Chapter 13, Problem 1Q

To determine

To Find: The greater number of atoms present in 1 kg of iron or 1 kg of aluminum.

Answer to Problem 1Q

1 kg of aluminum

Explanation of Solution

Given:

The mass of iron, $m_{Fe}=1\text{kg}$

The mass of aluminum, $m_{Al}=1\text{kg}$

Formula used:

If n is the number of moles, m is the mass of the substance and M is the molar mass, then:

  $\begin{array}{l}n=\frac{m}{M}\\ N=n{N}_A\\ N_A=6.023\times {10}^{23}\end{array}$

Here, N is the number of atoms.

Calculation:

From the periodic table:

  $\begin{array}{l}{M}_{Al}=26.98\text{g/mol}\\ M_{Fe}=55.93\text{g/mol}\end{array}$

Substitute the given values:

  $\begin{array}{l}{n}_{Al}=\frac{1000}{26.98}=37.06\text{mol}\\ n_{Fe}=\frac{1000}{55.93}=17.87\text{mol}\end{array}$

  $\begin{array}{l}{N}_{Al}=n_{Al}{N}_A\\ N_{Fe}=n_{Fe}{N}_A\\ n_{Al}>n_{Fe}\\ N_{Al}>N_{Fe}\end{array}$

Conclusion:

The number of atoms of 1 kg of aluminum will be more as the molar mass of aluminum is less than the molar mass of iron.