Question

6. Consider the hypothetical reaction : A + B -> C
This rapid reaction gives the following data:
Experiment [A-] (M) [B-](M) Initial Rate (M/s)
1 0.1 0.50 0.053
2 0.2 0.30 0.127
3 0.4 0.60 1.02
4 0.2 0.60 0.254
5 0.4 0.30 0.509

(i) Write the rate law for this reaction.
(ii) Calculate the average rate constant with proper units.
(iii) Calculate to the rate when [A] = 0.30M and [B] = 0.40M

Answer 1

Answer on the Question #57954

6. Consider the hypothetical reaction: A + B -> C

This rapid reaction gives the following data:

Experiment [A-] (M) [B-] (M) Initial Rate (M/s)

1 0.1 0.50 0.053

2 0.2 0.30 0.127

3 0.4 0.60 1.02

4 0.2 0.60 0.254

5 0.4 0.30 0.509

(i) Write the rate law for this reaction.

(ii) Calculate the average rate constant with proper units.

(iii) Calculate to the rate when [A] = 0.30M and [B] = 0.40M

(i)+(ii)

$$r = k [ A ] ^ {x} [ B ] ^ {y}$$

Trial 2: $r_2 = k[0.2]^x [0.3]^y = 0.127$

Trial 4: $r_4 = k[0.2]^x [0.6]^y = 0.254$

Divide $r_4$ by $r_2$ :

$$2 = 2 ^ {y};$$ $$y = 1.$$

Trial 3: $r_3 = k[0.4]^x [0.6]^y = 1.02$

Trial 4: $r_4 = k[0.2]^x [0.6]^y = 0.254$

Divide $r_4$ by $r_3$ (gives approximately 4):

$$4 = 2 ^ {x};$$ $$x = 2.$$

Therefore:

$$r = k [ A ] ^ {2} [ B ]$$

Calculate the constant from each trial:

$$k = \frac {r}{[ A ] ^ {2} [ B ]} [ M ] ^ {- 2} s ^ {- 1}$$ $$k _ {1} = \frac {0 . 0 5 3 \frac {M}{s}}{[ 0 . 1 M ] ^ {2} [ 0 . 5 M ]} = 1 0. 6 0 0 [ M ] ^ {- 2} s ^ {- 1};$$ $$k _ {2} = \frac {0 . 1 2 7 \frac {M}{s}}{[ 0 . 2 M ] ^ {2} [ 0 . 3 M ]} = 1 0. 5 8 3 [ M ] ^ {- 2} s ^ {- 1};$$ $$k _ {3} = \frac {1 . 0 2 \frac {M}{s}}{[ 0 . 4 M ] ^ {2} [ 0 . 6 M ]} = 1 0. 6 2 5 [ M ] ^ {- 2} s ^ {- 1};$$ $$k _ {4} = \frac {0 . 2 5 4 \frac {M}{s}}{[ 0 . 2 M ] ^ {2} [ 0 . 6 M ]} = 1 0. 5 8 3 [ M ] ^ {- 2} s ^ {- 1};$$ $$k _ {5} = \frac {0 . 5 0 9 \frac {M}{s}}{[ 0 . 4 M ] ^ {2} [ 0 . 3 M ]} = 1 0. 6 0 4 [ M ] ^ {- 2} s ^ {- 1}.$$

The average constant:

$$\begin{array}{l} \boldsymbol {k} _ {\text {a v g}} = \frac {k _ {1} + k _ {2} + k _ {3} + k _ {4} + k _ {5}}{5} = \frac {1 0 . 6 0 0 + 1 0 . 5 8 3 + 1 0 . 6 2 5 + 1 0 . 5 8 3 + 1 0 . 6 0 4}{5} \\ = 1 0. 5 9 9 [ M ] ^ {- 2} s ^ {- 1} \approx \mathbf {1 0 . 6} [ M ] ^ {- 2} s ^ {- 1} \\ \end{array}$$

The final rate law:

$$\boldsymbol {r} = \mathbf {1 0 . 6} [ \boldsymbol {A} ] ^ {2} [ \boldsymbol {B} ]$$

(iii) When $[A] = 0.30M$ and $[B] = 0.40M$ , rate equals to:

$$\boldsymbol {r} = \mathbf {1 0 . 6} [ \boldsymbol {M} ] ^ {- 2} \boldsymbol {s} ^ {- 1} * [ \mathbf {0 . 3 M} ] ^ {2} * [ \mathbf {0 . 4 M} ] = \mathbf {0 . 3 8 1 6 M / s}$$

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