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 $25.0g$?

3. How many moles of $C$are in localid="1653459359665" $25.0g$of dipyrithione?

4. How many moles of dipyrithione contain localid="1652950310084" $8.2\times {10}^{24}$atoms of $N$?

Short answer

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

(b) Moles of dipyrithione are inlocalid="1653459381494" $25g$is $0.10$.

(c) Moles of $C$are in localid="1653459373891" $25.0g$of dipyrithione $10.$

(d) $6.8$moles of dipyrithione contain localid="1652950325214" $8.2\times {10}^{24}$atoms of $N$.

Step-by-step solution

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 $\mathrm{C}=12,\mathrm{N}=14,\mathrm{O}=16,\mathrm{S}=32,\mathrm{H}=1$

$m$= localid="1652950370359" $10\times 12+8+2\times 14+16\times 2+32\times 2$

$m$= localid="1653501007290" $244\mathrm{amu}$

Hence The molar mass of dipyrithione is localid="1653501023514" $244\mathrm{amu}.$

Part (b) Step 1: Given Information

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

Part (b) Step 2: Explanation

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

We know that

localid="1653500955622" role="math" $$\begin{gathered} \mathrm{moles}=\frac{\mathrm{weight}\mathrm{in}\mathrm{g}}{\mathrm{molar}\mathrm{mass}} \\ \mathrm{n}=\frac{25\mathrm{g}}{44\mathrm{amu}} \\ \mathrm{n}=0.10\mathrm{moles} \end{gathered}$$

Hence the moles of localid="1653500985672" $25\mathrm{g}$dipyrithione is localid="1653500971504" $0.10\mathrm{moles}$.

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 = localid="1652950390577" $10\times 0.01$moles of $\mathrm{C}$.

Moles = $10$.

Part (d) Step 1: Given Information

We need to find that How many moles of dipyrithione contain $8.2X{10}^{24}$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 $6.022x10²³$, we calculate for the answer as shown below.localid="1653501968963" $$\begin{gathered} n=8.2\times {10}^{24}\mathrm{atoms}\mathrm{of}\mathrm{N}\times \frac{1\mathrm{molecule}\mathrm{dipyrithione}}{2\mathrm{atoms}\mathrm{of}\mathrm{N}}\times \frac{1\mathrm{mole}\mathrm{dipyrithione}}{N_A\mathrm{molecules}\mathrm{dipyrithione}} \\ n=8.2\times {10}^{24}\cancel{\mathrm{atoms}\mathrm{of}\mathrm{N}}\times \frac{1\cancel{\mathrm{molecule}\mathrm{dipyrithione}}}{2\cancel{\mathrm{atoms}\mathrm{of}\mathrm{N}}}\times \frac{1\mathrm{mole}\mathrm{dipyrithione}}{6\times {10}^{23}\cancel{\mathrm{molecule}\mathrm{dipyrithione}}} \end{gathered}$$
$n=6.8$moles dipyrithione .