Calculate the concentration

Question

At a certain temperature this reaction follows second-order kinetics with a rate constant of 8.45 M^-1•s^-1:

2H₃PO₄(aq) -> P₂O₅ (aq) + 3H₂O (aq)

Suppose a vessel contains H₃PO₄ at a concentration of 1.48M. Calculate the concentration of H₃PO₄ in the vessel 0.320 seconds later. You may assume no other reaction is important.

Round your answer to 2 significant digits

Answer 1

A second-order irreversible reaction is described by the following rate equation

-r_A = kC_A² where -r_A is the rate of disappearance of A, k is the reaction rate constant, and C_A is the concentration of A.

-r_A = -dC_A/dt where -dC_A is the decrease in concentration of A and dt is the change in time.

Integrating this equations gives us the following relationship:

1/C_A - 1/C_A0 = kt where C_A is the concentration at time, t, and C_A0 is the initial concentration of A.

Given in our problem:

k = 8.45 M^-1s^-1

C_A0 = 1.48 M

t = 0.320 seconds

We are solving for C_A (the concentration at the specified time).

1/C_A - (1/1.48 M) = (8.45 M^-1s^-1)(0.32 s)

1/C_A - 0.676 M^-1 = 2.704 M^-1

1/C_A = 3.38 M^-1

C_A = 0.296 M