Question

Consider the reaction

X + Y→ Z

From the following data, obtained at 360 K, (a)determine the order of the reaction, and  (b)determine the initial rate of disappearance of X when the concentration of X is 0.30 M and that of Y is 0.40 M.

Initial Rate of Disappearance of X (M/s)	[X](M)	[Y](M)
0.053	0.10	0.50
0.127	0.20	0.30
1.02	0.40	0.60
0.254	0.20	0.60
0.509	0.40	0.30

Answer 1

a)

Write the given reaction.

The general form of the rate law is given as follows:

…… (1)

Here, a and b are orders of reaction with respect to X and Y respectively and k is reaction rate constant.

To determine the order of reaction with respect to each reactant, compare any two rates in which only one reactant concentration changes.

The data collected for initial rate of disappearance of X at 360 K is shown below:

Exp.			Initial rate of disappearance of X (M/s)
1	0.10	0.50	0.053
2	0.20	0.30	0.127
3	0.40	0.60	1.02
4	0.20	0.60	0.254
5	0.40	0.30	0.509

Substitute the values of 3, 4 experiments in rate expression (1) and take the ratio to obtain value of a.

So, the order of reaction with respect to X is 2.

Then substitute the values of 2, 4 experiments in rate expression (1) and take the ratio to obtain value of b.

So, the order of reaction with respect to Y is 1.

Substitute the values of a and b in the rate expression (1) and obtain the rate law:

Order of the reaction is the sum of the powers to which reactant concentrations are raised in the rate law.

Thus, order of the reaction is 3.

(b)

To determine the initial rate of disappearance of X at given concentrations, first you need to calculate rate constant.

To calculate the value of k, substitute the values of first experiment in rate law:

The relation between rate of reaction and rate of disappearance of X is given by,

That is they are numerically equal.

We have concentrations:.

So, determine the initial rate of disappearance of X at these concentrations:

Thus, the initial rate of disappearance of X at specified concentrations is.

Answer 2

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Date 11 NSSON Page RANKA ko mate - 5.02 loiso) (0.102 (0.so) M²R. [x] = 0.30 IY = 0.40 мае 2 Cy Lчі = 10.6 [0.3] [4 ] Mate = 0.816 Ma