Chapter 10.2, Problem 21PP

Interpretation Introduction

Interpretation : The given mass of Si needs to be converted to representative particles and the representative particle needs to be identified.

Concept introduction : One mole of an element contains Avogadro number $\left(6.022\times {10}^{23}\right)$ of atoms (representative particles).

Answer to Problem 21PP

$\text{Number of atoms in 4}\text{.56}\times {\text{10}}^3\text{g of Si is}=9.8\times {10}^{25}$

The representative particles are atoms.

Explanation of Solution

Given information:

$\text{Weight of the Si is}=4.56\times {10}^{3}g.$

Formula used:

$\begin{array}{l}\text{Moles}=\frac{\text{weight }}{\text{gram molecular weight}}\\ \text{Number of atoms}=\text{moles}\times 6.022\times {10}^{23}\end{array}$

Calculation:

$\begin{array}{l}\text{Given weight of Si}=4.56\times {10}^{3}g.\\ \text{Atomic weight of Si}=28\\ \end{array}$

Substitute in the above formula

$\text{Moles}=\frac{\text{Weight}}{\text{Atomic weight}}$

$\begin{array}{l}\text{Number of atoms}=\frac{\text{Weight}}{\text{Atomic weight}}\times 6.022\times {10}^{23}\\ =\frac{4.56\times {10}^3}{28}\times 6.022\times {10}^{23}\\ =9.807\times {10}^{25}\end{array}$

The number of atoms of $4.56\times {10}^{3}g\text{ of Si is}=9.807\times {10}^{{}^{25}}$

Atoms are the representative particles.

Interpretation Introduction

Interpretation : The given mass of Ti needs to be converted to representative particles and the representative particle needs to be identified.

Concept introduction : One mole of an element contains Avogadro number $\left(6.022\times {10}^{23}\right)$ of atoms (representative particles).

Answer to Problem 21PP

The number of atoms in $\text{ 0}\text{.120}kg\text{ of Ti}=1.508\times {10}^{24}$.

The representative particlesare atoms.

Explanation of Solution

Given information:

$\text{Weight of the Ti is}=0.120kg$

Formula used:

$\begin{array}{l}\text{Moles}=\frac{\text{weight }}{\text{atomic weight}}\\ \text{Number of atoms}=\text{moles}\times 6.022\times {10}^{23}\end{array}$

Calculation:

$\begin{array}{l}\text{Given weight of Ti=0}\text{.120}\times {\text{10}}^{3}g\\ \text{Atomic weight of Ti}=47.9\end{array}$

Substitute in the above formula

$\text{Moles}=\frac{\text{Weight}}{\text{Atomic weight}}$

$\begin{array}{l}\text{Number of atoms}=\frac{\text{Weight}}{\text{Atomic weight}}\times 6.022\times {10}^{23}\\ =\frac{0.120\times {10}^3}{47.9}\times 6.022\times {10}^{23}\\ =1.508\times {10}^{24}\end{array}$

The number of atoms in $\text{ 0}\text{.120}kg\text{ of Ti}=1.508\times {10}^{24}$

Atoms are the representative particles.