Chapter 2, Problem 2.38P

Identify the elements in each chemical formula and tell how many atoms of each are present.

1. $K_{2}C{r}_2{O}_7$

${\text{C}}_{\text{5}}{\text{H}}_{\text{8}}{\text{NNaO}}_{\text{4}}$ (MSG, flavor enhancer)

${\text{C}}_{\text{10}}{\text{H}}_{\text{16}}{\text{N}}_{\text{2}}{\text{O}}_{\text{3}}\text{S}$ (vitamin B₇)

Interpretation Introduction

(a)

Interpretation:

The elements and the number of atoms of each element present in ${\text{K}}_{\text{2}}{\text{Cr}}_{\text{2}}{\text{O}}_{\text{7}}$ should be determined.

Concept Introduction:

An element is defined as the substance that consists of same type of atom in which there are same number of protons. An element cannot be broken down into simpler substances.

An element is always represented by a single unit. For example, $\text{Na}$ , $\text{Al}$ , $\text{S}$ ,etc. are all elements.

When two or more atoms combine together then we will be able to know which atoms and how many atoms are combined together. And, this representation is known as chemical formula.

Answer to Problem 2.38P

Elements present in ${\text{K}}_{\text{2}}{\text{Cr}}_{\text{2}}{\text{O}}_{\text{7}}$ are potassium, chromium and oxygen. It contains $\text{12}\text{.046}\text{×}{\text{10}}^{\text{23}}\text{atoms}$ of potassium, $\text{12}\text{.046}\text{×}{\text{10}}^{\text{23}}\text{atoms}$ atoms of chromium and $42.161\text{×}{\text{10}}^{\text{23}}\text{atoms}$ of oxygen.

Explanation of Solution

The symbol $\text{K}$ represents element potassium, symbol $\text{Cr}$ represents element chromium and symbol $\text{O}$ represents element oxygen.

As chemical name of ${\text{K}}_{\text{2}}{\text{Cr}}_{\text{2}}{\text{O}}_{\text{7}}$ is potassium dichromate and number $2$ is written at the bottom left corner of $\text{K}$ . So, it means that two moles of $\text{K}$ are present in this chemical formula.

Similarly, $2$ is written at the bottom left corner of $\text{Cr}$ . So, it means that two moles of $\text{Cr}$ are present in this chemical formula. Whereas $7$ is written at the bottom left corner of $\text{O}$ , hence there are seven moles of oxygen are present in this chemical formula.

Hence, number of atoms of atoms in a molecule of ${\text{K}}_{\text{2}}{\text{Cr}}_{\text{2}}{\text{O}}_{\text{7}}$ are as follows.

  $\begin{array}{l}\text{Number of K atoms = 2}\text{×}\text{6}\text{.023}\text{×}{\text{10}}^{\text{23}}\text{atoms}\\ \text{=}\text{12}\text{.046}\times {10}^{23}\text{ atoms}\\ \text{Number of Cr atoms = 2}\text{×}\text{6}\text{.023}\text{×}{\text{10}}^{\text{23}}\text{atoms}\\ \text{=}\text{12}\text{.046}\times {10}^{23}\text{ atoms}\\ \text{Number of O atoms = 7}\times 6.023\times {10}^{23}\text{ atoms}\\ \text{= 42}\text{.161}\times {10}^{23}\text{ atoms}\end{array}$

Interpretation Introduction

(b)

Interpretation:

The elements and the number of atoms of each element present in ${\text{C}}_{\text{5}}{\text{H}}_{\text{8}}{\text{NNaO}}_{\text{4}}$ should be determined.

Concept Introduction:

An element is defined as the substance that consists of same type of atom in which there are same number of protons. An element cannot be broken down into simpler substances.

An element is always represented by a single unit. For example, $\text{Na}$ , $\text{Al}$ , $\text{S}$ , etc. are all elements.

When two or more atoms combine together then we will be able to know which atoms and how many atoms are combined together. And, this representation is known as chemical formula.

Answer to Problem 2.38P

Elements present in ${\text{C}}_{\text{5}}{\text{H}}_{\text{8}}{\text{NNaO}}_{\text{4}}$ are carbon, hydrogen, nitrogen, sodium, and oxygen. It contains $30.\text{115 }\times {10}^{23}\text{ atoms}$ of carbon, $48.\text{184}\times {10}^{23}\text{ atoms}$ of hydrogen, $\text{6}\text{.023}\times {10}^{23}\text{ atoms}$ of nitrogen, $\text{6}\text{.023}\times {10}^{23}\text{ atoms}$ of sodium and $\text{24}\text{.092}\times {10}^{23}\text{ atoms}$ of oxygen.

Explanation of Solution

The symbol $\text{C}$ represents element carbon, symbol $\text{H}$ represents element hydrogen, symbol $\text{N}$ represents element nitrogen, symbol $\text{Na}$ represents element sodium and symbol $\text{O}$ represents element oxygen.

The number at the bottom left of each element in a chemical formula represents the number of moles of that particular element. As ${\text{C}}_{\text{5}}{\text{H}}_{\text{8}}{\text{NNaO}}_{\text{4}}$ is known monosodium glutamate and number $5$ is written at the bottom left corner of $\text{C}$ . So, it means that fivemoles of $\text{C}$ are present in this chemical formula.

Similarly, $8$ is written at the bottom left corner of $\text{H}$ . So, it means that eightmoles of $\text{H}$ are present in this chemical formula. As there is no number written at the bottom left corner of $\text{N}$ so, it means that there is only one mole of $\text{N}$ . Similarly, there is one mole of $\text{Na}$ is present.

Whereas $4$ is written at the bottom left corner of $\text{O}$ , hence there are fourmoles of oxygen are present in this chemical formula.

Hence, number of atoms in a molecule of ${\text{C}}_{\text{5}}{\text{H}}_{\text{8}}{\text{NNaO}}_{\text{4}}$ are as follows.

  $\begin{array}{l}\text{Number of C atoms = 5}\text{×}\text{6}\text{.023}\text{×}{\text{10}}^{\text{23}}\text{atoms}\\ \text{=}30.\text{115 }\times {10}^{23}\text{ atoms}\\ \text{Number of H atoms = 8}\text{×}\text{6}\text{.023}\text{×}{\text{10}}^{\text{23}}\text{atoms}\\ \text{=}48.\text{184}\times {10}^{23}\text{ atoms}\\ \text{Number of N atoms = 1}\times 6.023\times {10}^{23}\text{ atoms}\\ \text{= 6}\text{.023}\times {10}^{23}\text{ atoms}\\ \text{Number of Na atoms = 1}\times 6.023\times {10}^{23}\text{ atoms}\\ \text{= 6}\text{.023}\times {10}^{23}\text{ atoms}\\ \text{Number of O atoms = 4}\times 6.023\times {10}^{23}\text{ atoms}\\ \text{= 24}\text{.092}\times {10}^{23}\text{ atoms}\end{array}$

Interpretation Introduction

(c)

Interpretation:

The elements and the number of atoms of each element present in ${\text{C}}_{\text{10}}{\text{H}}_{\text{16}}{\text{N}}_{\text{2}}{\text{O}}_{\text{3}}\text{S}$ should be determined.

Concept Introduction:

An element is defined as the substance that consists of same type of atom in which there are same number of protons. An element cannot be broken down into simpler substances.

An element is always represented by a single unit. For example, $\text{Na}$ , $\text{Al}$ , $\text{S}$ , etc. are all elements.

When two or more atoms combine together then we will be able to know which atoms and how many atoms are combined together. And, this representation is known as chemical formula.

Answer to Problem 2.38P

Elements in ${\text{C}}_{\text{10}}{\text{H}}_{\text{16}}{\text{N}}_{\text{2}}{\text{O}}_{\text{3}}\text{S}$ were carbon, hydrogen, nitrogen, oxygen, and sulfur. It contains $6.023\times {10}^{24}\text{ atoms}$ of carbon, $96.\text{368}\times {10}^{23}\text{ atoms}$ of hydrogen, $\text{12}\text{.046}\times {10}^{23}\text{ atoms}$ of nitrogen, $\text{18}\text{.069}\times {10}^{23}\text{ atoms}$ of oxygen and $\text{6}\text{.023}\times {10}^{23}\text{ atoms}$ of sulfur.

Explanation of Solution

The symbol $\text{C}$ represents element carbon, symbol $\text{H}$ represents element hydrogen, symbol $\text{N}$ represents element nitrogen, symbol $\text{S}$ represents element sulfur and symbol $\text{O}$ represents element oxygen.

The number at the bottom left of each element in a chemical formula represents the number of atoms of that particular element. As ${\text{C}}_{\text{10}}{\text{H}}_{\text{16}}{\text{N}}_{\text{2}}{\text{O}}_{\text{3}}\text{S}$ is known as Vitamin ${\text{B}}_{\text{7}}$ . The number $10$ is written at the bottom left corner of $\text{C}$ . So, it means that tenmoles of $\text{C}$ are present in this chemical formula.

Similarly, $16$ is written at the bottom left corner of $\text{H}$ . So, it means that sixteenmoles of $\text{H}$ are present in this chemical formula. As there is $2$ written at the bottom left corner of $\text{N}$ so, it means that there are two moles of $\text{N}$ . Whereas, $3$ is written at the bottom left corner of $\text{O}$ , hence there are threemoles of oxygen present in this chemical formula. As there is no number at the bottom left corner of sulfur. Hence, there is only one mole of $\text{S}$ present in this chemical formula.

The number of atoms in a molecule of ${\text{C}}_{\text{10}}{\text{H}}_{\text{16}}{\text{N}}_{\text{2}}{\text{O}}_{\text{3}}\text{S}$ are as follows:

  $\begin{array}{l}\text{Number of C atoms = 10×}\text{6}\text{.023}\text{×}{\text{10}}^{\text{23}}\text{atoms}\\ \text{=}6.023\times {10}^{24}\text{ atoms}\\ \text{Number of H atoms = 16}\text{×}\text{6}\text{.023}\text{×}{\text{10}}^{\text{23}}\text{atoms}\\ \text{=}96.\text{368}\times {10}^{23}\text{ atoms}\\ \text{Number of N atoms = 2}\times 6.023\times {10}^{23}\text{ atoms}\\ \text{= 12}\text{.046}\times {10}^{23}\text{ atoms}\\ \text{Number of O atoms = 3}\times 6.023\times {10}^{23}\text{ atoms}\\ \text{= 18}\text{.069}\times {10}^{23}\text{ atoms}\\ \text{Number of S atoms = 1}\times 6.023\times {10}^{23}\text{ atoms}\\ \text{= 6}\text{.023}\times {10}^{23}\text{ atoms}\end{array}$