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Chapter 22: Problem 103

Both dimethylhydrazine, \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{NNH}_{2},\) and methylhydrazine, \(\mathrm{CH}_{3} \mathrm{NHN} \mathrm{H}_{2},\) have been used as rocket fuels. When dinitrogen tetroxide \(\left(\mathrm{N}_{2} \mathrm{O}_{4}\right)\) is used as the oxidizer, the products are \(\mathrm{H}_{2} \mathrm{O}, \mathrm{CO}_{2},\) and \(\mathrm{N}_{2} .\) If the thrust of the rocket depends on the volume of the products produced, which of the substituted hydrazines produces a greater thrust per gram total mass of oxidizer plus fuel? (Assume that both fuels generate the same temperature and that \(\mathrm{H}_{2} \mathrm{O}(g)\) is formed.)

Short Answer

Expert verified
Dimethylhydrazine generates a greater thrust per gram total mass of oxidizer plus fuel compared to methylhydrazine. This is because it produces a higher number of moles of gas products per gram of fuel and oxidizer, resulting in a greater thrust. Specifically, dimethylhydrazine produces \(0.0576\, \mathrm{moles/(g\, \mathrm{fuel} + g\, \mathrm{oxidizer})}\) while methylhydrazine produces \(0.0456\, \mathrm{moles/(g\, \mathrm{fuel} + g\, \mathrm{oxidizer})}\).

Step by step solution

01

Write the balanced chemical equations for both fuels

First, we will write the balanced chemical equations for the reactions of dimethylhydrazine and methylhydrazine with dinitrogen tetroxide. For dimethylhydrazine: \[\left(\mathrm{CH}_{3}\right)_{2} \mathrm{NNH}_{2} + 3\mathrm{N}_{2}\mathrm{O}_{4} \rightarrow 2\mathrm{CO}_{2} + 4\mathrm{H}_{2}\mathrm{O} + 6\mathrm{N}_{2} \] For methylhydrazine: \[\mathrm{CH}_{3} \mathrm{NHN} \mathrm{H}_{2} + 2\mathrm{N}_{2}\mathrm{O}_{4} \rightarrow \mathrm{CO}_{2} + 3\mathrm{H}_{2}\mathrm{O} + 4\mathrm{N}_{2} \]
02

Calculate the molar mass of each fuel and the oxidizer

In order to compare the thrust generated by each fuel, we need to find the molar mass of each fuel and the oxidizer. Dimethylhydrazine: \[\left(\mathrm{CH}_{3}\right)_{2} \mathrm{NNH}_{2}\]Molar mass = \(2\times(12.01 + 3\times1.01) + 14.01 + 2\times1.01 = 46.09\, g/mol\) Methylhydrazine: \[\mathrm{CH}_{3} \mathrm{NHN} \mathrm{H}_{2}\]Molar mass = \(12.01 + 3\times1.01 + 2\times(14.01) + 3\times1.01 = 60.10\, g/mol\) Dinitrogen tetroxide: \[\mathrm{N}_{2} \mathrm{O}_{4}\]Molar mass = \(2\times14.01 + 4\times16.00 = 92.02\, g/mol\)
03

Calculate the grams of oxidizer required for each fuel

To find out the grams of oxidizer required for each fuel, we need to use the balanced chemical equations obtained in step 1. For dimethylhydrazine, 3 moles of \(\mathrm{N}_{2}\mathrm{O}_{4}\) react with 1 mole of fuel: \[3\times92.02\, g\, \mathrm{N}_{2}\mathrm{O}_{4} / 46.09\, g\, \mathrm{fuel}\] For methylhydrazine, 2 moles of \(\mathrm{N}_{2}\mathrm{O}_{4}\) react with 1 mole of fuel: \[2\times92.02\, g\, \mathrm{N}_{2}\mathrm{O}_{4} / 60.10\, g\, \mathrm{fuel}\]
04

Calculate the moles of gas products produced per gram of fuel and oxidizer

We will use the stoichiometry of the balanced equations to calculate the moles of gas products produced per gram of fuel and oxidizer. For dimethylhydrazine: \[\frac{2\,\mathrm{moles}\, \mathrm{CO}_{2} + 4\,\mathrm{moles}\, \mathrm{H}_{2}\mathrm{O} + 6\, \mathrm{moles}\, \mathrm{N}_{2}}{46.09\, g\, \mathrm{fuel} + 3\times92.02\, g\, \mathrm{N}_{2}\mathrm{O}_{4}}\] For methylhydrazine: \[\frac{1\, \mathrm{moles}\, \mathrm{CO}_{2} + 3\,\mathrm{moles}\, \mathrm{H}_{2}\mathrm{O} + 4\, \mathrm{moles}\, \mathrm{N}_{2}}{60.10\, g\, \mathrm{fuel} + 2\times92.02\, g\, \mathrm{N}_{2}\mathrm{O}_{4}}\]
05

Determine which fuel generates a greater thrust

Now we will compare the moles of gas products produced per gram of fuel and oxidizer for the two fuels. The fuel with a greater number of moles of gas products per gram will produce a greater thrust. Dimethylhydrazine: \[\frac{2 + 4 + 6}{46.09 + 3\times92.02} = 0.0576\, \mathrm{moles/(g\, \mathrm{fuel} + g\, \mathrm{oxidizer})}\] Methylhydrazine: \[\frac{1 + 3 + 4}{60.10 + 2\times92.02} = 0.0456\, \mathrm{moles/(g\, \mathrm{fuel} + g\, \mathrm{oxidizer})}\] The results show that dimethylhydrazine produces a higher number of moles of gas products per gram of fuel and oxidizer and thus a greater thrust, compared to methylhydrazine.

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Write the chemical formula for each of the following com- pounds, and indicate the oxidation state of the group 6 \(\mathrm{A}\) element in each: (a) sulfur tetrachloride, (b) selenium trioxide, (c) sodium thiosulfate, (d) hydrogen sulfide, (e) sulfuric acid, ( ( ) sulfur dioxide, (g) mercury telluride.

Although the \(\mathrm{ClO}_{4}^{-}\) and \(\mathrm{IO}_{4}^{-}\) ions have been known for a long time, \(\mathrm{BrO}_{4}^{-}\) was not synthesized until \(1965 .\) The ion was synthesized by oxidizing the bromate ion with xenon difluoride, producing xenon, hydrofluoric acid, and the perbromate ion. (a) Write the balanced equation for this reaction. (b) What are the oxidation states of Br in the Br-containing species in this reaction?

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