Chemistry and Measurements - Unit 2
Unit 2: Chemistry and Measurements Notes
Learning Goals
By the end of this chapter, you will be able to:
Identify and use SI base units and derived units.
Apply significant figure rules.
Convert units using prefixes and equalities.
Use dimensional analysis for problem-solving.
Calculate and apply density.
Understanding Measurements
A measurement is a quantitative observation consisting of a number (comparison) and a unit (scale).
The Critical Importance of Units
Inconsistent units, as highlighted by the Mars Climate Orbiter failure, underscore the necessity for precise and consistent unit application in scientific and engineering endeavors.
Units of Measurement for Matter
Length
SI Unit: meter ( ext{m})
Volume
SI Unit: cubic meter ( ext{m}^3); 1 ext{ mL} = 1 ext{ cm}^3.
Mass
SI Unit: kilogram ( ext{kg})
Temperature
SI Unit: kelvin ( ext{K}), with Celsius (^ ext{o} ext{C}) as a common metric unit.
Time
SI Unit: second ( ext{s})
The Metric System Prefixes
The metric system uses prefixes based on powers of ten to denote multiples or submultiples of base units.
Distinguishing Mass and Volume
Weight: A force dependent on gravity.
Mass: The amount of stuff in an object, constant regardless of gravity.
Volume: The amount of three-dimensional space occupied by a substance, measured in ext{m}^3 or ext{mL/cm}^3.
Temperature Scales and Conversions
Celsius to Kelvin: (K = ^ ext{o} ext{C} + 273).
Kelvin to Celsius: (^ ext{o} ext{C} = ext{K} - 273).
Uncertainty in Measurements
All measurements have uncertainty, with the last digit being an estimated digit.
The precision of the measuring device determines the level of uncertainty.
Record all certain numbers plus one estimated digit.
Understanding Significant Figures
Significant figures (sf) are all known digits plus one estimated digit in a measurement.
Rules for identification:
Non-zero digits: Always significant (e.g., 234.54 ext{ g} has 5 sf).
Sandwiched zeros: Always significant (e.g., 107 ext{ m} has 3 sf).
Leading zeros: Not significant (e.g., 0.000324 ext{ m} has 3 sf).
Trailing zeros: Significant only if a decimal point is present (e.g., 1,000 ext{ mL} has 1 sf; 9.300 has 4 sf).
Exact Numbers: Have an unlimited number of significant figures (e.g., counted items, defined equalities).
Rules for Rounding Off Significant Figures
If the digit to be removed is < 5, the preceding digit stays the same.
If the digit to be removed is ext{= or} > 5, the preceding digit increases by 1.
Round only at the very end of multi-step calculations.
Significant Figures in Mathematical Operations
Multiplication/Division: The result has the same number of significant figures as the measurement with the least significant figures.
Addition/Subtraction: The result has the same number of decimal places as the measurement with the smallest number of decimal places.
Single Unit Conversion and Conversion Factors
Conversion factors are ratios of equivalent quantities used to change units (e.g., ( rac{12 ext{ in}}{1 ext{ ft}} ) or ( rac{1 ext{ ft}}{12 ext{ in}} )).
Dimensional Analysis for Problem-Solving
A method for converting units using conversion factors, treating units like algebraic variables.
Process: Identify given and desired, find conversion factors, set up so units cancel, calculate, round to correct significant figures, and sense-check the answer.
Dimensional Analysis Practice Problems
Problem: The distance between Santa Monica and Coachella is 143 ext{ miles}. Convert this distance to meters.
Given: 143 ext{ miles} (3 sf)
Conversion Factors: 1 ext{ mile} = 1.609 ext{ km}, 1 ext{ km} = 1000 ext{ m}
Calculation:
143 ext{ mi} imes rac{1.609 ext{ km}}{1 ext{ mi}} imes rac{1000 ext{ m}}{1 ext{ km}} = 230087 ext{ m}
Result (with 3 sf): 230,000 ext{ m} or 2.30 imes 10^5 ext{ m}
Problem: How many cups are in 2.0 ext{ liters}?
Given: 2.0 ext{ L} (2 sf)
Conversion Factors: 3.79 ext{ L} = 1 ext{ gal}, 1 ext{ gal} = 4 ext{ quarts}, 1 ext{ quart} = 4 ext{ cups}
Calculation:
2.0 ext{ L} imes rac{1 ext{ gal}}{3.79 ext{ L}} imes rac{4 ext{ qts}}{1 ext{ gal}} imes rac{4 ext{ cups}}{1 ext{ qt}} = 8.443… ext{ cups}
Result (with 2 sf): 8.4 ext{ cups}
Challenge Problem: A car drives 65 ext{ miles per hour}, convert that to meters per second.
Given: 65 rac{ ext{miles}}{ ext{hour}} (2 sf)
Conversion Factors: 1 ext{ mile} = 1609 ext{ m}, 1 ext{ hour} = 60 ext{ min}, 1 ext{ min} = 60 ext{ sec}
Calculation:
rac{65 ext{ miles}}{1 ext{ hour}} imes rac{1609 ext{ m}}{1 ext{ mile}} imes rac{1 ext{ hour}}{60 ext{ min}} imes rac{1 ext{ min}}{60 ext{ sec}} = 29.05 rac{ ext{m}}{ ext{s}}
Result (with 2 sf): 29 rac{ ext{m}}{ ext{s}}
Density
Definition: The ratio of an object's mass to its volume ( ext{Density} = rac{ ext{mass}}{ ext{volume}}).
Units: Typically ext{g/mL}, ext{g/cm}^3.
Determining Volume:
Geometric Dimensions: For regular shapes (V = LWH for rectangular prism).
Displacement Method: For irregular shapes, volume equals displaced fluid volume.
Density Practice Problems
Problem: What is the density of an object that has a mass of 14 ext{ grams} and a volume of 6.0 ext{ milliliters}?
Given: Mass = 14 ext{ g} (2 sf), Volume = 6.0 ext{ mL} (2 sf)
Calculation:
ext{Density} = rac{14 ext{ g}}{6.0 ext{ mL}} = 2.333… rac{ ext{g}}{ ext{mL}}
Result (with 2 sf): 2.3 rac{ ext{g}}{ ext{mL}}
Problem: What is the mass of a cube that has a density of 19.2 ext{ g/cm}^3 and is 5.4 ext{ cm} per side?
Given: Density = 19.2 rac{ ext{g}}{ ext{cm}^3} (3 sf), Side length = 5.4 ext{ cm} (2 sf)
Step 1: Calculate Volume:
V = ext{side}^3 = (5.4 ext{ cm})^3 = 157.464 ext{ cm}^3
Step 2: Calculate Mass:
ext{Mass} = ext{Density} imes ext{Volume} = 19.2 rac{ ext{g}}{ ext{cm}^3} imes 157.464 ext{ cm}^3 = 3023.3088 ext{ g}
Result (with 2 sf, limited by side length): 3.0 imes 10^3 ext{ g} or 3000 ext{ g}
Practice: What is the mass of an object that has a density of 3.5 ext{ g/mL} and a volume of 20.0 ext{ mL}?
Given: Density = 3.5 rac{ ext{g}}{ ext{mL}} (2 sf), Volume = 20.0 ext{ mL} (3 sf)
Calculation:
ext{Mass} = ext{Density} imes ext{Volume} = 3.5 rac{ ext{g}}{ ext{mL}} imes 20.0 ext{ mL} = 70.0 ext{ g}
Result (with 2 sf, limited by density): 70. ext{ g} or $$