Chapter 4, Problem 1ASA

To find the mass of a mole of an element, one looks up the atomic mass of the element in a table of atomic masses (see Appendix III or the Periodic Table). The molar mass of an element is simply the mass in grams of that element that is numerically equal to its atomic mass. For a compound substance, the molar mass is equal to the mass in grams that is numerically equal to the sum of the atomic masses in the formula of the substance. Find the molar mass of

$\text{Cu}\underset{\_}{}\text{g}/\text{mol}$ $\text{Cl}\underset{\_}{}\text{g}/\text{mol}$ $\text{H}\underset{\_}{}\text{g}/\text{mol}$

$\text{O}\underset{\_}{}\text{g}/\text{mol}$ ${\text{H}}_2\text{O}\underset{\_}{}\text{g}/\text{mol}$

Interpretation Introduction

Interpretation:

The molar masses of $\text{Cu}$, $\text{Cl}$, $\text{H}$, $\text{O}$, and ${\text{H}}_2\text{O}$ are to be stated.

Concept introduction:

The molar mass of a substance is equal to the mass of one mole of that substance. One mole of a substance contains $6.02\times {10}^{23}$ particles. The substance can be an atom, molecule or ion. The magnitude of molar mass is the same as the magnitude of atomic mass, molecular mass, and formula mass. The only difference between the molar mass and three other masses is that the molar mass is represented with a gram per mole unit.

Answer to Problem 1ASA

The molar masses of $\text{Cu}$, $\text{Cl}$, $\text{H}$, $\text{O}$, and ${\text{H}}_2\text{O}$ are $63.55\text{g}/\text{mol}$, $35.45\text{g}/\text{mol}$, $1.008\text{g}/\text{mol}$, $16.00\text{g}/\text{mol}$, and $18.016\text{g}/\text{mol}$ respectively.

Explanation of Solution

The molar mass of a substance has the same numerical value as its atomic or molecular but different unit. The molar mass is expressed in $\text{g}/\text{mol}$.

The atomic mass of copper $\left(\text{Cu}\right)$ is $63.55\text{amu}$. Therefore, the molar mass of copper is $63.55\text{g}/\text{mol}$.

The atomic mass of chlorine $\left(\text{Cl}\right)$ is $35.45\text{amu}$. Therefore, the molar mass of chlorine is $35.45\text{g}/\text{mol}$.

The atomic mass of hydrogen $\left(\text{H}\right)$ is $1.008\text{amu}$. Therefore, the molar mass of hydrogen is $1.008\text{g}/\text{mol}$.

The atomic mass of oxygen $\left(\text{O}\right)$ is $16.00\text{amu}$. Therefore, the molar mass of oxygen is $16.00\text{g}/\text{mol}$.

The molar mass of ${\text{H}}_2\text{O}$ is the sum of molar masses of each atom present in it. Therefore, the molar mass of ${\text{H}}_2\text{O}$ is calculated by the formula as shown below.

$\text{Molar}\text{mass}\text{of}{\text{H}}_{\text{2}}\text{O}=2\times \text{Molar}\text{mass}\text{of}\text{H}+\text{Molar}\text{mass}\text{of}\text{O}$

Substitute the values of molar masses of $\text{H}$ and $\text{O}$ in the above expression.

$\begin{array}{rll}\text{Molar}\text{mass}\text{of}{\text{H}}_{\text{2}}\text{O}& =& 2\times 1.008\text{g}/\text{mol}+16.00\text{g}/\text{mol}\\ & =& 2.016\text{g}/\text{mol}+16.00\text{g}/\text{mol}\\ & =& 18.016\text{g}/\text{mol}\end{array}$

Therefore, the molar mass of ${\text{H}}_2\text{O}$ is $18.016\text{g}/\text{mol}$.

Conclusion

The molar masses of $\text{Cu}$, $\text{Cl}$, $\text{H}$, $\text{O}$, and ${\text{H}}_2\text{O}$ are calculated as $63.55\text{g}/\text{mol}$, $35.45\text{g}/\text{mol}$, $1.008\text{g}/\text{mol}$, $16.00\text{g}/\text{mol}$, and $18.016\text{g}/\text{mol}$ respectively.