Question

Consider the general reaction : aA + bB --> cC and the following average rate date over some time period delta t: - delta A / delta t = 0.0080 M/sec - delta B / delta t = 0.0120 M/sec - delta C / delta t = 0.0160 M/secDetermine a set of possible coefficients to balance this equation.

Answer 1

Answer:

See explanation below.

Explanation:

For a general reaction, we have that the rates of appearance of products and disappearance of reactants is given by the general relationship:

aA + bB ⇒ cC + dD

- (1/a) ΔA/Δt = -(1/b) ΔB/Δt = +(1/c) ΔC/Δt = +(1/d) ΔD/Δt

For our question we can write :

- (1/a) ΔA/Δt  = - (1/b) ΔB/Δt = + (1/c) ΔC/Δt

- (1/a) 0.0080 = - (1/b) 0.0120 = + (1/c) 0.0160

We can form the following equations:

(1/a)0.080 = (1/b)0.0120  ⇒     b/a = 0.0120/0.0080 = 1.5

(1/a)0.080 = (1/c)0.0160  ⇒     c/a = 0.0160/0.0080 = 2.0

(1/b)0.0120 = (1/c)0.0160 ⇒    c/b = 0.0160/0.0120 = 1.33

Given this result, we can form the following two sets of values as an example:

For a = 1, b= 1.5 = 1/2, c= 2.0

For a= 2, b= 3, and c= 4

Working with fractional coefficients, although not typical is allowed,  so one can form an infinity set of coefficients  with fractions and integers, even though fractional coeffients are not custumarily used.