following to standard notation:
2.4 Scientific Notation
Convert the following to standard notation:
a) 4.68 x 10-1
b) 47.3 x 10-2
c) x 103

10. What if the decimal moves beyond the beginning or end of the number?
2.4 Scientific Notation
What if the decimal moves beyond the beginning or end of the number?
Example: 4.6 x 104
Each empty column is filled with a zero
Giving a final number…

11. Convert the following to standard notation:
2.4 Scientific Notation
Convert the following to standard notation:
a) x 10-6
b) 2.35 x 10-3
c) 6.0 x 103

12. Converting standard notation to scientific
2.4 Scientific Notation
Converting standard notation to scientific
First, find the decimal point
Move the decimal to the right of the first non-zero digit
The number of places moved is the exponent
If decimal moved left, exponent is positive
If decimal moved right, exponent is negative
EX:

13. a) 123 b) 0.00006 c) 0.000060 d) 1002.0 2.4 Scientific Notation
Convert the following to scientific notation:
a) 123 b) c) d)

14. Zeros and significant figures
2.4 Scientific Notation
Zeros and significant figures
Any zero placed due to the movement of the decimal point is not significant
If a significant zero was present before moving the decimal, it is still significant
*_______________________________________

15. 2.4 Scientific Notation
Scientific notation also provides a convenient way to write very large and small numbers
Note sig figs on each example!
Small numbers
m = ______________________
Large numbers
600,000,000,000mi = ___________________

16. 2.5 How to Handle Significant Figures and Scientific Notation When Doing Math
Two rules ensure the correct number of significant figures in calculations…
1. Multiplication and division
Round answer to the least number of sig figs…
2.0 cm  2 sig figs cm  2 sig figs
x 2 cm  1 sig fig x2.00 cm  2 sig figs
4 cm2  cm 

17. 2.5 How to Handle Significant Figures and Scientific Notation When Doing Math
2. Addition and subtraction
Result has the same precision (uncertainty) as least precise measurement

18. Answer the following with the correct number of significant figures:
2.5 How to Handle Significant Figures and Scientific Notation When Doing Math
Answer the following with the correct
number of significant figures:
a) 27.5 inches/2.0 hours =
b) 22.0 miles x 2.0 miles =
c) 221 min x 60s/min =
(exact number= no uncertainty)
(Sig. figs do not apply to this number)

19. 2.5 How to Handle Significant Figures and Scientific Notation When Doing Math
Answer the following with the correct number of significant figures:
a) 1555 inches inch inch =
b) 1555 cm cm cm =
c) 142 cm – 0.48 cm =
d) cm – 0.48 cm =

20. 2.6 Numbers with a Name – Units of Measure

21. 2.6 Numbers with a Name – Units of Measure
Mass
The measure of quantity of matter
Standard unit is the ______________________
1 kg is equal to pounds
Chemistry often uses gram (g)
1 g is equal to ______________________________
453.6 g is equal to __________________________

22. 2.6 Numbers with a Name – Units of Measure
Other Common non-SI units used in Chem
Pressure
SI unit is pascals (Pa)
Temperature
SI unit is Kelvin (K, not K)
Kelvin is called the absolute temperature scale

23. 2.6 Numbers with a Name – Units of Measure
Standard units are often too large or small, so we adjust using prefixes…Instead of saying m…

24. 2.6 Numbers with a Name – Units of Measure
Unit Conversions: Use conversion factors and unit analysis
Example: 1g = 1000mg Conversion factors:
How many mg are in 56.4g?
How many grams are in 679.5mg?

25. 2.6 Numbers with a Name – Units of Measure
More conversions:
4736m to Km
3.3kg to g
.442mg to kg (try using two steps!)

26. 2.6 Numbers with a Name – Units of Measure
Temperature conversions
Conversion between Celsius and Fahrenheit
Conversion between Celsius and Kelvin
Adjust the number by

27. 2.6 Numbers with a Name – Units of Measure
Comparisons among the three scales

28. 2.7 Density: A Useful Physical Property of Matter
“Compactness” of matter
Defined as mass per unit volume
___________________________________

29. 2.7 Density: A Useful Physical Property of Matter

30. 2.7 Density: A Useful Physical Property of Matter
Intensive property
Extensive property

31. 2.7 Density: A Useful Physical Property of Matter
Determining density
Mass is measured with a balance
Volume
For regular shaped objects (cube), volume is measured with a ruler. V= LxWxH
For irregular shaped objects, measurement is done by displacement
Measures the volume of liquid displaced when object is submerged

32. 2.7 Density: A Useful Physical Property of Matter
What is the density of the following?
a) A cube that is 10.0 mm x 10.0 mm x mm and has a mass of g
b) A small statue that has a mass of g and displaces mL of water

33. 2.10 Measuring Energy
Conservation: when something is neither created nor destroyed during a conversion Conservation of mass/matter: Conservation of energy: Although each can be converted to the other, neither can be created nor destroyed!

34. 2.10 Measuring Energy
Energy: the capacity to do work. Can be used (kinetic) or stored (potential)
SI energy unit is the joule (J)
A familiar energy unit is the calorie (c)
1 calorie = _____________________
Food Calories actually =
1Calorie =
1 Calorie =

35. 2.10 Measuring Energy
“Q”= Chemical energy stored in a substance can be measured by burning the substance in a calorimeter. (More on that in lab 4)
Water is heated by the burning substance
Temperature change is measured
Heat =
Units of Q depend on…

36. 2.10 Measuring Energy
Calorimetry Problem”
14.4g of m&m’s are burned in a calorimeter. The heat released from the candy raises the temperature of 100.g water 33.3oC.
Calculate the heat released from the candy…
Heat = Q=(masswater)(Cwater)(Dt)

37. 2.8 Doing Calculations in Chemistry – Unit Analysis
General strategy for solving numerical problems
Write down the given measurements with the unit
Find the conversion factor between the unit you have and the unit you are looking for
Multiply given value by the conversion factor, canceling out the old unit and leaving the desired unit

38. 2.8 Doing Calculations in Chemistry – Unit Analysis
Example: How many minutes are in 4 hours?
The given information is 4 hours
The conversion factor between hours and minutes is there are 60 minutes in 1 hour
Multiply them together so the old unit cancels

39. 2.8 Doing Calculations in Chemistry – Unit Analysis
You can perform this process multiple times to reach the final answer including unit desired.
Just remember to arrange the conversions so the correct units cancel each other out

40. 2.8 Doing Calculations in Chemistry – Unit Analysis
How many seconds are in 3.5 weeks?
Conversions: 60 seconds = 1 minute minutes = 1 hour hours = 1 day 7 days = 1 week

41. 2.8 Doing Calculations in Chemistry – Unit Analysis
The density of air is g/mL. Therefore 10.0L of air has a mass of 13.0g.
What is this mass in Kg? (1Kg=1000g)
What is 13.0g on mg? (1g=1000mg)

42. End of part 4
Complete Practice Problems
Homework Text Book Practice Problems
2.3, 2.6, 2.9, , , , 2.24, 2.26, , 2.32, 2.34, 2.36, 2.54