CHM103 Chapter 1_3 noR (1)
Chapter 1: Matter, Measurements, and Calculations
Page 1
Overview of essential concepts of matter, measurements, and calculations relevant to science.
Page 2: Temperature Scales
The three commonly used temperature scales are:
Fahrenheit (°F): Developed by Daniel Gabriel Fahrenheit in 1724.
Celsius (°C): Introduced by Anders Celsius in 1742; widely used in scientific contexts.
Kelvin (K): Introduced by William Thomson (Lord Kelvin) in 1848; used in absolute temperature measurement.
Key conversion examples:
77.0 °F can be converted to 25.0 °C.
25.0 °C equals 298.2 K.
Page 3: Relationships Between Temperature Scales
Significant temperature benchmarks:
Water boils at 212°F, 100°C, and 373 K.
Water freezes at 32°F, 0.0°C, and 273 K.
Absolute zero: -459°F, -273°C, and 0 K.
Page 4: Temperature Conversions
Conversion formulas:
Fahrenheit to Celsius:[ °C = \frac{5}{9}(°F - 32) ]
Example: For 77.0 °F:
[ °C = \frac{5}{9}(77.0 - 32) = \frac{5}{9}(45) = 25.0 °C ]
To convert Celsius to Kelvin:[ K = °C + 273.15 ]
Example: For 25.0 °C:
[ K = 25.0 + 273.15 = 298.15 = 298.2 K ]
Significant figures: maintain the same precision as the original measurement.
Page 5: Conversions Between Temperature Scales
General formulas for conversions:
Fahrenheit to Celsius:[ °C = \frac{5}{9}(°F - 32) ]
Celsius to Fahrenheit:[ °F = \frac{9}{5}(°C) + 32 ]
Kelvin to Celsius:[ °C = K - 273.15 ]
Celsius to Kelvin:[ K = °C + 273.15 ]
Page 6: Example Conversion
Convert 68.0 °F to Celsius.
Available answers:
5.7 °C
20.0 °C
64.8 °C
90.4 °C
Page 7: More Examples
Convert 41.0 °F to Celsius and then Kelvin.
Possible outcomes:
-9.2 °C, 263.9 K
5.0 °C, 278.2 K
16.2 °C, 289.4 K
41.8 °C, 347.0 K
Page 8: Commonly-Used Metric Units
Overview of relationships between metric units and English units:
Length:
Meter (m): 1 m = 1.094 yd
Centimeter (cm): 100 cm = 1 m, 1 cm = 0.394 in.
Millimeter (mm): 1000 mm = 1 m, 1 mm = 0.0394 in.
Kilometer (km): 1 km = 1000 m, 1 km = 0.621 mi.
Volume:
Cubic decimeter (dm³) = 1 L = 1.057 qt
Other volumetric conversions within mL and cm³.
Mass:
Gram (g), milligram (mg), and kilogram (kg) conversions to ounces and other respective units.
Temperature relations:
1°C = 1 K = 1.80°F
Energy: Calorie and joule conversions to BTU.
Time: maintained in standard second (s).
Page 9: Scientific Notation
Scientific notation structure: M x 10^n.
M is the mantissa ranging from 1 to 10.
Examples:
1.001 x 10^10 means ten billion.
1.001 x 10^-7 means one ten millionth.
Page 10: Standard Decimal Position
The standard position for decimal representation is right after the first non-zero digit of M.
Significance of the exponent n:
Positive n indicates shifts to the right.
Negative n indicates shifts to the left.
Page 11: Quiz on Scientific Notation
Understanding to express regular numbers in scientific notation and vice versa:
Example 1: 535,000
Choices: a) 535 x 10^3 b) 53.5 x 10^4 c) 5.35 x 10^5
Example 2: 0.00830
Choices: a) 830 x 10^-5 b) 8.30 x 10^-3 c) 0.830 x 10^-2
Page 12
Continuation of Chapter 1.
Page 13: Multiplication in Scientific Notation
Process:
Multiply mantissa values of both numbers to yield M'.
Sum the exponent values for n'.
Final result format: M' x 10^n'.
Example:(3.0 x 10^8) x (4.0 x 10^-2) = 12.0 x 10^6 = 1.2 x 10^7.
Page 14: Division in Scientific Notation
Process:
Divide mantissa values to yield M'.
Subtract denominator's n from numerator's n to yield n'.
Final result format: M' x 10^n'.
Example:[ \frac{3.0 x 10^8}{4.0 x 10^{-2}} = 0.75 x 10^{10} = 7.5 x 10^9 ]
Page 15: Significant Figures
Definition: Numbers in measurement conveying certainty and an estimate.
Rules for counting significant figures:
Leading zeros: Never significant.
Buried zeros: Always significant.
Trailing zeros: Generally significant.
Page 16: Measurement Example
Sample lengths provided:
3 cm
3.4 cm
3.36 cm
3.355 cm
Determination needed for the accurate length of the rectangle.