Mixtures type word problem

• November 3rd 2010, 05:20 PM
jegues
Mixtures type word problem
50 g of a certain chemical is added to 200mL of water; the chemical dissolves in water at a rate proportional to the product of the amount of undissolved chemical and the difference between concentrations in a saturated solution and the existing concentration in the solution. A saturated solution contains 25g of chemical in 100mL of solution.

(a) Show that the differential equation that describes the situation is,

$\frac{dx}{dt} = \frac{k}{200}(50-x)^{2}, x(0) = 0$

where x(t) is the number of grams of dissolved chemical at time t.

These word problems always cause me trouble. The question seems so complicated I don't even know what to start with.

Can someone help me get started?
• November 3rd 2010, 05:41 PM
skeeter
breaking down and translating the problem statement (hope you're not color blind) ...

Quote:

the chemical dissolves in water at a rate proportional to the product of the amount of undissolved chemical and the difference between concentrations in a saturated solution and the existing concentration in the solution.
dx/dt = k(50-x)(25/100 - x/200)

if you put that together and you'll get the desired DE