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emjay66
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I am attempting to complete a basic question involving molecular separation from Alonso & Finn "Fundamental University Physics" Second Edition, Chapter 2, Question 9. The Problem states
"Using the data in table 2-1 and A-1, estimate the average separation in molecules of hydrogen at STP (gas), in water (liquid), and in iron (solid)."
Now, Table 2-1 contains density values (relative to water). The relevant values are:
Iron = 7.86
Water (4 Degrees C) = 1.000
Hydrogen = [itex]8.988\times 10^{-5}[/itex]
Table A-1 is the periodic table of the elements and the relevant values for this are:
Hydrogen = 1.00797
Oxygen = 15.9994
Iron = 55.847
I will only show my attempt to compute the answer for Hydrogen since I feel I am (probably) making the same mistake throughout.
An inspection of the answers in the back showed that for Hydrogen they obtained:
3.39*10^-7 cm for spherical geometry and 1.14 * 10^-8 cm for cubic geometry
Firstly I assume a Hydrogen "molecule" is two atoms of Hydrogen
I also assume the calculation for a mass of 1kg of the relevant substance
the molecular mass of a Hydrogen molecule = 2 * 1.00797 = 2.01594 g/mol
Number of mole of Hydrogen in 1kg = 1000/2.01594 496.047 mol
Number of Hydrogen molecules = 496.047 * (6.02*10^23) = 2.986*10^26 molecules
Number of Hydrogen molecules at STP = 2.986*10^26 * (8.988*10^(-5)) = 2.68*10^22 molecules
At this point (for a cube) I know 1kg = 1000 cubic centimetres
which means the cube root of 2.68*10^22 (= 29940610.46) would give the number of molecules along one edge (10cm)
which (to me) would mean that 10/29940610 = 3.34*10^(-7) cm, which is clearly wrong.
For the Spherical geometry I reasoned [itex]1000 = \frac{4}{3}\pi\,r^3 [/itex] which would mean [itex]r = (\frac{3000}{4\pi})^{1/3} [/itex] = 6.2 cm which means the diameter would be
12.4 cm. This would give a separation of 4.4*10^(-7) cm, which is also wrong.
I understand that my thinking is clearly faulty, so some pointers in the right direction would be nice. Thank you in advance.
"Using the data in table 2-1 and A-1, estimate the average separation in molecules of hydrogen at STP (gas), in water (liquid), and in iron (solid)."
Now, Table 2-1 contains density values (relative to water). The relevant values are:
Iron = 7.86
Water (4 Degrees C) = 1.000
Hydrogen = [itex]8.988\times 10^{-5}[/itex]
Table A-1 is the periodic table of the elements and the relevant values for this are:
Hydrogen = 1.00797
Oxygen = 15.9994
Iron = 55.847
I will only show my attempt to compute the answer for Hydrogen since I feel I am (probably) making the same mistake throughout.
An inspection of the answers in the back showed that for Hydrogen they obtained:
3.39*10^-7 cm for spherical geometry and 1.14 * 10^-8 cm for cubic geometry
Firstly I assume a Hydrogen "molecule" is two atoms of Hydrogen
I also assume the calculation for a mass of 1kg of the relevant substance
the molecular mass of a Hydrogen molecule = 2 * 1.00797 = 2.01594 g/mol
Number of mole of Hydrogen in 1kg = 1000/2.01594 496.047 mol
Number of Hydrogen molecules = 496.047 * (6.02*10^23) = 2.986*10^26 molecules
Number of Hydrogen molecules at STP = 2.986*10^26 * (8.988*10^(-5)) = 2.68*10^22 molecules
At this point (for a cube) I know 1kg = 1000 cubic centimetres
which means the cube root of 2.68*10^22 (= 29940610.46) would give the number of molecules along one edge (10cm)
which (to me) would mean that 10/29940610 = 3.34*10^(-7) cm, which is clearly wrong.
For the Spherical geometry I reasoned [itex]1000 = \frac{4}{3}\pi\,r^3 [/itex] which would mean [itex]r = (\frac{3000}{4\pi})^{1/3} [/itex] = 6.2 cm which means the diameter would be
12.4 cm. This would give a separation of 4.4*10^(-7) cm, which is also wrong.
I understand that my thinking is clearly faulty, so some pointers in the right direction would be nice. Thank you in advance.