Q157CP - Chemistry: Molecular Nature Of Matter And Change

Question

The rocket fuel hydrazine (N₂H₄) is made by the three-step Raschig process, which has the following overall equation: 

$\mathit{N}\mathit{a}\mathit{O}\mathit{C}\mathit{I}\mathbf{\left(}\mathit{a}\mathit{q}\mathbf{\right)}\mathbf{+}\mathbf{2}\mathit{N}{\mathit{H}}_{\mathbf{3}}\mathbf{\left(}\mathit{a}\mathit{q}\mathbf{\right)}\mathbf{\to }{\mathit{N}}_{\mathbf{2}}\mathit{H}\mathbf{4}\mathbf{\left(}\mathit{a}\mathit{q}\mathbf{\right)}\mathbf{+}\mathit{N}\mathit{a}\mathit{C}\mathit{I}\mathbf{\left(}\mathit{a}\mathit{q}\mathbf{\right)}\mathbf{+}{\mathit{H}}_{\mathbf{2}}\mathit{O}\mathbf{\left(}\mathit{I}\mathbf{\right)}$

What is the percent atom economy of this process?

Step-by-Step Solution

Answer

The percent atom economy for this process is 29.54%.

Step 1: Formula for percent atom economy

The formula for percent atom economy can be denoted as,

$\%atomeconomy=\frac{Number of moles\times molar mass of desiredproduct}{sum of number of moles of products\times molar mass for allproduct}\times 100$

Step 2: Finding the percent atom economy

The values can be substituted as,

$$\begin{gathered} \%atomeconomy=\frac{{\left(1mol\times {\displaystyle \frac{32.05g}{1mol}}\right)}_{N_2{H}_4}}{{\left(1mol\times {\displaystyle \frac{32.05g}{1mol}}\right)}_{N_2{H}_4}{\left(1mol\times {\displaystyle \frac{58.44g}{1mol}}\right)}_{NaCI}+{\left(1mol\times {\displaystyle \frac{18.02g}{1mol}}\right)}_{H_{2}O}}\times 100 \\ \%atomeconomy=29.54\% \end{gathered}$$