Given the following general reaction:
A + 2B + 3C -> P + 4Q.
Show how the change in concentration of C with time is related to the change in concentration of A, B, P, and Q with time.
C changes three times as fast as A, 1.5 times as fast as B, and C also changes three times fast as P (but in the opposite direction).
Remember, these type kinetics problems are always based upon ‘pairs’ of substances. A quick setup is to equate the rates of the two substances of interest and switch the coefficients. One of the rates will be given. Solve for the unknown in terms of the given rate value. For this problem…
A + 2B + 3C => P + 4Q
1 (∆[C])/∆t=3 ([∆A])/([∆t])
2 (∆[C])/∆t=3 ([∆B])/([∆t])
1 (∆[C])/∆t=3 ([∆P])/([∆t])
4 (∆[C])/∆t=3 ([∆Q])/([∆t])
To determine how the change in concentration of C is related to the change in concentration of A, B, P, and Q with time, we need to analyze the stoichiometry of the reaction. The stoichiometry refers to the balanced coefficients of the reactants and products in the chemical equation.
In the given reaction: A + 2B + 3C -> P + 4Q
We can observe that for every 1 mol of A, 2 moles of B, and 3 moles of C, we produce 1 mol of P and 4 moles of Q. This information allows us to establish the relationship between the concentrations of these species.
Let's represent the change in concentration of a species, X, with time using the symbol [X]. Therefore, d[X]/dt denotes the rate of change in the concentration of X over time.
Based on the stoichiometry of the reaction, we can deduce the following relationships:
d[A]/dt = -1 * d[P]/dt (Since the coefficient of A in the balanced equation is -1 for P)
d[B]/dt = -2 * d[P]/dt (Since the coefficient of B in the balanced equation is -2 for P)
d[C]/dt = -3 * d[P]/dt (Since the coefficient of C in the balanced equation is -3 for P)
d[C]/dt = -3/4 * d[Q]/dt (Since the coefficient of C in the balanced equation is -3/4 for Q)
These equations relate the rates of change in the concentrations of A, B, C, P, and Q with respect to time. By knowing any one of them, we can calculate the rates of change of all the other species.