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Sample Problem A piece of copper has a mass of 57.54 g. It is 9.36 cm long, 7.23 cm wide, and 0.95 mm thick. Calculate density (g/cm3).
Strategy 1. Get dimensions in common units.
m = 57.54 gL = 9.36 cmW = 7.23 cmThickness (Height) = 0.95 mm = 0.095 cm 2. Calculate volume in cubic centimeters.
V = LxWxH = (9.36 cm)(7.23 cm)(0.095 cm) =
3. Calculate the density. D = m/V Be sure to check sig figs
Sample Problem
Sample Problem: Mercury (Hg) has a density of 13.6 g/cm3. What is the mass of 95 mL of Hg in grams? In pounds?
First, note that 1 cm3 = 1 mL Strategy1.Use density as a conversion factor to calculate mass (g)
from volume.
2.Convert mass (g) to mass (lb)
Need to know conversion factor; 454 g = 1 lb
Density as a conversion factor
Intensive property - is a physical property of matter that does not depend on the system size or the amount of material in the system
Examples: density, color hardness, melting point, boiling point
Extensive property – any property that depends on the size of the system. A property that changes as the amount of matter changes.
Examples: mass, volume, temperature, energy released/absorbed
Extensive & Intensive Properties
State of matter: gas, liquid, solid
Kinetic Molecular Theory: A theory of the behavior of matter at the molecular level
Kinetic Energy: The energy of a moving object, dependent on its mass and velocity
K.E. = 1/2mv2
Classification of Matter
Matter has both
Macroscopic –measurable and observable to the naked eye
Macroscopic properties - color, length
Submicroscopic or particulate –not measurable with a microscope
Particle size, chemical bond length
Matter at the Macroscopic and Particulate Levels
Measurement System – in summer work
◦ Length base unit – meter Conversions: 2.54 cm = 1 inch
◦ Mass base unit – kilogram Conversions: 453.5 g = 1 pound (only on earth!)
◦ Time base unit – second Conversions: 1 hour = 60 minutes;
1 minute= 60 seconds (NOTE THESE ARE EXACT NUMBERS)
Units of Measurement
A problem solving method –
◦ Example: how many seconds in a day ??
◦ 1 day 24 hours 60 min 60 sec = 1 day 1 hour 1 min
Dimensional Analysis -1
Find the surface area of a room 20 feet by 12 feet in square meters. ( Use 2.54 cm = 1 inch)
Dimensional Analysis-2
Using density as a conversion – What is the mass of a gold cube with 2 inch sides? (density of gold =19.3 g/cm3)
Hint: need volume in cubic centimeters -
Dimensional Analysis -3
Accurate – close to the true value Precision – reproducibility of the
measurement
Percent Error:
Accuracy vs. Precision
State the problem◦ Organize the information◦ Determine what you know & what you need to know
Determine the strategy◦ May stem from prior knowledge
Write down each step◦ NO WORK NO CREDIT!!
Check your answer◦ Is it reasonable????
Problem Solving