Q. 7.82 - An Introduction to General, Organic, and Biological Chemistry

Question

Ibuprofen, an anti-inflammatory drug in Advil, has the formula . $C_{13}{H}_{18}{0}_2$

Ibuprofen is an anti inflammatory.

1. What is the molar mass of ibuprofen?
2. How many grams of ibuprofen are in $0.525$ mole?
3. How many moles of $C$ are in $12$g of ibuprofen?
4. How many moles of ibuprofen contain $1.22 x {10}^{23}$ atoms of $C$?

Step-by-Step Solution

Answer

(a) The molar mass of ibuprofen is$206.$

(b) $108.15 g$ of ibuprofen are in $0.525 moles.$

(c) $0.75$ moles of $\mathrm{C}$ are in $12 g$ of ibuprofen.

(d) $0.015$ moles of ibuprofen contains $1.22 x {10}^{23}$ atoms of $\mathrm{C}.$

Part (a) Step 1: Given Information

We are given that Ibuprofen, an anti-inflammatory drug in Advil, has the formula $C_{13}{H}_{18}{0}_2$. and we need to fine the molar mass .

Part (a) Step 2: Explanation

We are given that the chemical formula of ibuprofen $C_{13}{H}_{18}{0}_2$ and we have to find the molar mass Where $C =12,O =16, H=1$

$\mathrm{m}=12\left(\mathrm{amu}\right)\times 13+16\left(\mathrm{amu}\right)\times 2+18\times 1\left(\mathrm{amu}\right)$

m = $206 \mathrm{amu}$

Hence the molar mass of ibuprofen is $206$ amu.

Part (b) Step 1: Given Information

We need to find that How many grams of ibuprofen are in $0.525$mole .

Part (b) Step 2: Explanation

We have to given that the moles of ibuprofen is $0.525$

We know that 

$$\begin{gathered} \mathrm{moles} = \frac{\mathrm{weight} \mathrm{in} \mathrm{g}}{\mathrm{molar} \mathrm{mass}\left(\mathrm{amu}\right)} \\ 0.525 = \frac{\mathrm{W} \left(\mathrm{g}\right)}{206 \left(\mathrm{amu}\right)} \\ \mathrm{W} = 108.15 \mathrm{g} \end{gathered}$$

Part (c) Step 1: Given Information

We need to find that How many moles of C are in $12.0 g$of ibuprofen.

Part (c) Step 2: Explanation

We see the formula $C_{13}{H}_{18}{0}_2$.$1$mol of ibuprofen = $13$ mol of$\mathrm{C}$.

So the no of moles in $12 g$ of ibuprofen is $12/206$.

Moles of ibuprofen are $0.058$moles.

So $0.058$moles of ibuprofen are$13\times 0.058$ moles of $C$ are $0.75$ moles of $\mathrm{C}$.

Hence the no of moles of carbon present in $12$g of ibuprofen are$0.75$.

Part (d) Step 1: Given Information

We need to find that How many moles of ibuprofen contain $1.22x{10}^{23}$ atoms of C?

Part (d) Step 2: Explanation

We are given $1.22x{10}^{23}$ atoms of carbon.

So 

$$\begin{gathered} \mathrm{moles} = \frac{1.22\times {10}^{23}}{6\times {10}^{23}} \\ \mathrm{moles} = 0.20 \mathrm{mole} \end{gathered}$$

And we know that 

$1$mol of ibuprofen = $13$ mol of$\mathrm{C}$.

$0.20$moles of carbon contains =  $\frac{\cancel{0.2}}{\cancel{13}}=0.015$moles of ibuprofen.