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This question involves the concepts of density, volume, and mass.
(a) The volume occupied by this amount of water is "90 m³".
(b) The length of an edge of each small cube is "83 μm".
(c) The length of the edge of each small cube is "equal" to the diameter of a molecule.
(a)
The volume can be found using the following formula:
[tex]V = \frac{nM}{\rho}[/tex]
where,
V = volume occoupied = ?
n = no. of moles = 5 mol
M = molar mass = 18 g/mol
[tex]\rho[/tex] = density of water = 1 g/m³
Therefore,
[tex]V=\frac{(5\ mol)(18\ g/mol)}{1\ g/m^3}\\\\[/tex]
V = 90 m³
(b)
First, we will find the volume of an individual molecule:
[tex]V_i =\frac{V}{nN_A}[/tex]
where,
[tex]N_A[/tex] = Avogadro's number = 6.02 x 10²³ molecules/mol
Therefore,
[tex]V_i=\frac{90\ m^3}{5\ mol(6.02\ x\ 10^{23}\ molecules/mol)}[/tex]
Vi = 3 x 10⁻²³ m³
This volume can be given as a volume of the sphere:
[tex]V_i=\frac{4}{3}\pi r^3\\\\r=\sqrt[3]{\frac{3(3\ x\ 10^{-23}\ m^3)}{4\pi}}[/tex]
r = 4.15 x 10⁻⁷ m
Diameter = d = 2r = 2(4.15 x 10⁻⁷ m)
d = 8.3 x 10⁻⁷ m = 83 μm
since the cubes are adjacent to each other. Therefore, the diameter will be equal to the edge length.
Edge Length = L = d
L = 8.3 x 10⁻⁷ m = 83 μm
(c)
The edge length is equal to the diameter of the molecule.
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