Chapter 1, Problem 1.88EP

A mixture contains the following five pure substances:

Cl₂, C₂Cl₆, H₂CO₃, H₂SO₄, and HC1.

1. a. How many different kinds of diatomic molecules are present in the mixture?
2. b. How many different kinds of atoms are present in the mixture?
3. c. How many total atoms are in a mixture sample containing four molecules of each component?
4. d. How many total carbon atoms are present in a mixture sample containing three molecules of each component?

Interpretation Introduction

Interpretation:

The number of diatomic molecules that is present in the mixture has to be given.

Concept Introduction:

The composition of a chemical compound can be presented in a very precise was with the use of chemical formula.  Chemical formula uses chemical symbols of the elements that is present in the compound and numerical subscripts that represent how many number of atoms of each element is present in the compound.

Answer to Problem 1.88EP

In the given mixture of five molecules, two diatomic molecules are present.

Explanation of Solution

Given molecules in mixture are ${\text{Cl}}_{\text{2}}\text{,}{\text{C}}_{\text{2}}{\text{H}}_{\text{6}}\text{,}{\text{H}}_{\text{2}}{\text{CO}}_{\text{3}}\text{,}{\text{H}}_{\text{2}}{\text{SO}}_{\text{4}}\text{,}\text{and}\text{HCl}$.

Diatomic molecule is the one that contains a total of two atoms in it.  Looking into the above chemical formulas, the molecule that contains two atoms in it is found to be ${\text{Cl}}_{\text{2}}\text{and}\text{HCl}$ only.  Therefore, two diatomic molecules are present.

Interpretation Introduction

Interpretation:

The different kind of atoms that is present in the mixture has to be given.

Concept Introduction:

The composition of a chemical compound can be presented in a very precise was with the use of chemical formula.  Chemical formula uses chemical symbols of the elements that is present in the compound and numerical subscripts that represent how many number of atoms of each element is present in the compound.

Answer to Problem 1.88EP

Five kinds of atoms are present in the mixture.

Explanation of Solution

Given molecules in mixture are ${\text{Cl}}_{\text{2}}\text{,}{\text{C}}_{\text{2}}{\text{H}}_{\text{6}}\text{,}{\text{H}}_{\text{2}}{\text{CO}}_{\text{3}}\text{,}{\text{H}}_{\text{2}}{\text{SO}}_{\text{4}}\text{,}\text{and}\text{HCl}$.

Looking into the molecules in the given mixture, it is found that there are five kind of atoms present in the given molecules and they are $S,C,H,O,andCl$.

Interpretation Introduction

Interpretation:

The total number of atoms that is present in the mixture that contains four molecules of each component has to be given.

Concept Introduction:

The composition of a chemical compound can be presented in a very precise was with the use of chemical formula.  Chemical formula uses chemical symbols of the elements that is present in the compound and numerical subscripts that represent how many number of atoms of each element is present in the compound.

Answer to Problem 1.88EP

There are a total of 100 atoms present.

Explanation of Solution

Given molecules in mixture are ${\text{Cl}}_{\text{2}}\text{,}{\text{C}}_{\text{2}}{\text{H}}_{\text{6}}\text{,}{\text{H}}_{\text{2}}{\text{CO}}_{\text{3}}\text{,}{\text{H}}_{\text{2}}{\text{SO}}_{\text{4}}\text{,}\text{and}\text{HCl}$.

Number of atoms in $C{l}_2$:  As this molecule has a subscript “2”, the total number of atoms in $C{l}_2$ is two.

Number of atoms in $C_2{H}_6$:  The total number of atoms is present in molecule is by summing up the subscript.  Two carbon atoms and six hydrogen atoms are present in it.  The total number of atoms in $C_2{H}_6$ is 8 atoms.

Number of atoms in $H_{2}C{O}_3$:  The total number of atoms is present in molecule is by summing up the subscript.  Two hydrogen atoms, one carbon atom and three oxygen atoms are present in it.  The total number of atoms in $H_{2}C{O}_3$ is 6 atoms.

Number of atoms in $H_{2}S{O}_4$:  The total number of atoms is present in molecule is by summing up the subscript.  Two hydrogen atoms, one sulfur atom and four oxygen atoms are present in it.  The total number of atoms in $H_{2}S{O}_4$ is 7 atoms.

Number of atoms in $HCl$:  The total number of atoms is present in molecule is by summing up the subscript.  One hydrogen atom and one chlorine atom is present in it.  The total number of atoms in $HCl$ is 2 atoms.

The total number of atoms that is present in mixture which contains one molecule of each component can be found by summing up the number of atoms in all molecules.  This gives the total number of atoms as 25.

If the mixture contains four molecules of each component, then the total number of atoms can be found as shown below,

  $\begin{array}{l}Totalnumberofatoms=4*25\\ =100\end{array}$

Therefore, there are 100 atoms present in the mixture that contains four molecules of each component.

Interpretation Introduction

Interpretation:

The total number of carbon atoms that is present in the mixture that contains three molecules of each component has to be given.

Concept Introduction:

The composition of a chemical compound can be presented in a very precise was with the use of chemical formula.  Chemical formula uses chemical symbols of the elements that is present in the compound and numerical subscripts that represent how many number of atoms of each element is present in the compound.

Answer to Problem 1.88EP

There are a total of 9 carbon atoms present.

Explanation of Solution

Given molecules in mixture are ${\text{Cl}}_{\text{2}}\text{,}{\text{C}}_{\text{2}}{\text{H}}_{\text{6}}\text{,}{\text{H}}_{\text{2}}{\text{CO}}_{\text{3}}\text{,}{\text{H}}_{\text{2}}{\text{SO}}_{\text{4}}\text{,}\text{and}\text{HCl}$.

Number of atoms in $C{l}_2$:  As this molecule has a subscript “2”, the total number of atoms in $C{l}_2$ is two.

Number of atoms in $C_2{H}_6$:  The total number of atoms is present in molecule is by summing up the subscript.  Two carbon atoms and six hydrogen atoms are present in it.  The total number of atoms in $C_2{H}_6$ is 8 atoms.

Number of atoms in $H_{2}C{O}_3$:  The total number of atoms is present in molecule is by summing up the subscript.  Two hydrogen atoms, one carbon atom and three oxygen atoms are present in it.  The total number of atoms in $H_{2}C{O}_3$ is 6 atoms.

Number of atoms in $H_{2}S{O}_4$:  The total number of atoms is present in molecule is by summing up the subscript.  Two hydrogen atoms, one sulfur atom and four oxygen atoms are present in it.  The total number of atoms in $H_{2}S{O}_4$ is 7 atoms.

Number of atoms in $HCl$:  The total number of atoms is present in molecule is by summing up the subscript.  One hydrogen atom and one chlorine atom is present in it.  The total number of atoms in $HCl$ is 2 atoms.

The total number of carbon atoms that is present in mixture which contains one molecule of each component can be found by summing up the number of carbon atoms in all molecules.  This gives the total number of carbon atoms as 3.

If the mixture contains three molecules of each component, then the total number of carbon atoms can be found as shown below,

  $\begin{array}{l}Totalnumberofcarbonatoms=3*3\\ =9\end{array}$

Therefore, there are 9 carbon atoms present in the mixture that contains three molecules of each component.