Q.15.C.29 - An Introduction to General, Organic, and Biological Chemistry

Question

The insect repellant DEET is an amide that can be made from the amidification of 3-methylbenzoic acid with diethylamine.

A 6.0 can of DEET repellant contains 25% DEET.

a. Draw the line angle formula of DEET.

b. Give the molecular formula of DEET.

c. What is the molar mass of DEET?

d. How many grams of DEET in one spray can?

e. Hoe many molecules of DEET in one spray can?

Step-by-Step Solution

Answer

a. The line angle formula is given as follows:

b. The molecular formula of DEET is${\mathrm{C}}_{12}{\mathrm{H}}_{17}\mathrm{NO}$ .

c. The molar mass of DEET is  191.3 g/mol.

d. 44 grams of DEET is present in one spray can.

e. $1.4\times {10}^{23}$ molecules are present in one spray can.

Step 1: Part (a) Given information

To give the line angle formula of DEET.

Step 2: Part (a) Explanation

The IUPAC name of DEET  is N,N-Diethyl-3-methylbenzamide. It is an insect or a mosquito repellant that is slightly yellowish oil.

The line angle formula of DEET is given as follows:

Step 1: Part (b) Given information

To give the molecular formula of DEET.

Step 2: Part (b) Explanation

The IUPAC name of DEET  is N,N-Diethyl-3-methylbenzamide. It is an insect or a mosquito repellant that is slightly yellowish oil.

The molecular formula gives the presence of the total number of atoms present in a moiety. Therefore, the molecular formula of DEET is ${\mathrm{C}}_{12}{\mathrm{H}}_{17}\mathrm{NO}$.

Step 1: Part (c) Given information

To give the molar mass of DEET.

Step 2: Part (c) Explanation

The IUPAC name of DEET  is N,N-Diethyl-3-methylbenzamide. It is an insect or a mosquito repellant that is slightly yellowish oil.

The molar mass represents the sum of the atomic masses of each atom present in a compound. DEET is composed of carbon, hydrogen, nitrogen, and oxygen atoms.

The molecular formula of DEET is ${\mathrm{C}}_{12}{\mathrm{H}}_{17}\mathrm{NO}$.

Thus, the molar mass of DEET is given as:

$$\begin{gathered} \mathrm{Molar} \mathrm{mass} \mathrm{of} \mathrm{DEET}= \mathrm{atomic} \mathrm{mass} \mathrm{of} \mathrm{C}+ \mathrm{atomic} \mathrm{mass} \mathrm{of} \mathrm{H}+ \mathrm{atomic} \mathrm{mass} \mathrm{of} \mathrm{O}+ \mathrm{atomic} \mathrm{mass} \mathrm{of} \mathrm{N} \\ =12\times 12+1\times 17+16\times 1+14\times 1 \\ =144+17+16+14=191 \mathrm{g}/\mathrm{mol} \end{gathered}$$

Thus, the molar mass of DEET is 191 g/mol.

Step 1: Part (d) Given information

To give the grams of DEET.

Step 2: Part (d) Explanation

The IUPAC name of DEET  is N,N-Diethyl-3-methylbenzamide. It is an insect or a mosquito repellant that is slightly yellowish oil.

One spray can contain 44 g of DEET.

Step 1: Part (e) Given information

To give the number of molecules of DEET.

Step 2: Part (e) Explanation

The number of molecules in one mole is the same for all substances; this number is known as Avogadro's number $(6.022140857\times {10}^{23})$.

Thus, in 44 grams of DEET, the number of moles will be:

$$\begin{gathered} \mathrm{Number} \mathrm{of} \mathrm{moles}=\frac{\mathrm{given} \mathrm{mass}}{\mathrm{molar} \mathrm{mass}} \\ =\frac{44}{191}=0.230 \mathrm{mole} \end{gathered}$$

Thus, in 0.230 moles, the number of molecules are given as follows:

$$\begin{gathered} \mathrm{Number} \mathrm{of} \mathrm{molecule}=0.230\times 6.022140857\times {10}^{23} \\ =1.38\times {10}^{23} \mathrm{molecules} \end{gathered}$$

Thus, the number of molecules are $1.4\times {10}^{23}$.