Chapter 6.1, Problem 4RQ

Interpretation Introduction

Interpretation: The given table needs to be completed for mass of samples, number of moles and atoms in sample.

Concept Introduction: In 1 mol of a substance there are $6.022\times {10}^{23}$ particles. This is known as Avogadro’s number and represented by symbol N_A.

Answer to Problem 4RQ

  $\text{Number of moles of Cu}=\text{0}\text{.674 mol}$

  $\text{Number of atoms or molecules of Cu}=4.05\times {10}^{23}\text{ atoms}$

  $\text{mass of K}=\text{33}\text{.38 g}$

  $\text{Number of atoms or molecules of K=5}{\text{.15×10}}^{\text{23}}$

  $\text{mass of Ar}=\text{23}\text{.7g}$

  $\text{Number of atoms or molecules of Ar=1}{\text{.185×10}}^{\text{2}}$

  $\text{Number of moles of Cs}=\text{0}{\text{.0144×10}}^{\text{-3}}$

  $\text{Number of atoms or molecules of Cs}=\text{0}{\text{.086×10}}^{\text{20}}$

  $\text{mass of He}=\text{19}\text{.04 g}$

  $\text{Number of atoms or molecules of He}=\text{28}{\text{.66×10}}^{\text{23}}$

  $\text{Mass of Si=0}\text{.179g}$

  $\text{Number of atoms of Si}=\text{0}\text{.0639 mol}$

Explanation of Solution

The number of moles can be calculated from mass and molar mass as follows:

  $\text{Number of moles}=\frac{\text{Given mass}}{\text{Atomic mass}}$

Putting the values,

  $\text{Number of moles of Cu=}\frac{\text{42}\text{.8 g}}{\text{63}\text{.5 g/mol}}=0.674\text{ mol}$

The number of atoms or molecules in the given mass of an atom can be calculated as follows:

  $\text{Number of molecules or atoms of Cu}=\text{moles×Avogadro's number}$

  $=0.674\times 6.022\times {10}^{23}\text{ atoms}$

  $=4.05\times {10}^{23}\text{ atoms}$

The mass of K can be calculated as follows:

  $\text{Number of moles of K=}\frac{\text{Given mass}}{\text{Atomic mass}}$

  $0.856=\frac{xgm}{39}$

  $x=0.856\times 39$

  $x=33.38gm$

Now, number of atoms of K can be calculated as follows:

  $\text{Number of molecules or atoms of K}=\text{moles×Avogadro's number}$

  $=0.856\times 6.022\times {10}^{23}$

  $=5.15\times {10}^{23}$

The number of moles of Ar can be calculated as follows:

  $\text{Moles}=\frac{\text{number of atoms or molecules of Ar}}{\text{Avogadro's number}}$

  $=\frac{7.14\times {10}^{25}}{6.022\times {10}^{23}}$

  $=1.185\times {10}^2$

Now, from number of moles, mass of Ar can be calculated as follows:

  $\text{Number of moles of Ar=}\frac{\text{Given mass}}{\text{Atomic mass}}$

  $1.185\times {10}^2=\frac{xgm}{20}$

  $x=1.185\times {10}^2\times 20$

  $x=23.7gm$

The number of moles can be calculated as follows:

  $\text{Number of moles}=\frac{\text{Given mass}}{\text{Atomic mass}}$

  $=\frac{1.92\times {10}^{-8}}{132.9}$

  $=0.0144\times {10}^{-3}$

Now, number of molecules can be calculated as follows:

  $\text{Number of molecules or atoms}=\text{moles×Avogadro's number}$

  $=0.0144\times {10}^{-3}\times 6.022\times {10}^{23}$

  $=0.086\times {10}^{20}$

The mass of He can be calculated as follows:

  $\text{Number of moles}=\frac{\text{Given mass}}{\text{Atomic mass}}$

  $4.76=\frac{xgm}{4}$

  $x=4.76\times 4$

  $x=19.04gm$

The number of molecules can be calculated as follows:

  $\text{Number of molecules or atoms}=\text{moles×Avogadro's number}$

  $=4.76\times {10}^{-3}\times 6.022\times {10}^{23}$

  $=28.66\times {10}^{23}$

The number of moles of Si can be calculated as follows:

  $n_{Si}=\frac{3.85\times {10}^{22}}{6.022\times {10}^{23}}$

  $=0.639\times {10}^{-1}$

  $=0.0639$

Now, mass can be calculated as follows:

  $\text{Number of moles=}\frac{\text{Given mass}}{\text{Atomic mass}}$

  $0.0639=\frac{xgm}{28.08}$

  $x=0.0639\times 28.08$

  $x=1.79gm$