The chemical reaction which makes water from hydrogen and oxygen is 2H + 0 --> H20:
Law of mass action says rate of chemical reaction is proportional to product of reactants", and so rate of creation of water, W(t) in terms of amount of oxygen x(t) and hydrogen h(t) (in moles) is directed by equation dW/dt = f(W) = k(x0 - W)(h0 - 2W)2;
where x0 = 45 moles is initial amount of oxygen, and h0 = 120 moles is initial amount of hydrogen.
i) Determine any equilibrium points of equation for W(t) and test their stability - the diagram of f(W) may prove useful here. Conclude what you believe final result of reaction will be. How much, if any, of two chemicals will remain, and how much water will be developed?
ii) Taking k = 2 x 10^(-4)s^(-1), write the Euler scheme (using t = 0.1 (say), to solve equation, and verify the conclusions in (a) by doing the simulation.