Chapter 7, Problem 8PS

To determine

Find the weights of a carbon atom and hydrogen atom

Answer to Problem 8PS

The weights of hydrogen atom and carbon atom are

$H=1.008\text{u},C=12.011\text{u}$

Explanation of Solution

Given:

  $\begin{array}{l}\text{Weight}\text{of}{C}_2{H}_6\text{molecule}=30.07\text{u}\\ \text{Weight}\text{of}{C}_3{H}_8\text{molecule}=44.097\text{u}\end{array}$

Suppose $C$ represents the weight of a carbon atom and $H$ , the weight of a hydrogen atom

Since a molecule of $C_2{H}_6$ is made up of $2$ carbon atoms and six hydrogen atoms and weighs $30.07\text{u}$ , therefore

  $2C+6H=\mathrm{30.07...........}(1)$

Since a molecule of $C_3{H}_8$ is made up of $3$ carbon atoms and eight hydrogen atoms and weighs $44.097\text{u}$ , therefore

  $3C+8H=\mathrm{44.097..........}(2)$

To solve, first multiply equation $(1)$ by 3 and equation $(2)$ by 2

The resulting equations are

  $\begin{array}{l}6C+18H=\mathrm{90.21............}(3)\hfill \\ 6C+16H=\mathrm{88.194...........}(4)\hfill \end{array}$

Subtracting the equation $(4)$ from $(3)$ to get

  $\begin{array}{l}6C+18H-(6C+16H)=90.21-88.194\\ 6C+18H-6C-16H=2.016\\ 2H=2.016\\ H=1.008\end{array}$

Put this value of $H$ in $(1)$ to get

  $\begin{array}{l}2C=30.07-6H\\ =30.07-6\times 1.008\\ =24.022\end{array}$

Then

  $\begin{array}{cc}C& =\frac{24.022}{2}\\ & =12.011\end{array}$

Thus, the weights of a carbon atom and a hydrogen atom are

$H=1.008\text{u},C=12.011\text{u}$