Respuesta :
1) Mass of one copper atom: [tex]1.063\cdot 10^{-22} kg[/tex]
2) There are [tex]9.33\cdot 10^{24}[/tex] atoms in the cube
3) Mass of the cubical block: 992 kg
Explanation:
1)
We are told here that the mass of one mole of copper is
[tex]M=64 g[/tex]
for
[tex]n=1 mol[/tex] (number of moles)
We also know that the number of atoms inside 1 mole of substance is equal to Avogadro number:
[tex]N_A = 6.022\cdot 10^{23}[/tex]
This means that [tex]N_A[/tex] atoms of copper have a mass of M = 64 g. Therefore, we can find the mass of one copper atom by dividing the total mass by the avogadro number:
[tex]m=\frac{M}{N_A}=\frac{64}{6.022\cdot 10^{23}}=1.063\cdot 10^{-22} kg[/tex]
2)
We are told that the diameter of a copper atom is
[tex]d=2.28\cdot 10^{-10} m[/tex]
We can assume that the atoms are arranged in a cube, and that they are all attached to each other; so the side of the cube can be written as size of one atom multiplied by the number of atom per side:
[tex]L=Nd[/tex]
where
N is the number of atoms (rows) in one side of the cube
Since the side of the cube is
L = 4.8 cm = 0.048 m
We find N:
[tex]N=\frac{L}{d}=\frac{0.048}{2.28\cdot 10^{-10}}=2.11\cdot 10^8[/tex]
This is the number of atom rows per side; therefore, the total number of atoms in the cube is
[tex]N^3=(2.11\cdot 10^8)^3=9.33\cdot 10^{24}[/tex]
3)
The total mass of the cubical block of copper will be given by the mass of one atom of copper multiplied by the total number of atoms, so:
[tex]M= N^3 m[/tex]
where:
[tex]N^3 = 9.33\cdot 10^{24}[/tex] is the number of atoms in the cube
[tex]m=1.063\cdot 10^{-22} kg[/tex] is the mass of one atom
Therefore, substituting, we find:
[tex]M=(9.33\cdot 10^{24})(1.063\cdot 10^{-22})=992 kg[/tex]
So, the mass of the cubical block is 992 kg.
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#LearnwithBrainly
(i) Mass of one copper atom 1.063×10⁻²²kg
(ii) There are 9.33×10²⁴ atoms in the cube
(iii) Mass of the cubical block is 992 kg
mass of one atom:
The mass of one mole of copper is M = 64g
also, 1 mole of any substance contains 6.022 × 10²³ atoms
Therefore mass of one atom of copper will be:
[tex]m = \frac{64}{6.022\times10^{23}}kg\\\\m=1.063\times10^{-22}kg[/tex]
So, the mass of one atom is 1.063×10⁻²²kg
number of atoms:
It is given that the diameter of a copper atom is:
[tex]d=2.28\times10^{-10}m[/tex]
The length of the given cube is
L = 4.8cm = 0.048m
So the number of in length L will be:
[tex]n=\frac{L}{d}=\frac{0.048}{2.28\times10^{-10}}\\\\n=2.11\times 10^8[/tex]
so the number of atoms in the cube of volume V = [tex]L^3[/tex] will be:
[tex]n^3=(2.11\times10^8)^3\\\\N=n^3=9.33\times10^{24}[/tex] atoms will be in the cube of length 4.8cm
mass of the cubical block:
Now the mass of the cube will be:
[tex]M=Nm=n^3m\\\\M=9.33\times10^24\times1.063\times10^{-22}kg\\\\M=992kg[/tex]
So, the mass of the cubical block is 992 kg.
Learn more about moles conversion:
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