Chapter 17, Problem 64A

Which contains more atoms: 1 kg of lead or 1 kg of aluminum?

To determine

The atom containing more atoms.

Answer to Problem 64A

1 kg ofaluminium contains more atoms.

Explanation of Solution

Given:

The given elements are,

1 kg lead and 1 kg aluminium.

Formula Used:

From mole concept,

1 mole of any element contains $6.022\times {10}^{23}$ atoms.

Calculation:

For lead,

The atomic mass of lead is 207.2

So,

1 mole of lead = 207.2 g

So, number of atoms in 207.2 g of lead is $6.022\times {10}^{23}$

Therefore, number of atoms in 1 kg of lead will be

  $\begin{array}{l}n=\frac{6.022\times {10}^{23}}{207.2}\times 1000\\ =29.06\times {10}^{23}\text{atoms}\end{array}$

Now, for aluminium

The atomic mass of aluminium is around 27

So,

1 mole of aluminium = 27 g

So, number of atoms in 27 g of aluminiumis $6.022\times {10}^{23}$

Therefore, number of atoms in 1 kg of aluminium will be

  $\begin{array}{l}n=\frac{6.022\times {10}^{23}}{27}\times 1000\\ =223.04\times {10}^{23}\text{atoms}\end{array}$

So, 1 kg of aluminium contains more atoms.

Conclusion:

Therefore, 1 kg of aluminium contains more atoms.