Chapter 2, Problem 2.66P

(a)

Interpretation Introduction

Interpretation:

Molecular mass of ${\text{NH}}_{\text{4}}{}^{\text{+}}$ has to be calculated to five significant figures.

Concept Introduction:

In a molecule or ion, the sum of atomic mass of all the atoms is known as molecular mass.  Atomic mass of an atom is the average of all the isotope of the particular element.  Molecular mass can be used to calculate the mass percentage of the atom present in the molecule.

Explanation of Solution

Given ion is ${\text{NH}}_{\text{4}}{}^{\text{+}}$.  This has one nitrogen atom, four hydrogen atoms and a positive charge.  Atomic mass of electron is $9.10\times {10}^{-31}\text{kg}$ which is very negligible.  Hence, this is not considered in calculation of molecular mass.

Atomic mass of $\text{H}$ is $\text{1}\text{.00794}\text{g/mol}$.  Atomic mass of nitrogen is $\text{14}\text{.0067}\text{g/mol}$.  Molecular mass of ${\text{NH}}_{\text{4}}{}^{\text{+}}$ is calculated as shown below.

    $\begin{array}{c}\text{Molecular}\text{mass}\text{of}{\text{NH}}_{\text{4}}{}^{\text{+}}=\text{atomic}\text{mass}\text{of}\text{N}+4(\text{atomic}\text{mass}\text{of}\text{H)}\\ =14.0067\text{g/mol + 4(1}\text{.00794}\text{g/mol)}\\ =14.0067\text{g/mol + 4}\text{.03176}\text{g/mol}\\ =\text{18}\text{.038}\text{g/mol}\end{array}$

Therefore, molecular mass of ${\text{NH}}_{\text{4}}{}^{\text{+}}$ is $\text{18}\text{.038}\text{g/mol}$.

(b)

Interpretation Introduction

Interpretation:

Molecular mass of ${\text{HO}}_{\text{2}}{}^{-}$ has to be calculated to five significant figures.

Concept Introduction:

Refer part (a).

Explanation of Solution

Given ion is ${\text{HO}}_{\text{2}}{}^{-}$.  This has one oxygen atom, two hydrogen atoms and a negative charge.  Atomic mass of electron is $9.10\times {10}^{-31}\text{kg}$ which is very negligible.  Hence, this is not considered in calculation of molecular mass.

Atomic mass of $\text{H}$ is $\text{1}\text{.00794}\text{g/mol}$.  Atomic mass of oxygen is $\text{15}\text{.9994}\text{g/mol}$.  Molecular mass of ${\text{HO}}_{\text{2}}{}^{-}$ is calculated as shown below.

    $\begin{array}{c}\text{Molecular}\text{mass}\text{of}{\text{HO}}_{\text{2}}{}^{-}=\text{atomic}\text{mass}\text{of}\text{H}+2(\text{atomic}\text{mass}\text{of}\text{O)}\\ =1.00794\text{g/mol + 2(15}\text{.9994}\text{g/mol)}\\ =1.00794\text{g/mol + 31}\text{.9988}\text{g/mol}\\ =\text{33}\text{.007}\text{g/mol}\end{array}$

Therefore, molecular mass of ${\text{HO}}_{\text{2}}{}^{-}$ is $\text{33}\text{.007}\text{g/mol}$.

(c)

Interpretation Introduction

Interpretation:

Molecular mass of ${\text{AgCl}}_{\text{2}}{}^{-}$ has to be calculated to five significant figures.

Concept Introduction:

Refer part (a).

Explanation of Solution

Given ion is ${\text{AgCl}}_{\text{2}}{}^{-}$.  This has one silver atom, two chlorine atoms and one negative charge.  Atomic mass of electron is $9.10\times {10}^{-31}\text{kg}$ which is very negligible.  Hence, this is not considered in calculation of molecular mass.

Atomic mass of $\text{Ag}$ is $\text{107}\text{.8682}\text{g/mol}$.  Atomic mass of chlorine is $\text{35}\text{.453}\text{g/mol}$.  Molecular mass of ${\text{AgCl}}_{\text{2}}{}^{-}$ is calculated as shown below.

    $\begin{array}{c}\text{Molecular}\text{mass}\text{of}{\text{AgCl}}_{\text{2}}{}^{-}=\text{atomic}\text{mass}\text{of}\text{Ag}+2(\text{atomic}\text{mass}\text{of}\text{Cl)}\\ =107.8682\text{g/mol + 2(35}\text{.453}\text{g/mol)}\\ =107.8682\text{g/mol + 70}\text{.906}\text{g/mol}\\ =\text{178}\text{.77}\text{g/mol}\end{array}$

Therefore, molecular mass of ${\text{AgCl}}_{\text{2}}{}^{-}$ is $\text{178}\text{.77}\text{g/mol}$.

(d)

Interpretation Introduction

Interpretation:

Molecular mass of ${\text{PCl}}_{\text{6}}{}^{-}$ has to be calculated to five significant figures.

Concept Introduction:

Refer part (a).

Explanation of Solution

Given ion is ${\text{PCl}}_{\text{6}}{}^{-}$.  This has one phosphorus atom, six chlorine atoms and a negative charge.  Atomic mass of electron is $9.10\times {10}^{-31}\text{kg}$ which is very negligible.  Hence, this is not considered in calculation of molecular mass.

Atomic mass of $\text{P}$ is $\text{30}\text{.973761}\text{g/mol}$.  Atomic mass of chlorine is $\text{35}\text{.453}\text{g/mol}$.  Molecular mass of ${\text{PCl}}_{\text{6}}{}^{-}$ is calculated as shown below.

    $\begin{array}{c}\text{Molecular}\text{mass}\text{of}{\text{PCl}}_{\text{6}}{}^{-}=\text{atomic}\text{mass}\text{of}\text{P}+6(\text{atomic}\text{mass}\text{of}\text{Cl)}\\ =30.973761\text{g/mol + 6(35}\text{.453}\text{g/mol)}\\ =30.973761\text{g/mol + 212}\text{.718}\text{g/mol}\\ =\text{243}\text{.69}\text{g/mol}\end{array}$

Therefore, molecular mass of ${\text{PCl}}_{\text{6}}{}^{-}$ is $\text{243}\text{.69}\text{g/mol}$.