Q. 7.4 - An Introduction to General, Organic, and Biological Chemistry

Question

Calculate each of the following: 

1. number of $\mathrm{Li}$ atoms in $4.5$ moles of $\mathrm{Li}$
2.  number of ${\mathrm{CO}}_2$ molecules in $0.0180$ mole of ${\mathrm{CO}}_2$
3. moles of $\mathrm{Cu}$ in $7.8\times {10}^{21}$ atoms of Cu
4. moles of ${\mathrm{C}}_2{\mathrm{H}}_6$ in $3.75\times {10}^{23}$ molecules of ${\mathrm{C}}_2{\mathrm{H}}_6$
   

Step-by-Step Solution

Answer

Required solution are:

1. $2.7\times {10}^{24}$ atoms of lithium
2. $1.08\times {10}^{22}$ molecules of ${\mathrm{CO}}_2$
   
3. $0.0129$ moles of $\mathrm{Cu}$
   
4. $0.622$moles of ${\mathrm{C}}_2{\mathrm{H}}_6$
   

Part (a) Step 1: Given Information

We need to find number of $\mathrm{Li}$ atoms in $4.5$ moles of  $\mathrm{Li}$

Part(a) Step 2: Explanation

We use Avogadro's number as conversion factor  to convert between moles of substance and number of particles it contain.

Conversion factor= $\frac{6.02\times {10}^{23} particles}{1 mole}$

Number of $\mathrm{Li}$ atoms=  $$\begin{gathered} \frac{6.02\times {10}^{23} atoms}{1 mole}\times 4.5 mole \\ = 2.7\times {10}^{24} atoms \end{gathered}$$

Hence, number of $\mathrm{Li}$ atoms in $4.5$ mole of lithium is $2.7\times {10}^{24}$

Part (b) Step 1: Given Information

We need to find number of  ${\mathrm{CO}}_2$ molecules in $0.0180$ moles of it.

Part(b) Step 2: Explanation

We use Avogadro's number as conversion factor  to convert between moles of substance and number of particles it contain.

Conversion factor= $\frac{6.02\times {10}^{23} molecules}{1 mole}$

Number of  ${\mathrm{CO}}_2$ molecules =  $$\begin{gathered} \frac{6.02\times {10}^{23}}{1 mole}\times 0.0180 mole \\ = 1.08\times {10}^{22} \end{gathered}$$

Hence, number of ${\mathrm{CO}}_2$ molecules in $0.0180$ mole of ${\mathrm{CO}}_2$ is $1.08\times {10}^{22}$

Part (c) Step 1: Given Information

We need to find number of moles of $\mathrm{Cu}$ in $7.8\times {10}^{21}$ atoms of $\mathrm{Cu}$

Part(c) Step 2: Explanation

We use Avogadro's number as conversion factor  to convert between moles of substance and number of particles it contain.

Conversion factor= $\frac{1 mole}{6.02\times {10}^{23}}$

Number of  moles =  $$\begin{gathered} \frac{1 mole}{6.02\times {10}^{23}}\times 7.8\times {10}^{21} \\ =1.29\times {10}^{-2} \\ =0.0129 \end{gathered}$$

Hence, number of  moles in $7.8\times {10}^{21}$ atoms of  $\mathrm{Cu}$ is $0.0129$ .

Part (d) Step 1: Given Information

We need to find number of moles of ${\mathrm{C}}_2{\mathrm{H}}_6$ in $3.75\times {10}^{23}$ molecules of ${\mathrm{C}}_2{\mathrm{H}}_6$

Part(d) Step 2: Explanation

We use Avogadro's number as conversion factor  to convert between moles of substance and number of particles it contain.

Conversion factor=  $\frac{1 mole}{6.025\times {10}^{23}}$

Number of  moles =  $$\begin{gathered} \frac{1 mole}{6.025\times {10}^{23} molecules}\times 3.75\times {10}^{23} molecules \\ =0.622 moles \end{gathered}$$

Hence, number of  moles in $3.75\times {10}^{23}$ molecules of  ${\mathrm{C}}_2{\mathrm{H}}_6$ is  $0.622$.