For the reaction a+b+c→d+e, the initial reaction rate was measured for various initial concentrations of reactants. the following data were collected: trial [a] (m) [b] (m) [c] (m) initial rate (m/s) 1 0.20 0.20 0.20 6.0×10−5 2 0.20 0.20 0.60 1.8×10−4 3 0.40 0.20 0.20 2.4×10−4 4 0.40 0.40 0.20 2.4×10−4for the reaction a+b+c -> d+e, the initial reaction rate was measured for various initial concentrations of reactants. the following data were collected: trial [a] (m) [b[ (m) [c] (m) initial rate (m/s)1 0.20 0.20 0.20 6.0 x 10^-52 0.20 0.20 0.60 1.8 x 10^-43 0.40 0.20 0.20 2.4 x 10^-44 0.40 0.40 0.20 2.4 x 10^-4reaction order respect to a = 2reaction order in respect to b = 0reaction order in respect to c = 1the value of the rate constant k for this reaction = 7.5*10^-3 m^-2 * s^-1given the data calculated in parts a, b, c, and d, determine the initial rate for a reaction that starts with 0.75m of reagent a and 0.90m of reagents b and c?

Answer : The initial rate for a reaction will be

Explanation :

Rate law is defined as the expression which expresses the rate of the reaction in terms of molar concentration of the reactants with each term raised to the power their stoichiometric coefficient of that reactant in the balanced chemical equation.

For the given chemical equation:

Rate law expression for the reaction:

where,

a = order with respect to A

b = order with respect to B

c = order with respect to C

Expression for rate law for first observation:

....(1)

Expression for rate law for second observation:

....(2)

Expression for rate law for third observation:

....(3)

Expression for rate law for fourth observation:

....(4)

Dividing 1 from 2, we get:

Dividing 1 from 3, we get:

Dividing 3 from 4, we get:

Thus, the rate law becomes:

Now, calculating the value of 'k' by using any expression.

Putting values in equation 1, we get:

Now we have to calculate the initial rate for a reaction that starts with 0.75 M of reagent A and 0.90 M of reagents B and C.

Therefore, the initial rate for a reaction will be