# The following data were collected for the reaction M + N --> P +Q The following data were collected for the reaction M + N --> P + Q Init.cntrtn         init. rate (mol L^-1s^-1) M        ...

The following data were collected for the reaction M + N --> P +Q

The following data were collected for the reaction M + N --> P + Q

Init.cntrtn         init. rate (mol L^-1s^-1)

M              N

.010        .010                R1 2.5x10^-6

.020        .010                R2 5.0x10^-6

.020        .030                R3 4.5x10^-5

what is the rate law ?what is value of the rate constant with correct units

## Expert Answers info

jerichorayel | Certified Educator

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The rate law is an equation that can determine how fast the reaction will proceed. For this problem, we can write the rate law as:

rate = k [M]^x [N]^y

x and y are variables that can be derived from the given rate and concentrations.

1. Isolate the [M]. To do that, we  try to inspect which among the table has constant value of [N]. We can see that Rates 1 and 2 has same value for [N]. Now we can solve for x

rate 1      (0.01)^x       2.5x10^-6

------ = ---------    = -------------

rate 2      (0.02)^x       5.0x10^-6

=    (1/2)^x   =  1/2

**solve for x

X = 1

2. Now do the same thing for [N]. We can see rate 2 and 3 has the same number of [M] and therefore we can isolate [N].

rate 2      (0.01)^y       5.0x10^-6

------ = ---------    = -------------

rate 3      (0.03)^y       4.5x10^-5

= (1/3)^y = (1/9)

**solve for y

y = 2

3. substitute the value of the derived x and y values.

rate = k [M]^x [N]^y
will now become:

rate = k [M]^1 [N]^2 or
rate = k [M] [N]^2

4. Now we are solving for the value of the rate constant (k). Using any of the values given, we can solve the value of the rate constant by simply substituting the value from the given data.

rate = k [M] [N]^2

k =    rate
-----------
[M] [N]^2

** we use the value of rate 3

k =  (4.5x10^-5 mol/L-s)
---------------
(0.02mol/L)(0.03mol/L)^2

k = 2.5 L^2mol^-2s^-1  OR
2.5 L^2/mol^2-s

5. The order of the equation is the sum of the exponent x and y. Therefore the order of the equation is 3rd order.

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