In a chemical reaction, one unit of compound Y and one unit of compound Z are converted into a single unit of compound X. Let x be the amount of compound X formed. The rate of formation of X is proportional to the product of the amounts of unconverted compounds Y and Z. So, dx/dt = k(y₀ - x)(z₀ - x), where y₀ and z₀ are the initial amounts of compounds Y and Z. From this equation, you obtain

(a) Solve for x as a function of t.(b) Use the result of part (a) to find x as t ∞ for(1) y₀0, 

(2) y₀ > z₀,

(3) y₀ = z₀.

Transcribed Image Text:

1 (yo - x)(zo - x) Yo dx = fk dt.