Question

The atomic mass of silver is 107.9. A cube of silver weighs 30.3g, and its density is 10.6 g/cm3.

Calculate

(i) the volume of the sample.

(ii) The number of silver atoms in the sample

(iii) If we consider the sample is composed of spherical atom each with radius r and volume vatom=4/3 pi * R^3 ,and if we assume that the total volume of the spheres in the sample is 74.0 % of the total volume of the sample, calculate the radius of a single silver atom in picometers.

Answer 1

density = mass/volume

or, volume = mass/ density = 30.3gm/10.6gm cm^3 = 2.86 cm^3

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moles of Silver = mass of silver/ molar mass of silver = 30.3gm/107.9 = 0.281 moles

Number of atoms in 1 mole = 6.023 *10^23.

So, number of atoms in 0.281 moles = 0.281 * 6.023 *10^23= 1.69 810^23

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Volume of the shpere = 2.86 cm^3 * 74% = 2.116 cm ^3

volume of 1 such sphere = 2.116 cm ^3/ 1.69 *10^23 =125.23 *10^-23

4/3pi 8 r^3 = 1.69 *10^-8 cm = 169 pm