Q. 7.3 - An Introduction to General, Organic, and Biological Chemistry

Question

Calculate each of the following:
a. Number of $C$ atoms in $0.500$ mole of $C$.
b. Number of $S{O}_2$ molecules in $1.28$ moles of $S{O}_2$
c. Moles of $Fe$ in $5.22\times {10}^{22}$  atoms of $Fe$.
d. Moles of $C_2{H}_{6}O$ in $8.50\times {10}^{24}$ molecules of $C_2{H}_{6}O$.

Step-by-Step Solution

Answer

(a) Number of carbon atoms = $3.01\times {10}^{23}$

(b) Number of $S{O}_2$ molecules =$7.71\times {10}^{23}$

(c) Moles of $Fe$=$0.0867$

(d) Moles of $C_2{H}_{6}O$ = $14.1$

Part(a) Step 1 : Given information.

We have been given that,

Moles=$0.500$

We need to find the number of $C$ atoms.

Part(a) Step 2 : Simplify.

Let's calculate the number of carbon atoms in moles. 

 As we know, 

                  $1 mole =6.0221\times {10}^{23 }atoms$

              

     $Number of atoms =0.500\times \frac{6.02\times {10}^{23}}{1 mole of C}=3.01\times {10}^{23} atoms.$

Therefore, the number of carbon atoms in  mole of carbon atoms is $3.01\times {10}^{23}$ atoms.

Part(b) Step 1 : Given information.

We have been given that,

Moles=$1.28$

We need to find the number of $S{O}_2$ molecules.

Part(b) Step 2 : Simplify.

We know,

$$\begin{gathered} 1 moles=6.0221\times {10}^{23} molecules. \\ Number of molecules=1.28\times \frac{6.02\times {10}^{23}}{1 moles of C} molecules \\ =7.71\times {10}^{23} molecules. \end{gathered}$$

Therefore the number of molecules = $7.71\times {10}^{23}$.

Part(c) Step 1 : Given information.

We have been given that,

number of atoms =$5.22\times {10}^{22}$

We need to find number of moles.

Part(c) Step 2 : Simplify.

We are given that no of molecules = $5.22\times {10}^{22}$

We know that $N_A=6\times {10}^{23}$

And we know that,

$moles = \frac{no.of molecules}{N_A}$

$$\begin{gathered} moles = \frac{5.22\times {10}^{22}}{6\times {10}^{23}} \\ moles = 0.0867 \end{gathered}$$

The number of moles of $Fe$ in $5.22\times {10}^{22}$ molecules of $Fe$ is $0.0867$ moles.

Part(d) Step 1 : Given information.

We have been given that,

Number of molecules=$8.50\times {10}^{24}$

We need to find the moles.

Part(d) Step 2 : Simplify.

We are given that no. of molecules = $8.50\times {10}^{24}$

We know that $N_A=6\times {10}^{23}$

And we know that:

$moles = \frac{no.of molecules}{N_A}$

$$\begin{gathered} moles = \frac{8.50\times {10}^{24}}{6\times {10}^{23}} \\ moles = 14.1 \end{gathered}$$

Number of moles of $C_2{H}_{6}O$ in $8.50\times {10}^{24}$ molecules is $14.1$moles.