Chapter 2, Problem 2.102P

(a)

Interpretation Introduction

Interpretation:

The formula and molecular mass of ammonium sulfate 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 2.102P

The molecular formula for ammonium sulfate is ${\left({\text{NH}}_4\right)}_2{\text{SO}}_4$. Its molecular mass is $132.14\text{ amu}$.

Explanation of Solution

Ammonium and sulfate are polyatomic ions. The formula for the sulfate ion is ${\text{SO}}_4{}^{2-}$. The sulfate ion carries a charge of $-2$. The charge on an ammonium ion is ${\text{NH}}_4{}^{+}$. To balance the $-2$ charge on the sulfate ion, the sulfate ion combines with two ammonium ions, each carrying a charge of $+1$.

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 ammonium sulfate, two ammonium polyatomic ions associate with one sulfate polyatomic ion. Hence the molecular formula becomes ${\left({\text{NH}}_4\right)}_2{\text{SO}}_4$.

The formula to calculate the molecular mass of ${\left({\text{NH}}_4\right)}_2{\text{SO}}_4$ (ammonium sulfate) is,

$\text{Molecular mass}=\left[\begin{array}{l}\left(2\right)\left(\text{atomic mass of nitrogen}\right)+\\ \left(8\right)\left(\text{atomic mass of hydrogen}\right)+\\ \left(1\right)\left(\text{atomic mass of sulphur}\right)+\\ \left(4\right)\left(\text{atomic mass of oxygen}\right)\end{array}\right]$ (2)

Substitute $14.01\text{ amu}$ for the atomic mass of nitrogen, $1.008\text{ amu}$ for the atomic mass of hydrogen, $32.06\text{ amu}$ for the atomic mass of sulfur and $16\text{ amu}$ for the atomic mass of oxygen in equation (2).

$\begin{array}{c}\text{Molecular mass}=\left[\left(2\right)\left(14.01\text{ amu}\right)+\left(8\right)\left(1.008\text{ amu}\right)+\left(1\right)\left(32.06\text{ amu}\right)+\left(4\right)\left(16\text{ amu}\right)\right]\\ =28.02\text{ amu}+8.064\text{ amu}+32.06\text{ amu}+64\text{ amu}\\ =132.14\text{ amu}\end{array}$

Conclusion

The molecular formula for ammonium sulfate is ${\left({\text{NH}}_4\right)}_2{\text{SO}}_4$. Its molecular mass is $132.14\text{ amu}$.

(b)

Interpretation Introduction

Interpretation:

The formula and molecular mass of sodium dihydrogen phosphate 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 2.102P

The molecular formula for sodium dihydrogen phosphate is ${\text{NaH}}_2{\text{PO}}_4$. Its molecular mass is $119.98\text{ amu}$.

Explanation of Solution

Phosphate is a polyatomic ion. The formula for the phosphate ion is ${\text{PO}}_4{}^{3-}$. The phosphate ion carries a charge of $-3$. When a ${\text{H}}^{+}$ ion adds to the phosphate ion, it loses a negative charge and the residue charge on the resultant polyatomic ion ${\text{HPO}}_4{}^{2-}$(hydrogen phosphate) is $-2$. The addition of another ${\text{H}}^{+}$ ion to the hydrogen phosphate creates the polyatomic ion dihydrogen phosphate ${\text{H}}_2{\text{PO}}_4{}^{-}$ with a $-1$ charge on it as follows:

$2{\text{H}}^{+}+{\text{PO}}_4{}^{3-}\to {\text{H}}_2{\text{PO}}_4{}^{-}$

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 $-1$ charge on the dihydrogen phosphate ion, the ion combines with one sodium ion carrying $+1$ charge.

Hence the molecular formula for sodium dihydrogen phosphate becomes ${\text{NaH}}_2{\text{PO}}_4$.

The formula to calculate the molecular mass of ${\text{NaH}}_2{\text{PO}}_4$ (sodium dihydrogen phosphate) is,

$\text{Molecular mass}=\left[\begin{array}{l}\left(1\right)\left(\text{atomic mass of sodium}\right)+\\ \left(2\right)\left(\text{atomic mass of hydrogen}\right)+\\ \left(1\right)\left(\text{atomic mass of phosphorus}\right)+\\ \left(4\right)\left(\text{atomic mass of oxygen}\right)\end{array}\right]$ (3)

Substitute $22.99\text{ amu}$ for the atomic mass of sodium, $1.008\text{ amu}$ for the atomic mass of hydrogen, $30.97\text{ amu}$ for the atomic mass of phosphorus and $16\text{ amu}$ for the atomic mass of oxygen in equation (3).

$\begin{array}{c}\text{Molecular mass}=\left[\left(1\right)\left(22.99\text{ amu}\right)+\left(2\right)\left(1.008\text{ amu}\right)+\left(1\right)\left(30.97\text{ amu}\right)+\left(4\right)\left(16\text{ amu}\right)\right]\\ =22.99\text{ amu}+2.016\text{ amu}+30.97\text{ amu}+64\text{ amu}\\ =119.98\text{ amu}\end{array}$

Conclusion

The molecular formula for sodium dihydrogen phosphate is ${\text{NaH}}_2{\text{PO}}_4$. Its molecular mass is $119.98\text{ amu}$.

(c)

Interpretation Introduction

Interpretation:

The formula and molecular mass of potassium bicarbonate 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 2.102P

The molecular formula for potassium bicarbonate is ${\text{KHCO}}_3$. Its molecular mass is $100.12\text{ amu}$.

Explanation of Solution

Carbonate is a polyatomic ion. The formula for the carbonate ion is ${\text{CO}}_3{}^{2-}$. The carbonate ion carries a charge of $-2$. When a ${\text{H}}^{+}$ ion adds to the carbonate ion, it loses a negative charge and the residue charge on the resultant polyatomic ion ${\text{HCO}}_3{}^{-}$(bicarbonate) is $-1$. The reaction is as follows:

${\text{H}}^{+}+{\text{CO}}_3{}^{2-}\to {\text{HCO}}_3{}^{-}$

Potassium belongs to the $1\text{A}\left(1\right)$ group in the periodic table and hence loses one electron to form ${\text{K}}^{+}$(potassium ion). To balance the $-1$ charge on the bicarbonate ion, the ion combines with one potassium ion carrying $+1$ charge.

Hence the molecular formula for potassium bicarbonate becomes ${\text{KHCO}}_3$.

The formula to calculate the molecular mass of ${\text{KHCO}}_3$ (potassium bicarbonate) is,

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

Substitute $39.10\text{ amu}$ for the atomic mass of potassium, $1.008\text{ amu}$ for the atomic mass of hydrogen, $12.01\text{ amu}$ for the atomic mass of carbon and $16\text{ amu}$ for the atomic mass of oxygen in equation (4).

$\begin{array}{c}\text{Molecular mass}=\left[\left(1\right)\left(39.10\text{ amu}\right)+\left(1\right)\left(1.008\text{ amu}\right)+\left(1\right)\left(12.01\text{ amu}\right)+\left(3\right)\left(16\text{ amu}\right)\right]\\ =39.10\text{ amu}+1.008\text{ amu}+12.01\text{ amu}+48\text{ amu}\\ =100.12\text{ amu}\end{array}$

Conclusion

The molecular formula for potassium bicarbonate is ${\text{KHCO}}_3$. Its molecular mass is $100.12\text{ amu}$.