A cube made of platinum (Pt) has an edge length of 1.80 cm. The density of Pt is

Question

A cube made of platinum (Pt) has an edge length of 1.80 cm. The density of Pt is 21.45 g/cm^3. Calculate the number of Pt atoms in the cube. Atoms are spherical in shape. Therefore, the Pt atoms in the cube cannot fill all the available space. If only 74.0 percent of the space inside the cube is taken up by Pt atoms, calculate the radius in picometers of a Pt atom. The mass of a single Pt atom is 3.240 times 10^-22 g. (The volume of a sphere of radius r is (4/3) pi r^3. The volume of a cube is l^3 where l is the length of a side. Avogadro's number is 6.022 times 10^23. J

Explanation / Answer

Ans a) The voulme of cube is side^3 = 1.8^3 = 5.832 cm3

Density = mass / voulme

therefore, Mass = 21.45 g/cm3 * 5.832 cm3

= 125 gms

wt of pt in a cube = 125 gms

wt of one mole of pt is 78 gms

so no of pt item in a cube = 125/75

= 1.67

= 1670 * 10 ^-3

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