IChO 2003 · Theory problem 8

A dimethylhydrazine and dinitrogen tetroxide propellant

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A fuel/oxidant system consisting of N,N-dimethylhydrazine \(\ce{(CH3)2NNH2}\) and \(\ce{N2O4}\) (both liquids) is commonly used in space vehicle propulsion. Components are mixed stoichiometrically so that \(\ce{N2}\), \(\ce{CO2}\) and \(\ce{H2O}\) are the only products (all gases under the same reaction conditions). How many moles of gases are produced from 1 mol of \(\ce{(CH3)2NNH2}\)?

(a) 8 ( )
(b) 9 ( )
(c) 10 ( )
(d) 11 ( )
(e) 12 ( )

Official English text of the problem.

Answers

  • 8. (b): \(\boxed{9\ \mathrm{mol}}\) of gases.

Solution

8. N,N-dimethylhydrazine (CN(C)N) has molecular formula \(\ce{C2H8N2}\). For \(1\ \mathrm{mol}\) of fuel:

  • Balancing carbon gives \(2\ \mathrm{mol}\) of carbon dioxide, \(\ce{CO2}\) (O=C=O).
  • Balancing hydrogen gives \(4\ \mathrm{mol}\) of water, \(\ce{H2O}\) (O).
  • These products require \(2(2)+4=8\ \mathrm{mol}\) of oxygen atoms, supplied by \(2\ \mathrm{mol}\) of dinitrogen tetroxide, \(\ce{N2O4}\) ([O-][N+](=O)[N+](=O)[O-]).
  • The reactants therefore contain \(2+2(2)=6\ \mathrm{mol}\) of nitrogen atoms, producing \(3\ \mathrm{mol}\) of dinitrogen, \(\ce{N2}\) (N#N).

The balanced reaction is

\[ \ce{(CH3)2NNH2(l) + 2N2O4(l) -> 3N2(g) + 2CO2(g) + 4H2O(g)}. \]

All three products are gases under the stated conditions, so

\[ n_{\text{gas}}=(3+2+4)\ \mathrm{mol} =\boxed{9\ \mathrm{mol}}. \]

Thus, select (b).

The answers were checked against the official answers published by the organisers.