Chapter 10.2, Problem 26SSC

Interpretation Introduction

Interpretation:

The given quantities need to be arranged from smallest to largest in terms of mass.

Concept introduction:

The relation between number of moles and mass of a substance is represented as follows:

$n=\frac{m}{M}$

Here, m is mass and M is molar mass.

Also, number of moles is related to Avogadro’s number and number of units as follows:

$N=n\times N_A$

Thus, the relation between number of units and mass will be:

$\begin{array}{l}\frac{N}{N_A}=\frac{m}{M}\\ \text{or,}\\ m=\frac{N}{N_A}\times M\end{array}$

Explanation of Solution

Given Information:

$1.0$ mol of Ar, $3.0\times {10}^{24}$ atoms of Ne, and $20$ g of Kr.

Calculation:

The first step is to convert the given quantities in terms of mass.

The number of moles of Ar is given 1.0 mol. The molar mass of Ar is 39.95 g/mol. This is mass of 1 mol of Ar thus, mass of Ar will be 39.95 g.

Now, number of Ne atoms is $3.0\times {10}^{24}$. In 1 mol, the number of Ne atoms is equal to Avogadro’s number that is $6.022\times {10}^{23}$ thus, number of moles of given number of Ne atoms can be calculated as follows:

$n=\frac{N}{N_A}$

Molar mass of Ne is 20.18 g/mol thus, mass of Ne can be calculated as follows:

$m=\frac{N}{N_A}\times M$

Putting the values,

$m=\frac{3.0\times {10}^{24}\text{ atoms}}{6.022\times {10}^{23}\text{ atoms/mol}}\times 20.18\text{ g/mol}=100.53\text{ g}$

Conclusion

Therefore, arranging the given quantities from smallest to largest gives 20 g of Kr to have smallest mass followed by $1\text{ mole Ar}$ and $3.0\times {10}^{24}$ atoms of Ne has the largest mass.