Chapter 17, Problem 63A

Why don’t equal masses of golf balls and table-tennis balls contain the same number of balls? Also, why don’t equal masses of pure carbon and oxygen contain the same number of atoms?

To determine

To Explain: An equal mass of tennis ball and golf balls contains different number of balls and an equal mass of oxygen and carbon atoms contain different number of atoms.

Explanation of Solution

Introduction:

Every object has its own mass which is different from other objects.

Mass of tennis ball is around 2.7 grams; mass of the golf ball is around 45.9 grams. If 100 grams of both types of balls are needed, then there would be only two golf balls and about 37 tennis balls will be required to make it 100 grams. So, mass required was 100 grams for both the tennis and golf balls but numbers of balls obtained are different. This is because the mass of tennis ball and golf ball is different.

Example of Tennis ball:

Mass required(100 grams)	Mass of one tennis ball	Total number of balls occupied in 100 grams is
100 grams	2.7 gram	$\frac{100}{2.7}=37$ 37 balls are occupied, if 100 grams of tennis balls are required

Example of golf ball:

Mass required(100 grams)	Mass of one golf ball	Total number of balls occupied in 100 grams is
100 grams	45.9 gram	$\frac{100}{45.9}\approx 2$ Nearly 2 balls are occupied, if 100 grams of golf balls are required

In case of carbon and oxygen, 2 grams of oxygen require 0.125 moles and for carbon 0.166 moles is required to make it 2 grams.

Where,

  $\begin{array}{l}numberofatoms\\ numberofatomswillmake2gramsofoxygen.\\ xnumberofatomswillmake2gramsofcarbon.\end{array}$

  $1mol=6.023\times 10^{23}$ number of atoms

  $0.125\times 6.023\times 10^{23}=7.53\times 10^{22}$ number of atoms will make2 grams of oxygen.

  $0.125\times 6.023\times 10^{23}=7.53\times 10^{22}$ number of atoms will make 2 grams of carbon.

This shows that, for obtaining the 2 grams of carbon and 2 grams of oxygen atoms, number carbon and oxygen atoms required would be different. This is because these two atoms have different masses.

Conclusion:

Equal mass of different object contains different number of objects.