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Solved: A cube made of platinum (Pt) has an edge length of
Chapter 2, Problem 109P(choose chapter or problem)
A cube made of platinum (Pt) has an edge length of 1.0 cm. (a) Calculate the number of Pt atoms in the cube, (b) Atoms are spherical in shape. Therefore, the Pt atoms in the cube cannot fill all of the available space. If only 74 percent of the space inside the cube is taken up by Pt atoms, calculate the radius in picometers of a Pt atom. The density of Pt is 21.45 \(\mathrm{g}/\mathrm{cm}^3\) and the mass of a single Pt atom is \(3.240 \times 10^{-22} \mathrm{g}\). [The volume of a sphere of radius is \((4 / 3) \pi r^{3}\).]
Questions & Answers
QUESTION:
A cube made of platinum (Pt) has an edge length of 1.0 cm. (a) Calculate the number of Pt atoms in the cube, (b) Atoms are spherical in shape. Therefore, the Pt atoms in the cube cannot fill all of the available space. If only 74 percent of the space inside the cube is taken up by Pt atoms, calculate the radius in picometers of a Pt atom. The density of Pt is 21.45 \(\mathrm{g}/\mathrm{cm}^3\) and the mass of a single Pt atom is \(3.240 \times 10^{-22} \mathrm{g}\). [The volume of a sphere of radius is \((4 / 3) \pi r^{3}\).]
ANSWER:
Step 1 of 2
(a) Here we have to calculate the number of platinum atoms present in a cube.
Given:
Length of edge = 1.0 cm
Density of pt = 21.45
Mass of platinum =
In order to calculate the number of platinum atoms, 1st we have to find out amount of Pt present in gram.
= 21.45 g
Then the number of atom present is,
=
Pt atoms.
Hence the number of atoms present in platinum is atoms.
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