Question

Using the given data, calculate the rate constant of this reaction.

Using the given data, calculate the rate constant of this reaction.

Answer 1

The reaction is A + B $\rightarrow$ C + D

Let the rate law be r = k [A] ^m [B] ⁿ    

From the table the rate law for the three readings will be as follows:

reading (1)    ------> 0.0153 = k (0.340 ) ^m (0.240)ⁿ                          ------------------------- (1)

reading (2)    ------> 0.0809 = k (0.340 ) ^m (0.552)ⁿ                          ------------------------- (2)

reading (3)    ------> 0.0245 = k (0.544 ) ^m (0.240)ⁿ                          ------------------------- (3)

Eqn (3) / Eqn (1) becomes $\frac{0.0245}{0.0153}=\frac{k(0.544)^{m}\left ( 0.240 \right )^{n}}{k(0.340)^{m}\left ( 0.240 \right )^{n}}$

                                    

                                               m = 1

Eqn (2) / Eqn (1) becomes $\frac{0.0809}{0.0153}=\frac{k(0.340)^{m}\left ( 0.552 \right )^{n}}{k(0.340)^{m}\left ( 0.240 \right )^{n}}$

                                    

                                                  n = 1

So rate law becomes r = k [A] ¹ [B] ¹    

                              r = k [A][B]  

Substitute the values of r, [A] & [B] from reading (1) we get

          0.0153 = k (0.340 )¹ (0.240)¹

          0.0153 = k (0.340 )(0.240)

                  k = 0.1875 M^-1 s^-1