Density

Density Relating mass and volume Notes, p. 118 Which is heavier: 1 pound of lead or 1 pound of feathers? SAME: Both weigh 1 lb.

Which has a greater volume: 1 pound of lead or 1 pound of feathers? FEATHERS! Why do the same masses of lead and feathers have such different volumes?

ANSWER: LEAD AND FEATHERS HAVE DIFFERENT DENSITIES. THE DENSITY OF LEAD (11.3 g/ cm3) IS MUCH GREATER DENSITY THAN THE DENSITY OF FEATHERS ( 0.025 g/cm3) Why are the ping pong ball, the soda cap, the beads, the cherry tomato, the di, popcorn kernal and the bolt all in different locations? What is the formula for density?

(You learned this in 9th grade or middle school) Density Equation and Units Density = Mass

Volume Units: mass volume d = m/v g mL or cm3

(recall 1 mL = 1 cm3) density g/mL or g/ cm3 The density of the aluminum cylinder on the left is 2.7 g/mL. What would be the density of two aluminum cylinders? m = 2.7 g

v = 1 mL m=? A) 1.4 g/mL B) 2.7 g/mL C) 5.4 g/mL D) Impossible to

determine v=? The density of the aluminum cylinder on the left is 2.7 g/mL. What would be the density of two aluminum cylinders? m = 2.7 g v = 1.0 mL

m = 5.4 g A) 1.4 g/mL B) 2.7 g/mL C) 5.4 g/mL D) Impossible to determine

v = 2.0 mL Calculating Density Using Correct Significant Figures Calculate the density of a piece of wood that has a mass of 5.0 g and a volume of 210 mL to the appropriate number of SF.

SIGNIFICANT FIGURES RULES FOR CALCULATIONS CALCULATIONS USING MEASURED VALUES CAN BE NO MORE ACCURATE THAN THE LEAST ACCURATE MEASUREMENT POINT OF CONFUSION: Definition of least accurate is different from addition and subtraction compared to multiplication and division Least accurate: Addition and Subtraction = Fewest places past decimal

Least accurate: Multiplication and Division = Fewest SF SIG FIGURES RULE SUMMARY COUNTING #S and Conversion factors INFINITE NONZERO DIGITS: ALWAYS ZEROS: LEADING : NEVER CAPTIVE: ALWAYS TRAILING :SOMETIMES

YES; SIGNIFICANT Decimal present? NO; NOT SIGNIFICANT Calculating Density Using Correct Significant Figures Calculate the density of a piece of wood that has a mass of 5.0 g and a volume of 210 mL to the appropriate number of SF.

Operation is division round to fewest SF 2 SF ANS: d = m/v = 5.0 g = 0.024 g/mL (2 SF) 210 mL 2 SF

Determining Density in the Lab using the water displacement method Explain how the density of an object could be using the following equipment: p. 125, HW 4-5, #1) Determine the density of Sponge Bob Square Pants to the correct of SF using the volume displacement method Step #1: Measure the mass to the correct number of SF

ANS: 7.50 g (record screen exactly) 7.50 g Determining the density of Sponge Bob Square Pants to the correct of SF using the volume displacement method Step #2: Measure the initial and final volume to the correct SF. Important assumption: Assume Sponge Bob does not act like

a normal sponge (justified by the fact he wears pants and talks) and does not actually absorb water. Record initial and Final Volumes and calculate V (Final initial) to the correct number of SF Volume Final: 52.0 mL - Volume Initial: 50.0 mL Volume Final: 2.0 mL

Determining the density of Sponge Bob Square Pants to the correct of SF using the volume displacement method Step #3: Plug in mass and volume into density equation d = m/v = 7.50 g/ 2.0 mL = 3.75 3.8 g/mL (2 SF) Note that unlike a typical sponge that floats, Sponge Bob sinks since has density > 1 g/mL (density of water)

p. 125, HW 4-5, #2) Determining Density from slope of mass vs. volume graph 2) A graph of mass vs volume data is given below for a gummy bear. p. 125, HW 6-1, #2) Determining Density from slope of mass vs. volume graph 2) A graph of mass vs volume data is given below for a gummy bear. Slope = y/ x = y/ y/ x = x =

y/ x = mass/ y/ x = volume Easiest points (0.0) and a point that most closely intersects marks. Density = 6.200 0.000 g 20. 00 0.000 mL

Density = 0.3100 g/mL p. 126, HW 6-1, #3 Same Mass, Smaller Volume = p. 126, HW 6-1, #3 Same Mass, Smaller Volume =

HIGHER DENSITY Homework Problem #4: Eureka! Density of Gold = 19.3 g/mL Density of Silver = 10.5 g/mL Calculate the volume occupied by 500. g of each metal: d = m/v dv = m v = m/d Gold: v = 500. g / 19.3 g/mL = 25.9 mL

Silver: v = 500. g / 10.5 g/mL = 47.6 mL Homework Problem #4: Archimedes and the gold crown Archimedes placed an equal mass of pure gold in water and compared the water displaced by the crown. Since the crown displaced more water, it was not pure gold.

Archimedes link HW 6-1, #5 Explain the following observation: Liquid water has a density of 1.0 g/ mL while solid water (ice) has a density of 0.91 g/mL Link to ice bomb 5a) Water molecules are packed more closely together in liquid than in ice.

In ice molecules pack in 6 membered rings leaving a hole in the center. 5b) No 5c) Volume expands when water freezes could burst bottle Applications of Density: Sink vs. Float and identifying a substance Different materials displace different volumes

6a)Regular soda has a density greater than 1 (sinks); diet soda density is less than 1 (floats) Sink or Float: Which can has a density less than 1 g/mL and which can has density greater

than 1 g/mL? Diet(sugar free) soda and soda in water 4b) Which has a higher concentration of sweet molecules, regular or diet soda? Diet

Regular Artificial sweetners produce the same sweet taste at a much lower concentration than sugar HW 6-1 #7 Densities of common objects which phases tends to have the lowest densities and which phase tends to have the highest densities? Propose an atomic level observation to account for the data.

What do you notice about the relationship between density and volume of different metals with the same mass? Solids have the greatest number of atoms/molecules per volume space; gases have the fewest number of atoms per space. Less dense materials require a larger volume for the same mass of material.

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