Please help me on (b) 1. Gold, which has a density of 19.32 g/cm3, is the most d
ID: 2274526 • Letter: P
Question
Please help me on (b)
1. Gold, which has a density of 19.32 g/cm3, is the most ductile metal and can be pressed into a thin leaf or drawn out into a long fiber. (a) If a sample of gold with a mass of 2.477g, is pressed into a leaf of 4.116 ?m thickness, what is the area (in m2) of the leaf? (b) If, instead, the gold is drawn out into a cylindrical fiber of radius 2.100 ?m, what is the length (in m) of the fiber?
I found the answer of (a) is 0.003 m^2 but I couldn't solve (b).....
2. One molecule of water (H2O) contains two atoms of hydrogen and one atom of oxygen. A hydrogen atom has a mass of 1.0 u and an atom of oxygen has a mass of 16 u, approximately.
(b) How many molecules of water are in the world's oceans, which have an estimated total mass of 1.4
Explanation / Answer
1b.
In case of a cylindrical fiber,
Length *area =volume = mass / density
Length = mass / (density*area)
Length = mass / [density*pi*(radius)^2 ]
Length = (2.477*10^-3)/ (19.32 * 10^3 * 3.1416 * (2.1*10^-6)^2 )
Length of fiber is 9254 m
2b.
Mass of H=1.0u Mass of O=16u
There are 2 atoms of H and 1 atom of O so mass of one water molecule is 18.0u. We must convert it to kg.
1atomic mass unit (u)=1.66 x 10^-27kg
(18.0u)(1.66053886x10^-27kg/1u) = 2.98896995x10^-26kg
Total mass=1.4x10^21kg
No. of molecule = 1.4 x 10^21kg / 2.9889 x 10^-26 kg = 4.68 x 10^46 molecules