Math and Measurement Review

Chemistry is the science of substances ― their structure, their properties, and the reactions that change them into other substances. Linus Pauling, “General Chemistry”

1 ≤ |a| < 10, n is an integer Scientific/Exponential Notation a x 10n 1 ≤ |a| < 10, n is an integer Negative exponent:

Express the following numbers in scientific notation 25 2500 −270000 0.25 −0.0000250 Read Appendix I: A

Never drop units! Examples that involve unit calculations Units are involved in calculations just as numbers. Never drop units! Your calculator does not deal with units. You must work on it!

a x 5 m A physical quantity can be considered as a product of a number and its unit. a x number unit 5 m

C A B a x − b x = (a − b) x AB = 15 m AC = 10 m CB = ? CB = AB − AC = 15 m − 10 m = (15 − 10) m = 5 m

H = 3 cm W = 6 cm Area = W x H = 6 cm x 3 cm = 18 cm2 a x • b x = ab x2 H = 3 cm W = 6 cm Area = W x H = 6 cm x 3 cm = 18 cm2

(a x)3 = a3 x3 What is the volume of a cube with edge length 5 cm? V = L3 = (5 cm)3 = 53 (cm)3 = 125 cm3

A B 15 m C 10 m D How many times is AB compared to CD in length?

A B 15 m Time consumed to move from A to B is 5 s. What is the average speed? meters per second

Chem 1211 and 1212

Mass is a measure of the amount of material in an object. Unit: kg Weight is the force that gravity exerts on an object. F = ma Unit: N G = mg Mass ≠ Weight

Chemistry is a discipline of science that strongly depends on experiments. Experiments  Measurements Some basic concepts related to measurements

Reliability of Measurements Accuracy refers to the agreement of a particular measurement with the true value.

experimental value (m) To quantify accuracy, define: absolute error = experimental value − true value True value = 50 m experimental value (m) absolute error (m) 52 2 50 51 1 48 −2 sign of error: direction |error|: size

relative error = absolute error / true value unknown relative error = absolute error / true value = absolute error / theoretical relative error is often given in percentage: | |: to make % error a positive number

experimental value (m) True value = 50 m experimental value (m) absolute error (m) 52 2 50 51 1 48 −2 What are the percent errors for the measurements listed in the table?

Based on source Random Error: random, cannot avoid. But can take average of multiple measurements to reduce to certain degree. Systematic Error: same direction, could fix

true value Random error only

Random error and systematic error. true value Random error and systematic error.

Reliability of Measurements Accuracy refers to the agreement of a particular measurement with the true value. Precision is the degree of agreement among several measurements. Accuracy ≠ Precision

The Results of Several Dart Throws Show the Difference Between Precise and Accurate

How to report a measurement?

mL

We report a measurement by recording ALL the certain digits + ONE uncertain digit Significant Figures (except leading zeros)

Chapter 1, Unnumbered Figure 2, Page 14

Or conversions involving prefixes:

1 ≤ |a| < 10, n is an integer Note: Scientific expression does not change the number of sig figs. a x 10n 1 ≤ |a| < 10, n is an integer Only need to count sig figs in “a”

Conversion factor = 1 #: copy from the relation between two units.

Physical quantity with given unit x Conversion factor = Physical quantity with desired unit 5.0 in = ? cm 3.2 m = ? mm 5.000 in = ? cm 3.2 cm = ? mm 5.000 in = ? m 6.81 cm2 = ? in2 19.21 cm = ? in 66 km/h = ? m/s 7.8 g/cm3 = ? kg/m3

Three Basic Physical Quantities Volume Density Temperature

Volume and its units 1 m = 10 dm = 100 cm How much room an object occupies in space. 1 m = 10 dm = 100 cm (1 m)3 = (10 dm)3 = (100 cm)3 1 m3 = 103 dm3 = 106 cm3 For liquid, define: 1 L = 1 dm3 Then: 1 mL = ? cm3 = 1 cm3

Density: mass of a substance per unit volume of the substance. Unit: kg/m3, g/cm3, g/mL Density is a property of substances. It is determined by the substance’s identity and external conditions, not by the substance’s mass or volume.

How to find density? How to find mass? balance How to find volume? • Liquid: graduated cylinder, beaker, buret, pipet… • Solid Regular shape: Measure dimensions, then calculate Irregular shape: water displacement

TK, Kelvin scale, K (not °K) Temperature: a measure of hotness or coldness of an object. Temperature scales TC, Celsius scale, °C TF, Fahrenheit scale, °F TK, Kelvin scale, K (not °K)

Temperature conversions Normal body temperature is 98.6 °F. Convert this temperature to the Celsius and Kelvin scales.