Ch. 2: Measurement and Problem Solving

1. Ch. 2: Measurement and Problem Solving Dr. Namphol Sinkaset Chem 152: Introduction to General Chemistry

2. I. Chapter Outline • Introduction • Scientific Notation • Significant Figures • Units of Measurement • Unit Conversions • Density as a Conversion Factor

3. I. Introduction • Global warming measurement. • Value? • Method? • Uncertainty?

4. II. Scientific Notation • Science deals with the very large and the very small. • Writing large/small numbers becomes very tedious, e.g. 125,200,000,000. • Scientific notation is a shorthand method of writing numbers.

5. II. Scientific Notation • Scientific notation consists of three different parts.

6. II. Converting to Scientific Notation

7. II. Steps for Writing Scientific Notation • Move decimal point to obtain a number between 1 and 10. • Write the result of Step 1 multiplied by 10 raised to the number of places you moved the decimal point. • If decimal point moved left, use positive exponent. • If decimal point moved right, use negative exponent.

8. II. Practice with Scientific Notation • Express the following in proper scientific notation. • 3,677,000,000 • 0.00024709 • 93 • 0.004 • 0.0040

9. III. Measurement in Science • Measurements are written to reflect the uncertainty in the measurement. • A “scientific” measurement is reported such that every digit is certain except the last, which is an estimate.

10. III. Reading a Thermometer • e.g. What are the temperature readings below?

11. III. Uncertainty in Measurement • Quantities cannot be measured exactly, so every measurement carries some amount of uncertainty. • When reading a measurement, we always estimate between lines – this is where the uncertainty comes in.

12. III. Significant Figures • The non-place-holding digits in a measurement are significant figures (sig figs). • The sig figs represent the precision of a measured quantity. • The greater the number of sig figs, the better the instrument used in the measurement.

13. III. Determining Sig Figs • All nonzero numbers are significant. • Zeros in between nonzero numbers are significant. • Trailing zeros (zeros to the right of a nonzero number) that fall AFTER a decimal point are significant. • Trailing zeros BEFORE a decimal point are not significant unless indicated w/ a bar over them or an explicit decimal point. • Leading zeros (zeros to the left of the first nonzero number) are not significant.

14. III. Exact Numbers • Exact numbers have no ambiguity and therefore, have an infinite number of sig figs. • These include counts, defined quantities, and integers in an equation. • e.g. 5 pencils, 1000 m in 1 km, C = 2πr.

15. III. Determining Sig Figs • e.g. Indicate the number of sig figs in the following. • 2.036 • 20 • 6.720 x 103 • 7920 • 135,001,000 • 0.0000260 • 820. • 1.000 x 1021

16. III. Calculations w/ Sig Figs • When doing calculations with measurements, it’s important that we don’t have an answer w/ more certainty (sig figs) than what we started with. • Sig figs are handled based on what math operation is being performed.

17. III. Multiplication • The answer is limited by the number with the least sig figs.

18. III. Division • The answer is also limited by the number with the least sig figs.

19. III. Addition • The answer has the same number of PLACES as the quantity carrying the fewest places. *Note that the number of sig figs could increase or decrease.

20. III. Subtraction • The answer has the same number of PLACES as the quantity carrying the fewest places. *Note that the number of sig figs could increase or decrease.

21. III. Addition/Subtraction • Addition and subtraction operations could involve numbers without decimal places. • The general rule is: “The number of significant figures in the result of an addition/subtraction operation is limited by the least precise number.”

22. III. Rounding • When rounding, consider only the last digit being dropped; ignore all following digits. • Round down if last digit is 4 or less. • Round up if last digit is 5 or more. • e.g. Rounding 2.349 to the tenths place results in 2.3!

23. III. Sample Problems • Evaluate the following to the correct number of sig figs. • 1.10 ´ 0.0025 ´ 31.09 ´ 3.0540 = ? • 89.456 ¸ 0.000005 = ? • 94.25 + 20.4 = ? • 20 + 273.15 = ? • 25.432567 – 73.259 = ? • 1252 – 360 = ?

24. III. Mixed Operations • In calculations involving both addition/subtraction and multiplication/division, we evaluate in the proper order, keeping track of sig figs. • DO NOT ROUND IN THE MIDDLE OF A CALCULATION!! • Carry extra digits and round at the end. • e.g. 3.897 ´ (782.3 – 451.88) = ?

25. III. Sample Problems • Evaluate the following to the correct number of sig figs. • (568.99 – 232.1) ¸ 5.3 = ? • (9443 + 45 – 9.9) ´ 8.1 ´ 106 = ? • (455 ¸ 407859) + 1.00098 = ? • (908.4 – 3.4) ¸ 3.52 ´ 104 = ?

26. IV. Units • All measured quantities have a number and a unit!!!! • Without a unit, a number has no meaning in science. • e.g. The string was 8.2 long. • ANY ANSWER GIVEN W/OUT A UNIT WILL BE GRADED HARSHLY.

27. IV. International System of Units • More commonly known as SI units. • Based on the metric system which uses a set of prefixes to indicate size. • There are a set of standard SI units for fundamental quantities.

28. IV. Prefix Multipliers

29. IV. Derived Units • Combinations of fundamental units lead to derived units. • e.g. volume, which is a measure of space, needs three dimensions of length, or m3. • e.g. speed, distance covered over time, m/s.

30. V. Unit Conversions • Problem solving is a big part of chemistry. • Converting between different units is the first type of problem we will cover. • Problems in chemistry generally fall into two categories: unit conversions or equation-based.

31. V. Units in Calculations • Always carry units through your calculations; don’t drop them and then add them back in at the end. • Units are just like numbers; they can be multiplied, divided, and canceled. • Unit conversions involve what are known as conversion factors.

32. V. General Conversions • Typically, we are given a quantity in some unit, and we must convert to another unit.

33. 5280 ft 1 mi 1 mi 5280 ft V. Conversion Factors • conversion factor: ratio used to express a measured quantity in different units • For the equivalency statement “5280 feet are in 1 mile,” two conversion factors are possible. OR

34. V. Conversion Example • If 1 in equals 2.54 cm, convert 24.8 inches to centimeters.

35. V. Conversion Factors

36. V. Sample Problems • Perform the following multistep unit conversions. • Convert 2400 cm to feet. • Convert 10 km to inches. • How many cubic inches are there in 3.25 yd3?

37. VI. Density • Density is a ratio of a substances mass to its volume (units of g/mL or g/cm3 are most common). • To calculate density, you just need an object’s mass and its volume.

38. VI. Density Problem • Density differs between substances, so it can be used for identification. • If a ring has a mass of 9.67 g and displaces 0.452 mL of water, what is it made of?

39. VI. Density as a Conversion Factor • Since density is a ratio between mass and volume, it can be used to convert between these two units. • If the density of water is 1.0 g/mL, the complete conversion factor is:

40. VI. Sample Problem • If the density of ethanol is 0.789 g/mL, how many liters are needed in order to have 1200 g of ethanol?