Chapter 4, Problem 4.103P

4-103 Caffeine, a central nervous system stimulant, has the molecular formula C8H10N402.

(a) How many moles of caffeine are present in 6.19 10²⁵ molecules of caffeine?

(b) Imagine you dissolve caffeine in water to a volume of 100.0 mL, which is known to have a density of 1.23 g/mL. How many molecules of caffeine are present in this volume?

(c) How many nitrogen atoms are present in 3.5 mg of caffeine?

(d) Complete the skeletal structure of caffeine, where all the bonded atoms are shown but double bonds, triple bonds, and/or lone pairs are missing.

(e) Identify the various types of geometries present in each central atom of caffeine using VSEPR theory.

(f) Determine the various relative bond angles associated with each central atom of caffeine using VSEPR theory

(g) What is the most polar bond in caffeine?

(h) Would you predict caffeine to be polar or nonpolar?

(j) Consider the combustion of caffeine, which results in formation of NO₂(g) as well as other expected products. Write a balanced chemical equation for this reaction.

(j) The heat of combustion for caffeine is 2211 kcall/mol. How much heat will be given off if 0.81 g of caffeine is burned completely?

(k) Calculate the weight of H₂O(g) that can be prepared from 8.00 g of caffeine mixed with 20.3 g of oxygen gas.

Interpretation Introduction

(a)

Interpretation:

Calculate the number of moles of caffeine in 6.19×10²⁵ molecules.

Concept Introduction:

The caffeine is a chemical, which is found abundantly in some beverage like tea, coffee, cola and mate etc. It is known to be a nervous system stimulant and used to improve the alertness of the brain.

According to Avogadro’s law, the number of units in 1 mol of a substance is equal to This is known as Avogadro’s number.

Answer to Problem 4.103P

6.19×10²⁵ molecules are equal to 103 moles of caffeine.

Explanation of Solution

The number of moles present in 6.19×10²⁵ molecules of caffeine can be calculated as follows:

$\begin{array}{l}\text{1mole of caffeine = 6}{\text{.022 ×10}}^{\text{23}}\text{molecules}\text{.}\\ \text{number of moles =}\frac{\text{given number of molecules}}{\text{Avadagro's number}}\\ \text{number of moles =}\frac{\text{6}{\text{.19×10}}^{\text{25}}}{\text{6}{\text{.022 ×10}}^{\text{23}}}\\ \text{number of moles in 6}{\text{.022 ×10}}^{\text{23}}\text{molecules=1}{\text{.0278×10}}^{\text{2}}\\ \text{number of moles in 6}{\text{.022 ×10}}^{\text{23}}\text{molecules=1}{\text{.03×10}}^{\text{2}}\\ \text{number of moles in 6}{\text{.022 ×10}}^{\text{23}}\text{molecules=103}\end{array}$.

Interpretation Introduction

(b)

Interpretation:

Calculate the number of molecules of caffeine in a solution, which has a density 1.23g/ml.

Concept Introduction:

The caffeine is a chemical, which is found abundantly in some beverage like tea, coffee, cola and mate etc. It is known to be a nervous system stimulant and used to improve the alertness of the brain.

Density of a substance is related to its mass and volume as follows:

$\text{density =}\frac{\text{mass}}{\text{volume}}$

From mass and molar mass, number of moles of substance can be calculated as follows:

$n=\frac{m}{M}$

Here, n is number of moles, m is mass and m is molar mass.

Also, according to Avogadro’s law, the number of units in 1 mol of a substance is equal to $6.023\times {10}^{23}$. This is known as Avogadro’s number.

Answer to Problem 4.103P

The number of molecules of caffeine in the solution is 3.82×10²³.

Explanation of Solution

The number of molecules present in 100ml solution of a density1.23g/ml can be calculated as follows:

$\begin{array}{l}\text{density =}\frac{\text{mass}}{\text{volume}}\\ \text{1}\text{.23 g/ml=}\frac{\text{mass}}{\text{100ml}}\\ \text{mass =123 g}\end{array}$

Mass of 1 mole of caffeine is.

$\begin{array}{l}\text{molecular mass of caffeine = mass of C}\times \text{8}+\text{mass of H}\times \text{10+mass of N}\times 4+\text{mass of O}\times \text{2}\\ \text{molecular mass of caffeine = 12}\times \text{8}+\text{1}\times \text{10+14}\times 4+\text{16}\times \text{2}\\ \text{molecular mass of caffeine = 194 }g\end{array}$

$\begin{array}{l}\text{No}\text{. of molecules in 194g caffeine = 6}\text{.022}\times {\text{10}}^{23}\\ \text{No}\text{. of molecules in 1g caffeine = }\frac{\text{6}\text{.022}\times {\text{10}}^{23}}{194}\\ \text{No}\text{. of molecules in 123g caffeine = }\frac{\text{6}\text{.022}\times {\text{10}}^{23}}{194}\times 123\\ \text{No}\text{. of molecules in 123g caffeine = }3.82\times {10}^{23}.\end{array}$.

Interpretation Introduction

(c)

Interpretation:

Calculate the number of molecules of nitrogen atoms in 3.5 mg of caffeine.

Concept Introduction:

The caffeine is a chemical, which is found abundantly in some beverage like tea, coffee, cola and mate etc. It is known to be a nervous system stimulant and used to improve the alertness of the brain.

From mass and molar mass, number of moles of substance can be calculated as follows:

$n=\frac{m}{M}$

Here, n is number of moles, m is mass and m is molar mass.

Also, according to Avogadro’s law, the number of units in 1 mol of a substance is equal to This is known as Avogadro’s number.

Answer to Problem 4.103P

The number of nitrogen atom in 3.5mg caffeine is4.32×10²².

Explanation of Solution

The number of nitrogen atom in 3.5mg caffeine can be calculated as follows:

$\begin{array}{l}\text{No}\text{. of molecules of caffeine molecules in 194g caffeine = 6}\text{.022}\times {\text{10}}^{23}\\ \text{No}\text{. of molecules of caffeine molecules in 1g caffeine = }\frac{\text{6}\text{.022}\times {\text{10}}^{23}}{194}\\ \text{No}\text{. of molecules of caffeine molecules in 3}\text{.5 g caffeine = }\frac{\text{6}\text{.022}\times {\text{10}}^{23}}{194}\times 3.5\\ \text{No}\text{. of molecules in 123g caffeine = }1.08\times {10}^{22}.\\ \text{No}\text{. of nitrogen atom in 1 molecule of caffeine = 4}\\ \text{No}\text{. of nitrogen atom in }1.08\times {10}^{22}\text{ molecule of caffeine = 4}\times 1.08\times {10}^{22}\\ \text{No}\text{. of nitrogen atom in }1.08\times {10}^{22}\text{ molecule of caffeine}=4.32\times {10}^2{}^2\end{array}$.

Interpretation Introduction

(d)

Interpretation:

Describe the skeletal structure of the caffeine.

Concept Introduction:

The caffeine is a chemical, which is found abundantly in some beverage like tea, coffee, cola and mate etc. It is known to be a nervous system stimulant and used to improve the alertness of the brain.

Answer to Problem 4.103P

The skeletal structure of the caffeine is.

Explanation of Solution

All caffeine is made up of two carbon rings, one has 4 carbon and other has 3. The ring is joined by a two shared carbon atom united by the double bond. The Lewis dot structure of the caffeine is depicted below.

Interpretation Introduction

(e)

Interpretation:

Describe the geometric details of the central atom of the caffeine.

Concept Introduction:

The caffeine is a chemical, which is found abundantly in some beverage like tea, coffee, cola and mate etc. It is known to be a nervous system stimulant and used to improve the alertness of the brain.

Answer to Problem 4.103P

The detailed geometric analysis of the central atom if the caffeine is described below.

Explanation of Solution

All caffeine is made up of two carbon rings, one has 4 carbon and other has 3. The ring is joined by a two shared carbon atom united by the double bond. Geometry exhibited by the caffeine’s central molecules is described below:

Interpretation Introduction

(f)

Interpretation:

Describe the bond angles of the caffeine.

Concept Introduction:

The caffeine is a chemical, which is found abundantly in some beverage like tea, coffee, cola and mate etc. It is known to be a nervous system stimulant and used to improve the alertness of the brain.

Answer to Problem 4.103P

The detailed bond angle analysis of the caffeine is given below.

Explanation of Solution

All caffeine is made up of two carbon rings, one has 4 carbon and other has 3. All tetrahedral and the trigonal planar structure have an angle of 109.5° and the bent nitrogen atom exhibit a bond angle of 120°. all the carbon atom in the ring has a bond angle of 120⁰.

Interpretation Introduction

(g)

Interpretation:

Describe the most polar bond in the caffeine molecule.

Concept Introduction:

The polarity in bond is due to difference in electronegitivity of atoms joined together via bond. The atom which is more electronegativity gets a partial negative charge and atom which is less electronegative or electropositive in nature gets a partial positive charge.

Answer to Problem 4.103P

C-O bonds.

Explanation of Solution

The structure of caffeine is as follows:

The bond formed between electronegative and electropositive atom will be polar in nature. Here, nitrogen and oxygen atoms are two electronegative atoms and carbon is electropositive atom. Thus, the C-N and C-O bonds will be polar in nature.

Since, oxygen is more electronegative than nitrogen, it gets more partial negative charge and the C-O bonds will be more polar.

Interpretation Introduction

(h)

Interpretation:

If the caffeine molecule is polar or non-polar should be determined.

Concept Introduction:

The polarity in bond is due to difference in electronegitivity of atoms joined together via bond. The atom which is more electronegativity gets a partial negative charge and atom which is less electronegative or electropositive in nature gets a partial positive charge.

Answer to Problem 4.103P

Polar.

Explanation of Solution

The structure of caffeine is as follows:

The bond formed between electronegative and electropositive atom will be polar in nature. Here, nitrogen and oxygen atoms are two electronegative atoms and carbon is electropositive atom. Thus, the caffeine molecule is polar in nature.

Interpretation Introduction

(i)

Interpretation:

The balanced chemical reaction for combustion of caffeine should be determined.

Concept Introduction:

The caffeine is a chemical, which is found abundantly in some beverage like tea, coffee, cola and mate etc. It is known to be a nervous system stimulant and used to improve the alertness of the brain.

From mass and molar mass, number of moles of substance can be calculated as follows:

$n=\frac{m}{M}$

Here, n is number of moles, m is mass and m is molar mass.

Answer to Problem 4.103P

${\text{2C}}_{\text{8}}{\text{H}}_{\text{10}}{\text{N}}_{\text{4}}{\text{O}}_{\text{2}}+27{\text{O}}_{\text{2}}\to 8{\text{NO}}_{\text{2}}+16{\text{CO}}_2+10{\text{H}}_{\text{2}}\text{O}$.

Explanation of Solution

The molecular formula of caffeine is ${\text{C}}_{\text{8}}{\text{H}}_{\text{10}}{\text{N}}_{\text{4}}{\text{O}}_{\text{2}}$

The combustion reaction takes place in the presence of oxygen. It is given that combustion of caffeine gives nitrogen dioxide. Combustion also produces carbon dioxide and water thus, the complete reaction for combustion of caffeine will be:

${\text{C}}_{\text{8}}{\text{H}}_{\text{10}}{\text{N}}_{\text{4}}{\text{O}}_{\text{2}}+{\text{O}}_{\text{2}}\to {\text{NO}}_{\text{2}}+{\text{CO}}_2+{\text{H}}_{\text{2}}\text{O}$

To balance the chemical reaction, give coefficient 2 to ${\text{C}}_{\text{8}}{\text{H}}_{\text{10}}{\text{N}}_{\text{4}}{\text{O}}_{\text{2}}$, 27 to ${\text{O}}_{\text{2}}$, 16 to ${\text{CO}}_{\text{2}}$, 10 to ${\text{H}}_{\text{2}}\text{O}$ and 8 to ${\text{NO}}_{\text{2}}$. Thus, the balanced chemical equation will be:

${\text{2C}}_{\text{8}}{\text{H}}_{\text{10}}{\text{N}}_{\text{4}}{\text{O}}_{\text{2}}+27{\text{O}}_{\text{2}}\to 8{\text{NO}}_{\text{2}}+16{\text{CO}}_2+10{\text{H}}_{\text{2}}\text{O}$.

Interpretation Introduction

(j)

Interpretation:

The heat of combustion for caffeine is 2211 kcal/mol. The heat given off if 0.81 g of caffeine is burned should be calculated.

Concept Introduction:

The caffeine is a chemical, which is found abundantly in some beverage like tea, coffee, cola and mate etc. It is known to be a nervous system stimulant and used to improve the alertness of the brain.

From mass and molar mass, number of moles of substance can be calculated as follows:

$n=\frac{m}{M}$

Here, n is number of moles, m is mass and m is molar mass.

Answer to Problem 4.103P

9.22 kcal.

Explanation of Solution

The heat of combustion for caffeine is 2211 kcal/mol. This means 2211 kcal of heat is released in combustion of 1 mol of caffeine. The mass of caffeine is 0.81 g and its molar mass is 194.2 g/mol thus, number of moles can be calculated as follows:

$n=\frac{m}{M}$

Putting the values,

$\begin{array}{c}n=\frac{0.81\text{ g}}{194.2\text{ g/mol}}\\ =4.171\times {10}^{-3}\text{ mol}\end{array}$

Since,

$1\text{ mol}\to \text{2211 kcal}$

Thus,

$4.171\times {10}^{-3}\text{ mol}\to \left(4.171\times {10}^{-3}\right)\text{2211 kcal}\to \text{9}\text{.22 kcal}$

Therefore, heat of combustion is 9.22 kcal.

Interpretation Introduction

(k)

Interpretation:

The weight of ${\text{H}}_{\text{2}}\text{O}\left(g\right)$ that can be prepared from 8.00 g caffeine mixed with 20.3 g of oxygen gas should be calculated.

Concept Introduction:

The caffeine is a chemical, which is found abundantly in some beverage like tea, coffee, cola and mate etc. It is known to be a nervous system stimulant and used to improve the alertness of the brain.

From mass and molar mass, number of moles of substance can be calculated as follows:

$n=\frac{m}{M}$

Here, n is number of moles, m is mass and m is molar mass.

Answer to Problem 4.103P

3.708 g.

Explanation of Solution

The balanced chemical equation for combustion of caffeine is as follows:

${\text{2C}}_{\text{8}}{\text{H}}_{\text{10}}{\text{N}}_{\text{4}}{\text{O}}_{\text{2}}+27{\text{O}}_{\text{2}}\to 8{\text{NO}}_{\text{2}}+16{\text{CO}}_2+10{\text{H}}_{\text{2}}\text{O}$

The number of moles of caffeine can be calculated as follows:

$n=\frac{m}{M}$

Putting the values,

$\begin{array}{l}n=\frac{8.00\text{ g}}{194.2\text{ g/mol}}\\ =0.0412\text{ mol}\end{array}$

Similarly, number of moles of oxygen gas will be:

$\begin{array}{l}n=\frac{20.3\text{ g}}{32\text{ g/mol}}\\ =0.634\text{ mol}\end{array}$

From the balanced chemical reaction, 2 moles of caffeine reacts with 27 moles of oxygen thus, 1 mol reacts with 13.5 mol of oxygen.

Thus, 0.0412 mol of caffeine required $13.5\times 0.0412\text{ mol}=\text{0}\text{.5562 mol}$ since, the number of moles of oxygen are 0.634 thus, oxygen is present in excess and limiting reactant will be caffeine.

Now, from balanced chemical reaction, 2 moles of caffeine gives 10 moles of ${\text{H}}_{\text{2}}\text{O}$ thus, 0.0412 mol will produce:

$n=\frac{10}{2}\times 0.0412\text{ mol=0}\text{.206mol}$

Thus, number of moles of ${\text{H}}_{\text{2}}\text{O}$ is 0.206 mol and molar mass is 18 g/mol thus, mass of ${\text{H}}_{\text{2}}\text{O}$ will be:

$m=n\times M$

Putting the values,

$m=\left(0.206\text{ mol}\right)\left(18\text{ g/mol}\right)=3.708\text{ g}$

Thus, the weight of ${\text{H}}_{\text{2}}\text{O}$ produced will be 3.708 g.