Measurement and Calculations in Chemistry – VOCAB Flashcards

Section R.1 Units of Measurement

• Nature of Measurement: A quantitative observation consists of two parts: a number and a scale (unit). Examples include 20 grams and 6.63 \times 10^{-34} \text{ joule} \cdot \text{seconds}.

• The Fundamental SI Units:

  • Physical Quantity: Mass

  • Name of Unit: kilogram

  • Symbol: kg

• Length

  • meter

  • m

• Time

  • second

  • s

• Temperature

  • kelvin

  • K

• Electric current

  • ampere

  • A

• Amount of substance

  • mole

  • mol

• Prefixes Used in the SI System (1 of 2)

  • Prefix | Symbol | Meaning | Exponential Notation

  • exa | E | 1,000,000,000,000,000,000 | 10^{18}

  • peta | P | 1,000,000,000,000,000 | 10^{15}

  • tera | T | 1,000,000,000,000 | 10^{12}

  • giga | G | 1,000,000,000 | 10^{9}

  • mega | M | 1,000,000 | 10^{6}

  • kilo | k | 1,000 | 10^{3}

  • hecto | h | 100 | 10^{2}

  • deka | da | 10 | 10^{1}

  • — | — | 1 | 10^{0}

• Prefixes Used in the SI System (2 of 2)

  • deci | d | 0.1 | 10^{-1}

  • centi | c | 0.01 | 10^{-2}

  • milli | m | 0.001 | 10^{-3}

  • micro | µ | 0.000001 | 10^{-6}

  • nano | n | 0.000000001 | 10^{-9}

  • pico | p | 0.000000000001 | 10^{-12}

  • femto | f | 0.000000000000001 | 10^{-15}

  • atto | a | 0.000000000000000001 | 10^{-18}

*See Appendix 1.1 for a review of exponential notation. - Note: Appendix reference for exponential notation is provided in the text.

Section R.2 Uncertainty in Measurement

• A digit that must be estimated is called uncertain.

• A measurement always has some degree of uncertainty.

• When reporting a measurement, record the certain digits and the first uncertain (estimated) digit.

• Example: Measurement of volume using a buret

  • The volume is read at the bottom of the liquid curve (meniscus).

  • Meniscus reading shown: about 20.15 mL.

  • Interpreting digits: the digits up to 20.15 are considered the certain part; the last digit is the first uncertain digit.

Section R.3 Significant Figures and Calculations

• Rules for Counting Significant Figures (1 of 5)

  • Nonzero integers always count as significant figures.

  • Example: 3456 has 4 sig figs.

• Rules for Counting Significant Figures (2 of 5)

  • Leading zeros do not count as sig figs.

  • Example: 0.048 has 2 sig figs.

• Rules for Counting Significant Figures (3 of 5)

  • Captive zeros (zeros between nonzero digits) always count as sig figs.

  • Example: 16.07 has 4 sig figs.

• Rules for Counting Significant Figures (4 of 5)

  • Trailing zeros are significant only if the number contains a decimal point.

  • Examples: 9.300 has 4 sig figs; 150 has 2 sig figs (depending on decimal notation).

• Rules for Counting Significant Figures (5 of 5)

  • Exact numbers have an infinite number of significant figures.

  • Examples: 1 inch = 2.54 cm, exactly; 9 pencils (counted).

• Practice Problem: Determine the number of significant figures in the following measurements:

  • 1.0070 \text{ g}

  • 0.0032 \text{ m}

  • 200 \text{ L}

  • 200.0 \text{ mL}

• Exponential Notation (example)

  • written as

  • 300 \longrightarrow 3.00 \times 10^{2}

  • Contains three significant figures.

  • Advantages: explicitly indicates the number of sig figs; allows writing very large or very small numbers with fewer zeros.

• Significant Figures in Mathematical Operations (1 of 2)

  • For multiplication or division, the number of significant figures in the result equals the least precise measurement used.

  • Example:

  • 1.342 \times 5.5 = 7.381 \longrightarrow 7.4

• Significant Figures in Mathematical Operations (2 of 2)

  • For addition or subtraction, the result has the same number of decimal places as the least precise measurement used.

  • Example:

  • 23.445 + 7.83 = 31.275 \longrightarrow 31.28

• Practice Problem: Perform the following calculations and report the answer with the correct number of significant figures:

  • (5.02 \text{ cm} \times 8.613 \text{ cm}) + 2.0 \text{ cm}

  • \frac{(12.60 \text{ g} - 5.1 \text{ g})}{2.345 \text{ mL}}

• Concept Check (1 of 4)

  • Question: You have water in each graduated cylinder as shown. If you add both samples to a beaker (assuming all liquid is transferred), how would you write the number describing the total volume? What limits the precision of the total volume?

Section R.4 Learning to Solve Problems Systematically

• Being a thoughtful problem solver:
  1) What is my goal? Or: Where am I going?
  2) Where am I starting? Or: What do I know?
  3) How do I proceed from where I start to where I want to go? Or: How do I get there?

Section R.5 Dimensional Analysis

• Dimensional Analysis principles:

  • Use when converting a given result from one system of units to another.

  • To convert from one unit to another, use the equivalence statement that relates the two units.

  • Derive the appropriate unit factor by looking at the direction of the required change (to cancel the unwanted units).

  • Multiply the quantity to be converted by the unit factor to give the quantity with the desired units.

• Example #1 (1 of 3): Convert 6.8 feet to inches.

  • Equivalence: 1 ft = 12 in.

  • Unit factors:

  • \frac{1 \text{ ft}}{12 \text{ in}} \quad \text{and} \quad \frac{12 \text{ in}}{1 \text{ ft}}

  • Calculation:

  • 6.8 \text{ ft} \times \frac{12 \text{ in}}{1 \text{ ft}} = 81.6 \text{ in}

  • With significant figures from 6.8 ft (2 sig figs), the result is rounded to 2 sig figs: 82 \text{ in.}.

• Example #1 (2 of 3): Continuation for unit factor selection and cancellation: the required change cancels unwanted units.

• Example #1 (3 of 3): Final numeric result with proper units:

  • Result: 82 \text{ in}

• Example #2 (2 of 2): Convert mass 4.50 lbs to grams.

  • Given: 1 kg = 2.2046 lbs; 1 kg = 1000 g.

  • Calculation:

  • 4.50 \text{ lb} \times \frac{1 \text{ kg}}{2.2046 \text{ lb}} \times \frac{1000 \text{ g}}{1 \text{ kg}} = 2.041 \times 10^{3} \text{ g (approximately } 2.04 \times 10^{3} \text{ g)}

• Practice Problem: Convert 5.0 \text{ miles} to kilometers, given 1 \text{ mile} = 1.609 \text{ km}.

• Practice Problem: A car travels at 60.0 \frac{\text{miles}}{\text{hour}}. What is its speed in meters per second? (1 \text{ mile} = 1.609 \text{ km}, 1 \text{ hour} = 3600 \text{ seconds})

• Concept Check (2 of 4)

  • Question: What data would you need to estimate the money you would spend on gasoline to drive your car from New York to Los Angeles? Provide estimates of values and a sample calculation.

Section R.6 Temperature

• Three systems for measuring temperature: Fahrenheit, Celsius, Kelvin.

• The three major temperature scales.

• Converting between scales:

  • TK = TC + 273.15

  • TF = \frac{9}{5}TC + 32

  • TC = \frac{5}{9}(TF - 32)

• Exercise: At what temperature are °C and °F equal (i.e., when does °C = °F)?

  • Solution outline:

  • Let x be the common value. Use the equation x = \frac{9}{5}x + 32 (since F = (9/5)C + 32 and C = F).

  • Solving yields x = -40, so

  • -40^\circ\text{C} = -40^\circ\text{F}.

• Practice Problem: Convert 98.6^\circ\text{F} (normal body temperature) to degrees Celsius and Kelvin.

• Practice Problem: The boiling point of liquid nitrogen is -196^\circ\text{C}. What is this temperature in Fahrenheit and Kelvin?

Section R.7 Density

• Density definition: density = mass / volume.

• Common units: g/cm^{3} or g/mL.

• \text{Density} = \frac{\text{mass}}{\text{volume}}

• Example #1: Mineral mass 17.8 g, volume 2.35 cm^{3};

  • \text{Density} = \frac{17.8 \text{ g}}{2.35 \text{ cm}^3}

• Practice Problem: A block of aluminum has a mass of 25.5 \text{ g} and a volume of $$9.4 \text{ cm}^3