Chapter 3, Problem 3.24QP

Calculate the molar mass of the following substances: (a) Li₂CO₃, (b) CS₂, (c) CHCl₃ (chloroform), (d) C₆H₈O₆ (ascorbic acid, or vitamin C), (e) KNO₃, (f) Mg₃N₂.

Interpretation Introduction

Interpretation:

The molar masses of molecules are given by using chemical formula to be calculated.

Concept introduction:

Molar mass is also known as molecular weight, which is the sum of the total mass in grams of all the atoms that present in a particular molecule. If we know the formula of a compound then we can easily determine the compound’s molar mass. We know that a formula consists of atoms and it is important to count atoms carefully, especially in compounds with polyatomic ions enclosed in parentheses.

$\text{Molar mass = }\frac{\text{grams}}{\text{mole}}$

Answer to Problem 3.24QP

The molar mass of the given substances

${\text{LiCO}}_{\text{3 }}$= $66.9499\frac{\text{grams}}{\text{mole}}$

Explanation of Solution

The given molecular formulas are recorded as shown above.

Record the given data

1. (a) ${\text{LiCO}}_{\text{3 }}$
2. (b) ${\text{CS}}_{\text{2}}$
3. (c) ${\text{CHCl}}_{\text{3}}$
4. (d) ${\text{C}}_{\text{6}}{\text{H}}_{\text{8}}{\text{O}}_{\text{6}}$
5. (e) ${\text{KNO}}_{\text{3}}$
6. (f) ${\text{Mg}}_{\text{3}}{\text{N}}_{\text{2}}$

To determine the molar mass of ${\text{LiCO}}_{\text{3 }}$.

${\text{LiCO}}_{\text{3}}{\text{ = 1 mol Li + 1 mol CO}}_{\text{3}}$

$\begin{array}{l}\text{=}\left(\text{1×6}\text{.941}\frac{\text{grams of Li}}{\text{1 mole}}\right)+\left(1\times 12.0107\frac{\text{grams of C}}{\text{1 mole}}\right)+\left(3\times \text{15}\text{.9994}\frac{\text{grams of oxygen}}{\text{1 mole}}\right)\\ =\left(6.941\right)+\left(12.0107+47.9982\right)\\ =6.941+60.0089\\ =66.9499\frac{\text{grams}}{\text{mole}}\end{array}$

First we should calculate the mass of the lithium atom, which is 6.941grams per mole. Then, we calculate the same for the mass of carbon and oxygen, which are 12.0107941grams per mole and 15.9994 grams per mole respectively. Then, by doing simple mathematical calculation we get the total molar mass of ${\text{LiCO}}_{\text{3 }}$ which is 66.9499 grams per mole.

Interpretation Introduction

Interpretation:

The molar masses of molecules are given by using chemical formula to be calculated.

Concept introduction:

Molar mass is also known as molecular weight, which is the sum of the total mass in grams of all the atoms that present in a particular molecule. If we know the formula of a compound then we can easily determine the compound’s molar mass. We know that a formula consists of atoms and it is important to count atoms carefully, especially in compounds with polyatomic ions enclosed in parentheses.

$\text{Molar mass = }\frac{\text{grams}}{\text{mole}}$

Answer to Problem 3.24QP

The molar mass of the given substances

${\text{CS}}_{\text{2}}$= $76.1407\frac{\text{grams}}{\text{mole}}$

Explanation of Solution

To determine the molar mass of ${\text{CS}}_{\text{2}}$.

${\text{CS}}_{\text{2}}{\text{ = 1 mol C + 1 mol S}}_{\text{2}}$

$\begin{array}{l}\text{=}\left(1\times 12.0107\frac{\text{grams of C}}{\text{1 mole}}\right)+\left(2\times 32.065\frac{\text{grams of sulfur}}{\text{1 mole}}\right)\\ =12.0107+64.13\\ =76.1407\frac{\text{grams}}{\text{mole}}\end{array}$

First we should calculate the mass of the carbon, which is 12.0107 grams per mole and then do the same for sulfur which is 15.9994 grams per mole. Then, by doing simple mathematical calculation we get the total molar mass of ${\text{CS}}_{\text{2}}$ which is 76.1407 grams per mole.

Interpretation Introduction

Interpretation:

The molar masses of molecules are given by using chemical formula to be calculated.

Concept introduction:

Molar mass is also known as molecular weight, which is the sum of the total mass in grams of all the atoms that present in a particular molecule. If we know the formula of a compound then we can easily determine the compound’s molar mass. We know that a formula consists of atoms and it is important to count atoms carefully, especially in compounds with polyatomic ions enclosed in parentheses.

$\text{Molar mass = }\frac{\text{grams}}{\text{mole}}$

Answer to Problem 3.24QP

The molar mass of the given substances

${\text{CHCl}}_{\text{3}}$= $119.3776\frac{\text{grams}}{\text{mole}}$

Explanation of Solution

To determine the molar mass of ${\text{CHCl}}_{\text{3}}$.

${\text{CHCl}}_{\text{3}}\text{ = 1 mol C + 1 mol H+ 3 mol Cl}$

$\begin{array}{l}\text{=}\left(\text{1×}12.0107\frac{\text{grams of C}}{\text{1 mole}}\right)+\left(1\times \text{1}\text{.00794}\frac{\text{grams of H}}{\text{1 mole}}\right)+\left(3\times \text{35}\text{.453}\frac{\text{grams of Chlorine}}{\text{1 mole}}\right)\\ =12.0107+1.00794+106.359\\ =119.3776\frac{\text{grams}}{\text{mole}}\end{array}$

First we should calculate the mass of the carbon, which is 12.0107 grams per mole and then do the same for hydrogen and chlorine, which are 1.00794 and 35.453 grams per mole respectively. Then, by doing simple mathematical calculation we get the total molar mass of ${\text{CHCl}}_{\text{3}}$(chloroform) which is 119.3776 grams per mole.

Interpretation Introduction

Interpretation:

The molar masses of molecules are given by using chemical formula to be calculated.

Concept introduction:

Molar mass is also known as molecular weight, which is the sum of the total mass in grams of all the atoms that present in a particular molecule. If we know the formula of a compound then we can easily determine the compound’s molar mass. We know that a formula consists of atoms and it is important to count atoms carefully, especially in compounds with polyatomic ions enclosed in parentheses.

$\text{Molar mass = }\frac{\text{grams}}{\text{mole}}$

Answer to Problem 3.24QP

The molar mass of the given substances

1. (a) ${\text{C}}_{\text{6}}{\text{H}}_{\text{8}}{\text{O}}_{\text{6}}$= $176.1241\frac{\text{grams}}{\text{mole}}$

Explanation of Solution

To determine the molar mass of ${\text{C}}_{\text{6}}{\text{H}}_{\text{8}}{\text{O}}_{\text{6}}$.

${\text{C}}_{\text{6}}{\text{H}}_{\text{8}}{\text{O}}_{\text{6}}\text{ = 6 mol C + 8 mol H+ 6 mol O}$

$\begin{array}{l}\text{=}\left(\text{6×}12.0107\frac{\text{grams of C}}{\text{1 mole}}\right)+\left(8\times \text{1}\text{.00794}\frac{\text{grams of H}}{\text{1 mole}}\right)+\left(6\times 15.9994\frac{\text{grams of Oxygen}}{\text{1 mole}}\right)\\ =72.0642+8.0635+95.9964\\ =176.1241\frac{\text{grams}}{\text{mole}}\end{array}$

First we should calculate the mass of the carbon, which is 12.0107 grams per mole and then do the same for hydrogen and oxygen, which are 1.00794 and 15.9994 grams per mole respectively. Then, by doing simple mathematical calculation we get the total molar mass of ${\text{C}}_{\text{6}}{\text{H}}_{\text{8}}{\text{O}}_{\text{6}}$(ascorbic acid, or vitamin C) which is 176.1241 grams per mole.

Interpretation Introduction

Interpretation:

The molar masses of molecules are given by using chemical formula to be calculated.

Concept introduction:

Molar mass is also known as molecular weight, which is the sum of the total mass in grams of all the atoms that present in a particular molecule. If we know the formula of a compound then we can easily determine the compound’s molar mass. We know that a formula consists of atoms and it is important to count atoms carefully, especially in compounds with polyatomic ions enclosed in parentheses.

$\text{Molar mass = }\frac{\text{grams}}{\text{mole}}$

Answer to Problem 3.24QP

The molar mass of the given substances

${\text{KNO}}_{\text{3}}$= $101.1032\frac{\text{grams}}{\text{mole}}$

Explanation of Solution

To determine the molar mass of ${\text{KNO}}_{\text{3}}$.

${\text{KNO}}_{\text{3}}{\text{ = 1 mol K + 1 mol NO}}_{\text{3}}$$\begin{array}{l}\text{=}\left(\text{1×39}\text{.0983}\frac{\text{grams of K}}{\text{1 mole}}\right)+\left(1\times \text{14}\text{.0067}\frac{\text{grams of Nitrogen}}{\text{1 mole}}\right)+\left(3\times 15.9994\frac{\text{grams of Oxygen}}{\text{1 mole}}\right)\\ =39.0983+14.0067+47.9982\\ =101.1032\frac{\text{grams}}{\text{mole}}\end{array}$

First we should calculate the mass of the potassium, which is 39.0983 grams per mole and then do the same for nitrogen and oxygen, which are 14.0067 and 15.9994 grams per mole respectively. Then, by doing simple mathematical calculation we get the total molar mass of ${\text{KNO}}_{\text{3}}$ which is 101.1032 grams per mole.

Interpretation Introduction

Interpretation:

The molar masses of molecules are given by using chemical formula to be calculated.

Concept introduction:

Molar mass is also known as molecular weight, which is the sum of the total mass in grams of all the atoms that present in a particular molecule. If we know the formula of a compound then we can easily determine the compound’s molar mass. We know that a formula consists of atoms and it is important to count atoms carefully, especially in compounds with polyatomic ions enclosed in parentheses.

$\text{Molar mass = }\frac{\text{grams}}{\text{mole}}$

Answer to Problem 3.24QP

The molar mass of the given substances

${\text{Mg}}_{\text{3}}{\text{N}}_{\text{2}}$= $100.9284\frac{\text{grams}}{\text{mole}}$

Explanation of Solution

To determine the molar mass of ${\text{Mg}}_{\text{3}}{\text{N}}_{\text{2}}$.

${\text{Mg}}_{\text{3}}{\text{N}}_{\text{2}}{\text{ = 3 mol Mg + 1 mol N}}_{\text{2}}$

$\begin{array}{l}\text{=}\left(3\times \text{24}\text{.3050}\frac{\text{grams of Mg}}{\text{1 mole}}\right)+\left(2\times \text{14}\text{.0067}\frac{\text{grams of Nitrogen}}{\text{1 mole}}\right)\\ =72.915+28.0134\\ =100.9284\frac{\text{grams}}{\text{mole}}\end{array}$

First we should calculate the mass of the magnesium, which is 24.3050 grams per mole and then do the same for nitrogen which is 14.0067 grams per mole. Then, by doing simple mathematical calculation we get the total molar mass of ${\text{Mg}}_{\text{3}}{\text{N}}_{\text{2}}$ which is 100.9284 grams per mole.