HChem WS 5.8 Density of Solids Problems Name _______________________ Period______ Date ___ Concern yourself with sig figs and be sure that your answer has proper unit labels. No naked numbers. For some of these problems, you may need to refer to the Density Reference sheet – available below. 1.
A block of aluminum has a mass of 33.2 g and displaces 12.3 ml of milk. What is the density of the aluminum? 2.
A cube of iron 5.4 cm on each side has a mass of 1,100 g. Determine the density of the iron. •
Is it likely that this cube of iron has some lead or aluminum mixed in with it? 3.
Determine the volume of water that a lump of lead with a mass of 75.5 g would displace. •
Determine the volume of oil that a lump of lead with a mass of 75.5 g would displace. 4.
Determine the mass of a lump of gold that measures 15.0 cm x 6.50 cm x 5.00 cm. •
If gold costs $29.67 per gram, how much money is the block of gold worth? 5.
Which is larger in size? 38.5 g of iron or a piece of aluminum that has the same mass? •
How many times larger? 6.
Determine the density of margarine if 197 g occupies 312 ml of space? •
Would the margarine sink or float in water? HCHem WS 5.8 Density of Solids Resource Sheet ANSWERS ‐ Pay attention to your unit labels. Note which cancel out, and which do not. 1.
2.
3.
4.
5.
6.
If the aluminum displaces 12.3 ml of milk, that is its volume, so solve: 33.2 g / 12.3 ml = 2.70 g/ml (3sf) 3 First you must calculate the volume of the cube. L * W * H = Volume so 5.4 cm * 5.4 cm * 5.4 cm = 157.5 cm 3
3
3
then solve 1,100 g / 157.5 cm = 7.0 g/cm or 7.0 g/ml (2sf) Remember that cm = ml •
Aluminum, since the actual density of iron is 7.87 g/ml, and the density of the block of iron in this problem less than the theoretical value, it must be mixed with a metal that is less dense than iron in order lower the density. Since Aluminum is less dense than iron (lead is more dense than iron), it would be a likely choice. Use your algebra skills to rewrite the density equation: V = m / D then solve: 75.5 g / 11.35 g/ml = 6.65 ml (3sf) The volume of the object is the volume of water it will displace. •
the same – the volume of fluid displaced by the object, does not change just because it is put in a different liquid. First you must calculate the volume of the cube. L * W * H = Volume 3 3
solve: 15.0 cm * 6.50 cm * 5.00 cm = 487.5 cm Remember that 487.5 cm = 487.5 ml Use your algebra skills to rewrite the density equation: m = D * V then solve: 19.3 g/ml * 487.5 ml = 9410 g (3sf) •
Solve using the original unrounded mass 9408.75 g * $29.67 = $279,157.61 Although significant figures should require us to round to $ 2,790,000 – not one gold dealer would round away the extra $1,576.61 since currency comes with its own rules – ignoring sig figs and always rounding to 2 places after the decimal. Aluminum is larger. You can tell this because if ever you have objects of the same mass, the one with the smaller density will always have the larger size. Of course you could calculate if you wish by using your algebra skills to rewrite the density equation V = m / D and solve with the two different densities. V for Fe = 38.5 g / 7.87 g/ml = 4.89 ml and V for Al = 38.5 g / 2.70 g/ml = 13.3 ml •
2.9 times larger You can calculate this by making a ratio of the two densities. Fe / Al solve: 7.87 / 2.70 = Since the iron density is 2.9 times greater, the aluminum will 2.9 times larger in size. Solve: 197 g / 312 ml = 0.631 g/ml (3sf) •
Margarine would float in water because the density of the margarine is less dense than water (1.0 g/ml) HCHem WS 5.8 Density of Solids Resource Sheet Name
Hydrogen
Helium
Neon
Nitrogen
Oxygen
Fluorine
Argon
Chlorine
Krypton
Xenon
Radon
Lithium
Potassium
Sodium
Rubidium
Calcium
Magnesium
Phosphorus
Beryllium
Francium
Cesium
Sulfur
Carbon
Carbon
Silicon
Boron
Strontium
Aluminum
Scandium
Bromine
Barium
Yttrium
Titanium
Selenium
Iodine
Europium
Germanium
Radium
Arsenic
Gallium
Vanadium
Lanthanum
Tellurium
Zirconium
Antimony
Cerium
Praseodymium
Ytterbium
Astatine
Neodymium
Zinc
Chromium
Promethium
Tin
Indium
Manganese
Samarium
Iron
Gadolinium
Terbium
Dysprosium
Niobium
Cadmium
Symbol
H
He
Ne
N
O
F
Ar
Cl
Kr
Xe
Rn
Li
K
Na
Rb
Ca
Mg
P
Be
Fr
Cs
S
C
C
Si
B
Sr
Al
Sc
Br
Ba
Y
Ti
Se
I
Eu
Ge
Ra
As
Ga
V
La
Te
Zr
Sb
Ce
Pr
Yb
At
Nd
Zn
Cr
Pm
Sn
In
Mn
Sm
Fe
Gd
Tb
Dy
Nb
Cd
Density (g/cm³)
0.00008988
0.0001785
0.0008999
0.0012506
0.001429
0.001696
0.0017837
0.003214
0.003733
0.005887
0.00973
0.534
0.862
0.971
1.532
1.54
1.738
1.82
1.85
1.87
1.873
2.067
3.513
2.267
2.3296
2.34
2.64
2.698
2.989
3.122
3.594
4.469
4.540
4.809
4.93
5.243
5.323
5.50
5.776
5.907
6.11
6.145
6.232
6.506
6.685
6.770
6.773
6.965
7 approximately
7.007
7.134
7.15
7.26
7.287
7.310
7.44
7.52
7.874
7.895
8.229
8.55
8.570
8.69
HCHem WS 5.8 Holmium
Cobalt
Nickel
Copper
Erbium
Polonium
Ununhexium
Thulium
Bismuth
Ununpentium
Lutetium
Lawrencium
Actinium
Molybdenum
Silver
Lead
Ununquadium
Technetium
Thorium
Thallium
Ununtrium
Palladium
Ruthenium
Rhodium
Hafnium
Einsteinium
Curium
Mercury
Copernicium
Americium
Berkelium
Californium
Protactinium
Tantalum
Rutherfordium
Uranium
Tungsten
Gold
Roentgenium
Plutonium
Neptunium
Rhenium
Platinum
Iridium
Osmium
Density of Solids Resource Sheet Ho
Co
Ni
Cu
Er
Po
Uuh
Tm
Bi
Uup
Lu
Lr
Ac
Mo
Ag
Pb
Uuq
Tc
Th
Tl
Uut
Pd
Ru
Rh
Hf
Es
Cm
Hg
Cn
Am
Bk
Cf
Pa
Ta
Rf
U
W
Au
Rg
Pu
Np
Re
Pt
Ir
Os
8.795
8.86
8.912
8.96
9.066
9.32
9.32 or greater
9.321
9.807
9.807 or greater
9.84
9.84 or greater
10.07
10.22
10.501
11.342
11.342 or greater
11.50
11.72
11.85
11.85 or greater
12.020
12.37
12.41
13.31
13.5 (Estimate)
13.51
13.5336
13.5336 or greater
13.69
14.79
15.10
15.37
16.654
18.1
18.95
19.25
19.282
19.282 or greater
19.84
20.45
21.02
21.46
22.560
22.610