Q. 7.81 - An Introduction to General, Organic, and Biological Chemistry

Question

A dandruff shampoo contains dipyrithione,${\mathrm{C}}_{10}{\mathrm{H}}_8{\mathrm{N}}_2{\mathrm{O}}_2{\mathrm{S}}_2$ , which acts as an antibacterial and antifungal agent. 

1. What is the molar mass of dipyrithione?
2. How many moles of dipyrithione are in $25.0 g$?

3. How many moles of $C$ are in $25.0 g$of dipyrithione?

4. How many moles of dipyrithione contain $8.2 \times {10}^{24}$atoms of $N$?

Step-by-Step Solution

Answer

(a) The molar mass of dipyrithione $244.$

(b) Moles of dipyrithione are in $25 g$ is $0.10$.

(c) Moles of $C$ are in $25.0 g$ of dipyrithione $10.$

(d) $6.8$moles of dipyrithione contain $8.2 \times {10}^{24}$atoms of  $N$.

Part (a) Step 1: Given Information

We need to find the molar mass of dipyrithione  and we are given that the chemical formula of dipyrithione is ${\mathrm{C}}_{10}{\mathrm{H}}_8{\mathrm{N}}_2{\mathrm{O}}_2{\mathrm{S}}_2$.

Part (a) Step 2: Explanation

So the molar mass of dipyrithione is $m$. and we know that $\mathrm{C} =12, \mathrm{N}=14,\mathrm{O} =16,\mathrm{S} =32,\mathrm{H}=1$

$m$ = $10\times 12+8+2\times 14+16\times 2+32\times 2$

$m$ = $244 \mathrm{amu}$

Hence The molar mass of dipyrithione is $244 \mathrm{amu} .$

Part (b) Step 1: Given Information

We need to find that How many moles of dipyrithione are in $25.0 g$?

Part (b) Step 2: Explanation

We are given that $25.0 g$of dipyrithione and we need to find the no, of moles of dipyrithione .

We know that 

$$\begin{gathered} \mathrm{moles} = \frac{\mathrm{weight} \mathrm{in} \mathrm{g}}{\mathrm{molar} \mathrm{mass}} \\ \mathrm{n}=\frac{25 \mathrm{g}}{44 \mathrm{amu}} \\ \mathrm{n} = 0.10 \mathrm{moles} \end{gathered}$$

Hence the moles of $25 \mathrm{g}$ dipyrithione  is $0.10 \mathrm{moles}$.

Part (c) Step 1: Given Information

We need to find that How many moles of $C$ are in  $25.0$g of dipyrithione.

Part (c) Step 2: Explanation

Dipyrithione is a chemical with formula, ${\mathrm{C}}_{10}{\mathrm{H}}_8{\mathrm{N}}_2{\mathrm{O}}_2{\mathrm{S}}_2$.

We know that,

 $10$ mole of carbon = $1$ mole of dipyrithione.

$0.01$mol of dipyrithione = $10\times 0.01$ moles of $\mathrm{C}$.

Moles = $10$.

Part (d) Step 1: Given Information

We need to find that How many moles of dipyrithione contain $8.2 X {10}^{24}$atoms of  $N$.

Part (d) Step 2: Explanation

Dipyrithione is a chemical with formula, $\mathrm{C}₁₀\mathrm{H}₈\mathrm{N}₂\mathrm{O}₂\mathrm{S}₂.$This means that each molecule of the substance has two $2$atoms of nitrogen. By using the dimensional analysis and Avogadro's number, equal to $6.022 x 10²³$, we calculate for the answer as shown below.$$\begin{gathered} n = 8.2\times {10}^{24}\mathrm{atoms} \mathrm{of} \mathrm{N} \times \frac{1 \mathrm{molecule} \mathrm{dipyrithione}}{2 \mathrm{atoms} \mathrm{of} \mathrm{N}} \times \frac{1 \mathrm{mole} \mathrm{dipyrithione}}{N_A \mathrm{molecules} \mathrm{dipyrithione}} \\ n = 8.2\times {10}^{24}\cancel{\mathrm{atoms} \mathrm{of} \mathrm{N}}\times \frac{1 \cancel{\mathrm{molecule} \mathrm{dipyrithione}}}{2 \cancel{\mathrm{atoms} \mathrm{of} \mathrm{N}}}\times \frac{1 \mathrm{mole} \mathrm{dipyrithione}}{6\times {10}^{23}\cancel{\mathrm{molecule} \mathrm{dipyrithione}}} \end{gathered}$$
$n = 6.8$moles dipyrithione .