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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: madoscar65 on January 03, 2011, 12:25:03 pm

Title: Application of differential equation help!!
Post by: madoscar65 on January 03, 2011, 12:25:03 pm: Hi peoples,
I need a little help with an extended response questions...
Two chemicals, A and B, are put together in a solution where they react form a compound, X. The rate of increase of the mass, x kg, of X is proportional to the proudct of the masses of unreacted A and B present at time t minutes. it takes 1 kg of A and 3 kg of B to form 4kg of X. Initially 2 kg of A and 3kg of B are put together in solution. One kg of X forms in one minute.

a. Set up the appropriate differential equation expressing dx/dt as a function of x.

So firstly, I know dx/dt = kAB, and I need to find A and B in terms of x.. " It takes 1 Kg of A and 3Kg of B to form 4kg of X" I can't seem to intepret this information into mathsmatical equation.. So hope you guys can help me out :)

Thanks in advance!!
Title: Re: Application of differential equation help!!
Post by: kamil9876 on January 03, 2011, 01:44:57 pm: Suppose that x kg of X are produced. That means that:

(1) $x/4$ kg of A must've been consumed, so we have $a=(2-\frac{x}{4})$

(2) $3x/4$ kg of B must've been consumed, so we have $b=(3- \frac{3x}{4})$

Now sub back in.
Title: Re: Application of differential equation help!!
Post by: madoscar65 on January 03, 2011, 02:20:41 pm: Thanks :) +1 Karma