Chapter 15, Problem 20TE

Which contains more atoms: $1\text{ kg}$ of lead, or $1\text{ kg}$ of aluminium?

To determine

Whether$1\text{ kg}$ of aluminium contains more atoms or $1\text{ kg}$ of lead.

Answer to Problem 20TE

$1\text{ kg}$ of aluminium contains more atoms as compare to $1\text{ kg}$ of lead.

Explanation of Solution

Write the expression to determine number of moles present in $1\text{ kg}$ of aluminium.

$n_{Al}\text{=}\frac{\text{total}\text{weight}}{\text{weight}\text{of}\text{1}\text{mole}\text{of}\text{aluminium}}$

Here,

Weight of 1 mole of aluminium is $26.98\text{ g}$

$n_{Al}$ is number of moles in $1\text{kg}$ aluminium

Substitute $1000\text{g}$ for total weight and $26.98\text{ g}$ for weight of 1 mole of aluminium.

$\begin{array}{c}{n}_{Al}=\frac{1000\text{g}}{26.98\text{ g}}\\ =37.06\text{moles}\\ \approx 37\text{moles}\end{array}$

Write the expression to determine number of moles present in $1\text{ kg}$ of lead.

$n_{Pb}\text{=}\frac{\text{total}\text{weight}}{\text{weight}\text{of}\text{1}\text{mole}\text{of}\text{lead}}$

Here,

Weight of 1 mole of lead is $207.02\text{ g}$

$n_{pb}$ is number of moles in $1\text{kg}$ lead

Substitute $1000\text{g}$for total weight and $207.02\text{ g}$for weight of 1 mole of lead.

$\begin{array}{c}{n}_{Pb}=\frac{1000\text{g}}{207.02\text{ g}}\\ =4.83\text{moles}\\ \approx 5\text{moles}\end{array}$

Conclusion:

Therefore, $1\text{ kg}$ of aluminium contains more atoms as compare to $1\text{ kg}$ of lead.