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

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### 1 Answer

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

**rate = k [M] [N]^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.**