Chapter U4.75, Problem 10E

Interpretation Introduction

Interpretation:

From the samples of 50 g of copper and 50 g of gold, the one that has more atoms needs to be deduced.

Concept Introduction:

Mass is a fundamental property of an object which is representative of the amount of matter present in that object.

The average mass of an atom is expressed in terms of atomic mass units (amu)

  $\text{1 amu = 1}{\text{.66×10}}^{\text{-24}}\text{ g -----(1)}$

Answer to Problem 10E

The sample with 50 g copper will have more atoms.

Explanation of Solution

Given:

Mass of copper = 50 g

Mass of gold = 50 g

Calculation:

Calculateatoms of copper in the 50 g sample as follows:

As per the periodic table, the atomic mass of an atom of copperis 63.5 amu

Based on the conversion expressed in equation (1):

  $\begin{array}{c}\text{Mass of an atom of Cu in grams =}\frac{63.5\text{ amu }\times \text{ 1}\text{.66}\times {\text{10}}^{-24}\text{ g}}{1\text{ amu}}\end{array}$

                $\begin{array}{c}=1.05\times {10}^{-22}\text{ g}\end{array}$

Now,

  $\begin{array}{c}\text{Number of copper atoms =}\frac{\text{Total Mass of copper sample}}{\text{Mass per copper atom}}\end{array}$

             $\begin{array}{c}=\frac{50\text{ g}}{1.05\times {10}^{-22}\text{ g/atom}}\end{array}$

             $\begin{array}{c}=4.76\times {10}^{21}\text{ atoms}\end{array}$

Calculate atoms of gold in the 50 g sample as follows:

As per the periodic table, the atomic mass of an atom of gold (Au) is 196.97 amu

Based on the conversion expressed in equation (1):

  $\begin{array}{c}\text{Mass of an atom of Au in grams=}\frac{196.97\text{ amu }\times \text{ 1}\text{.66}\times {\text{10}}^{-24}\text{ g}}{1\text{ amu}}\end{array}$

                $\begin{array}{c}=3.27\times {10}^{-22}\text{ g}\end{array}$

Now,

  $\begin{array}{c}\text{Number of gold atoms =}\frac{\text{Total Mass of gold sample}}{\text{Mass per gold atom}}\end{array}$

            $\begin{array}{c}=\frac{50\text{ g}}{3.27\times {10}^{-22}\text{ g/atom}}\end{array}$

            $\begin{array}{c}=1.53\times {10}^{21}\text{ atoms}\end{array}$

Conclusion

Thus, the sample weighing 50 g of copper will have more atoms.