Chapter 8, Problem 14PS

To determine

Find the atomic mass of the given elements.

Answer to Problem 14PS

The atomic mass of the sulfur (S) $=32$

The atomic mass of the nitrogen (N) $=14$

The atomic mass of the fluorine (F) $=19$

Explanation of Solution

Given:

The given elements are sulfur (S), nitrogen (N), and fluorine (F).

The atomic masses of the three compounds are given below.

  

Calculation:

From the table

  $\begin{array}{l}4S+4N=184\\ S+6F=146\\ 2N+4F=104\end{array}$

The determinants are

  $\begin{array}{l}D=\left[\begin{array}{ccc}4& 4& 0\\ 1& 0& 6\\ 0& 2& 4\end{array}\right]\\ =4\left(0\cdot 4-2\cdot 6\right)-4\left(1\cdot 4-0\cdot 6\right)+0\left(1\cdot 2-0\cdot 0\right)\\ =-64\\ D_S=\left[\begin{array}{ccc}184& 4& 0\\ 146& 0& 6\\ 104& 2& 4\end{array}\right]\\ =184\left(0\cdot 4-2\cdot 6\right)-4\left(146\cdot 4-104\cdot 6\right)+0\left(146\cdot 2-104\cdot 0\right)\\ =-2048\\ D_N=\left[\begin{array}{ccc}4& 184& 0\\ 1& 146& 6\\ 0& 104& 4\end{array}\right]\\ =4\left(146\cdot 4-104\cdot 6\right)-184\left(1\cdot 4-0\cdot 6\right)+0\left(1\cdot 104-0\cdot 146\right)\\ =-896\\ D_F=\left[\begin{array}{ccc}4& 4& 184\\ 1& 0& 146\\ 0& 2& 104\end{array}\right]\\ =4\left(0\cdot 104-2\cdot 146\right)-4\left(1\cdot 104-0\cdot 146\right)+184\left(1\cdot 2-0\cdot 0\right)\\ =-1216\end{array}$

Atomic mass of the sulfur (S) $=\frac{D_S}{D}=\frac{-2048}{-64}=32$

Atomic mass of the nitrogen (N) $=\frac{D_N}{D}=\frac{-896}{-64}=14$

Atomic mass of the fluorine (F) $=\frac{D_F}{D}=\frac{-1216}{-64}=19$