Using the data in the table, calculate the rate constant of this reaction. A+B⟶C+D

Question

Using the data in the table, calculate the rate constant of this reaction. (Include Final Units).

A+B⟶C+D

Trial [𝐀] (𝐌) [𝐁] (𝐌) Rate (M/s)

1. 0.250 0.310 0.0167

2. 0.250 0.682 0.0808

3. 0.375 0.310 0.0251

𝑘=?

Answer 1

A + B ==> C + C

Rate = k[A]^a[B]^b

So we need to find a and b, i.e the order of the reaction with respect to each reactant.

To do this, we use the data provided:

compare trial 1 and 2: [A] is constant, [B] increased by a factor of 2.2 and rate increased by a factor of 4.8. This tells us the reaction is 2nd order in B since (2.2)² = 4.8.

Next, compare trial 1 and 3: [B] is constant, [A] increased by a factor of 1.5 and rate increased by a factor of 1.5. This tells us the reaction is 1st order in A since (1.5)¹ = 1.5.

Thus, we can now write the rate equation as Rate = k [A][B]²

Pick any trial, and use the data to calculate k, the rate constant. Using trial 1, we have ...

0.0167 M/s = k [0.250][0.310]²

0.0157 M/s = 0.0240 k

k = 0.654 M^-2s^-1

Answer 2

This topic revolves around kinetics.

The general formula for the rate law will be the following:

Rate = k [A]^x * [B]^y

We can use the ratio of rate laws for experiment 1 and 2 to solve for y.

Rate₂ / Rate₁ = k * [0.250]^x * [0.682]^y / (k *[0.250]^x * [0.0167]^y)

The equation above can be simplified into the following:

Rate₂ / Rate₁ = [0.682]^y / [0.0167]^y

From here, substitute rate₂ and rate₁.

0.0808/0.0167 = [0.682]^y / [0.0167]^y

We can use the function of natural log to extract the exponent.

ln (0.0808/0.0167) = y ln(0.682 / 0.0167)

y = ~4.39

Repeat to solve for x now using rate 3 and rate 1 (as y is now constant)

Rate₃ / Rate₁ = k * [0.375]^x * [0.310]^y / (k *[0.250]^x * [0.310]^y)

The equation above can be simplified into the following:

Rate₃ / Rate₁ = [0.375]^x / [0.250]^x

From here, substitute rate₃ and rate₁.

0.0251/0.0167 = [0.375]^x / [0.250]]^x

We can use the function of natural log to extract the exponent.

ln (0.0251/0.0167) = y ln(0.375 / 0.250)

y = ~1.334

Use substitution to solve for rate for the original rate equation (Example here will be using equation 1)

Rate = k [A]^x * [B]^y

0.0167 = k [0.250]^1.334 * [0.310]^4.39

k = 0.148