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$C_2{H}_{6}O$.

Short 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$C_2{H}_{6}O$=$14.1$

Step-by-step solution

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,

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

$Numberofatoms=0.500\times \frac{6.02\times {10}^{23}}{1moleofC}=3.01\times {10}^{23}atoms.$

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,

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

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,

$moles=\frac{no.ofmolecules}{N_A}$

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

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:

$moles=\frac{no.ofmolecules}{N_A}$

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

Number of moles of $C_2{H}_{6}O$in localid="1652857798859" $8.50\times {10}^{24}$molecules is $14.1$moles.