Chapter 10, Problem 112A

Convert each to mass in grams.

a. $4.22\times {\text{ 10}}^{15}$ atoms c

b. $\text{8}\text{.65 }\times {\text{ 10}}^{25}$ atoms H

c. $\text{1}\text{.25 }\times {\text{ 10}}^{22}$ atoms O

d. $\text{4}\text{.44 }\times {\text{ 10}}^{23}$ atoms Pb

Interpretation Introduction

(a)

Interpretation:

$4.22\times {10}^{15}\text{ atoms}$ of U should be converted into mass of U in grams.

Concept introduction:

The number of moles of a compound is defined as the ratio of the given mass of the compound to the molar or molecular mass of the compound.

The mathematical expression is given by:

Number of moles = $\frac{\text{given mass of the compound}}{\text{molar mass of the compound}}$

The one mole of any substance is equal to the Avogadro number, , i.e., , $6.022\times {10}^{23}$ atoms.

Answer to Problem 112A

Mass of U in grams = $166.80\times {10}^{-8}\text{ g}$

Explanation of Solution

Since, one mole of any substance is equal to the Avogadro number, i.e., $6.022\times {10}^{23}$ atoms.

Number of moles = $\text{number of atoms ×}\frac{1\text{ mole}}{6.022\times 10\text{atoms}}$

Put the values,

Number of moles = $4.22\times {10}^{15}\text{ atoms ×}\frac{1\text{ mole}}{6.022\times 10\text{atoms}}$

$=0.70076\times {10}^{-8}\text{ mole}$

Number of moles = $\frac{\text{ mass of the compound}}{\text{molar mass of the compound}}$

Molar mass of U = 238.029 g/mole

Put the values,

$\text{0}\text{.70076}\times {\text{10}}^{-8}\text{ mole = }\frac{\text{mass}}{\text{238}\text{.029 g/mole}}$

$\text{Mass = 0}\text{.70076}\times {\text{10}}^{-8}\text{ mole }\times \text{238}\text{.029 g/mole}$

Mass of U in grams = $166.80\times {10}^{-8}\text{ g}$

Interpretation Introduction

(b)

Interpretation:

$8.65\times {10}^{25}\text{ atoms}$ of H should be converted into mass of U in grams.

Concept introduction:

The number of moles of a compound is defined as the ratio of the given mass of the compound to the molar or molecular mass of the compound.

The mathematical expression is given by:

Number of moles = $\frac{\text{given mass of the compound}}{\text{molar mass of the compound}}$

The one mole of any substance is equal to the Avogadro number, i.e., $6.022\times {10}^{23}$ atoms.

Answer to Problem 112A

Mass of H in grams = $144.76\text{ g}$

Explanation of Solution

Since, one mole of any substance is equal to the Avogadro number, i.e., $6.022\times {10}^{23}$ atoms.

Number of moles = $\text{number of atoms ×}\frac{1\text{ mole}}{6.022\times 10\text{atoms}}$

Put the values,

Number of moles = $8.65\times {10}^{25}\text{ atoms ×}\frac{1\text{ mole}}{6.022\times 10\text{atoms}}$

$=1.43639\times {10}^2\text{ mole}$

Number of moles = $\frac{\text{ mass of the compound}}{\text{molar mass of the compound}}$

Molar mass of H = 1.0078 g/mole

Put the values,

$1.43639\times {10}^2\text{ mole= }\frac{\text{mass}}{\text{1}\text{.0078 g/mole}}$

$\text{Mass = }1.43639\times {10}^2\text{ mole}\times \text{1}\text{.0078 g/mole}$

Mass of H in grams = $144.76\text{ g}$

Interpretation Introduction

(c)

Interpretation:

$1.25\times {10}^{22}\text{ atoms}$ of O should be converted into mass of U in grams.

Concept introduction:

Number of moles of a compound is defined as the ratio of given mass of the compound to the molar or molecular mass of the compound.

The mathematical expression is given by:

Number of moles = $\frac{\text{given mass of the compound}}{\text{molar mass of the compound}}$

The one mole of any substance is equal to the Avogadro number, i.e., $6.022\times {10}^{23}$ atoms.

Answer to Problem 112A

Mass of O in grams = $0.332\text{ g}$

Explanation of Solution

Since, one mole of any substance is equal to the Avogadro number, i.e., $6.022\times {10}^{23}$ atoms.

Number of moles = $\text{number of atoms×}\frac{1\text{ mole}}{6.022\times 10\text{atoms}}$

Put the values,

Number of moles = $1.25\times {10}^{22}\text{ atoms ×}\frac{1\text{ mole}}{6.022\times 10\text{atoms}}$

$=0.2076\times {10}^{-1}\text{ mole}$

Number of moles = $\frac{\text{ mass of the compound}}{\text{molar mass of the compound}}$

Molar mass of O = 15.999 g/mole

Put the values,

$0.2076\times {10}^{-1}\text{ mole = }\frac{\text{mass}}{\text{15}\text{.999 g/mole}}$

$\text{Mass = }1.43639\times {10}^2\text{ mole}\times \text{1}\text{.0078 g/mole}$

Mass of O in grams = $0.332\text{ g}$

Interpretation Introduction

(d)

Interpretation:

$4.44\times {10}^{23}\text{ atoms}$ of $\text{Pb}$ should be converted into mass of U in grams.

Concept introduction:

Number of moles of a compound is defined as the ratio of given mass of the compound to the molar or molecular mass of the compound.

The mathematical expression is given by:

Number of moles = $\frac{\text{given mass of the compound}}{\text{molar mass of the compound}}$

The one mole of any substance is equal to the Avogadro number, i.e., $6.022\times {10}^{23}$ atoms.

Answer to Problem 112A

Mass of $\text{Pb}$ in grams = $152.8\text{ g}$

Explanation of Solution

Since, one mole of any substance is equal to the Avogadro number, i.e., $6.022\times {10}^{23}$ atoms.

Number of moles = $\text{number of atoms ×}\frac{1\text{ mole}}{6.022\times 10\text{atoms}}$

Put the values,

Number of moles = $4.44\times {10}^{23}\text{ atoms ×}\frac{1\text{ mole}}{6.022\times 10\text{atoms}}$

$=0.7373\text{ mole}$

Number of moles = $\frac{\text{ mass of the compound}}{\text{molar mass of the compound}}$

Molar mass of $\text{Pb}$ in = 207.2 g/mole

Put the values,

$0.7373\text{ mole = }\frac{\text{mass}}{\text{207}\text{.2 g/mole}}$

$\text{Mass = }0.7373\text{ mole}\times \text{207}\text{.2 g/mole}$

Mass of $\text{Pb}$ in grams = $152.8\text{ g}$