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 ${\mathrm{C}}_2{\mathrm{H}}_6$
   

Short 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${\mathrm{C}}_2{\mathrm{H}}_6$
   

Step-by-step solution

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

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

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

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

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

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

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

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

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