Chapter 2, Problem 2.103P

(a)

Interpretation Introduction

Interpretation:

The formula and molecular mass of sodium dichromate are to be determined.

Concept introduction:

The molecular formula of a compound is a representation which suggests the total number of atoms of each element the compound is made of.

The molecular mass of a compound is defined as the sum of the atomic masses of all the atoms present in it.

The general formula to calculate the molecular mass of a compound is,

$\text{Molecular mass of the compound}=\left[\begin{array}{l}\Sigma \left(\text{number of atoms of the element}\right)\\ \left(\text{atomic mass of the element}\right)\end{array}\right]$ (1)

Answer to Problem 2.103P

The molecular formula for sodium dichromate is ${\text{Na}}_2{\text{Cr}}_2{\text{O}}_7$. Its molecular mass is $261.98\text{ amu}$.

Explanation of Solution

Dichromate is a polyatomic ion. The formula for the dichromate ion is ${\text{Cr}}_2{\text{O}}_7{}^{2-}$. The dichromate ion carries a charge of $-2$. Sodium belongs to the $1\text{A}\left(1\right)$ group in the periodic table and hence loses one electron to form ${\text{Na}}^{+}$(sodium ion). To balance the $-2$ charge on the dichromate ion, the ion combines with two sodium ions carrying $+1$ charge each.

Hence the molecular formula for sodium dichromate becomes ${\text{Na}}_2{\text{Cr}}_2{\text{O}}_7$.

The formula to calculate the molecular mass of ${\text{Na}}_2{\text{Cr}}_2{\text{O}}_7$ (sodium dichromate) is,

$\text{Molecular mass}=\left[\begin{array}{l}\left(2\right)\left(\text{atomic mass of sodium}\right)+\\ \left(2\right)\left(\text{atomic mass of chromium}\right)+\\ \left(7\right)\left(\text{atomic mass of oxygen}\right)\end{array}\right]$ (2)

Substitute $22.99\text{ amu}$ for the atomic mass of sodium, $52\text{ amu}$ for the atomic mass of chromium and $16\text{ amu}$ for the atomic mass of oxygen in equation (2).

$\begin{array}{c}\text{Molecular mass}=\left[\left(2\right)\left(22.99\text{ amu}\right)+\left(2\right)\left(52\text{ amu}\right)+\left(7\right)\left(16\text{ amu}\right)\right]\\ =45.98\text{ amu}+104\text{ amu}+112\text{ amu}\\ =261.98\text{ amu}\end{array}$

Conclusion

The molecular formula for sodium dichromate is ${\text{Na}}_2{\text{Cr}}_2{\text{O}}_7$. Its molecular mass is $261.98\text{ amu}$.

(b)

Interpretation Introduction

Interpretation:

The formula and molecular mass of ammonium perchlorate are to be determined

Concept introduction:

The molecular formula of a compound is a representation which suggests the total number of atoms of each element the compound is made of.

The molecular mass of a compound is defined as the sum of the atomic masses of all the atoms present in it.

The general formula to calculate the molecular mass of a compound is,

$\text{Molecular mass of the compound}=\left[\begin{array}{l}\Sigma \left(\text{number of atoms of the element}\right)\\ \left(\text{atomic mass of the element}\right)\end{array}\right]$ (1)

Answer to Problem 2.103P

The molecular formula for ammonium perchlorate is ${\text{NH}}_4{\text{ClO}}_4$. Its molecular mass is $117.49\text{ amu}$.

Explanation of Solution

Ammonium and perchlorate are polyatomic ions. The formula for the perchlorate ion is ${\text{ClO}}_4{}^{-}$. Ammonium ion is represented by the formula ${\text{NH}}_4{}^{+}$. Ammonium and perchlorate ions carry the charges $+1$ and $-1$ respectively. Hence they combine in the $1:1$ ratio to form a molecule of ammonium perchlorate.

Hence the molecular formula for ammonium perchlorate phosphate becomes ${\text{NH}}_4{\text{ClO}}_4$.

The formula to calculate the molecular mass of ${\text{NH}}_4{\text{ClO}}_4$ (ammonium perchlorate) is,

$\text{Molecular mass}=\left[\begin{array}{l}\left(1\right)\left(\text{atomic mass of nitrogen}\right)+\\ \left(4\right)\left(\text{atomic mass of hydrogen}\right)+\\ \left(1\right)\left(\text{atomic mass of chlorine}\right)+\\ \left(4\right)\left(\text{atomic mass of oxygen}\right)\end{array}\right]$ (3)

Substitute $14.01\text{ amu}$ for the atomic mass of nitrogen, $1.008\text{ amu}$ for the atomic mass of hydrogen, $35.45\text{ amu}$ for the atomic mass of chlorine and $16\text{ amu}$ for the atomic mass of oxygen in equation (3).

$\begin{array}{c}\text{Molecular mass}=\left[\left(1\right)\left(14.01\text{ amu}\right)+\left(4\right)\left(1.008\text{ amu}\right)+\left(1\right)\left(35.45\text{ amu}\right)+\left(4\right)\left(16\text{ amu}\right)\right]\\ =14.01\text{ amu}+4.032\text{ amu}+35.45\text{ amu}+64\text{ amu}\\ =117.49\text{ amu}\end{array}$

Conclusion

The molecular formula for ammonium perchlorate is ${\text{NH}}_4{\text{ClO}}_4$. Its molecular mass is $117.49\text{ amu}$.

(c)

Interpretation Introduction

Interpretation:

The formula and molecular mass of magnesium nitrite trihydrate are to be determined

Concept introduction:

The molecular formula of a compound is a representation which suggests the total number of atoms of each element the compound is made of.

The molecular mass of a compound is defined as the sum of the atomic masses of all the atoms present in it.

The general formula to calculate the molecular mass of a compound is,

$\text{Molecular mass of the compound}=\left[\begin{array}{l}\Sigma \left(\text{number of atoms of the element}\right)\\ \left(\text{atomic mass of the element}\right)\end{array}\right]$ (1)

Answer to Problem 2.103P

The molecular formula for magnesium nitrite trihydrate is $\text{Mg}{\left({\text{NO}}_2\right)}_2\cdot 3{\text{H}}_2\text{O}$. Its molecular mass is $170.38\text{ amu}$.

Explanation of Solution

Nitrite is a polyatomic ion. The formula for the carbonate ion is ${\text{NO}}_2{}^{-}$. The nitrite ion carries a charge of $-1$.

Magnesium belongs to the $2\text{A}\left(2\right)$ group in the periodic table and hence loses two electrons to form ${\text{Mg}}^{2+}$(magnesium ion). To balance the $+2$ charge on the magnesium ion, the ion combines with two nitrite ions carrying $-1$ charge on each.

While naming compounds containing polyatomic ions, when two or more of the same polyatomic ion are present, the ion appears in parentheses. The total number of the polyatomic ion is written as a subscript outside the parentheses.

In magnesium nitrite, two nitrite polyatomic ions associate with one magnesium ion. Hence the molecular formula becomes $\text{Mg}{\left({\text{NO}}_2\right)}_2$.

Magnesium nitrite trihydrate is the hydrated form of the ionic compound magnesium nitrite. Upon hydration, the molecule of magnesium nitrite bonds with three molecules of water to form a trihydrate molecule. In the molecular formula, the water molecules are shown after a centred dot. Hence the formula for magnesium nitrite trihydrate becomes $\text{Mg}{\left({\text{NO}}_2\right)}_2\cdot 3{\text{H}}_2\text{O}$.

The formula to calculate the molecular mass of $\text{Mg}{\left({\text{NO}}_2\right)}_2\cdot 3{\text{H}}_2\text{O}$ (magnesium nitrite trihydrate) is,

$\text{Molecular mass}=\left[\begin{array}{l}\left(1\right)\left(\text{atomic mass of magnesium}\right)+\\ \left(2\right)\left(\text{atomic mass of nitrogen}\right)+\\ \left(6\right)\left(\text{atomic mass of hydrogen}\right)+\\ \left(7\right)\left(\text{atomic mass of oxygen}\right)\end{array}\right]$ (4)

Substitute $24.31\text{ amu}$ for the atomic mass of magnesium, $1.008\text{ amu}$ for the atomic mass of hydrogen, $14.01\text{ amu}$ for the atomic mass of nitrogen and $16\text{ amu}$ for the atomic mass of oxygen in equation (4).

$\begin{array}{c}\text{Molecular mass}=\left[\left(1\right)\left(24.31\text{ amu}\right)+\left(2\right)\left(14.01\text{ amu}\right)+\left(6\right)\left(1.008\text{ amu}\right)+\left(7\right)\left(16\text{ amu}\right)\right]\\ =24.31\text{ amu}+28.02\text{ amu}+6.048\text{ amu}+112\text{ amu}\\ =170.38\text{ amu}\end{array}$

Conclusion

The molecular formula for magnesium nitrite trihydrate is $\text{Mg}{\left({\text{NO}}_2\right)}_2\cdot 3{\text{H}}_2\text{O}$. Its molecular mass is $170.38\text{ amu}$.