Is it possible for this equation
2C + D = E + F
to have a rate law of
rate = k [C]^2[D]^3
Of course. The rate law is determined experimentally and has nothing to do with the coefficients in the balanced chemical equation.
Really? How would the mechanism look like?
http://en.wikipedia.org/wiki/Rate_equation
To determine if the given equation can have a rate law of rate = k [C]^2 [D]^3, we need to compare the coefficients of each reactant in the balanced chemical equation with the exponents in the rate law.
In the given equation 2C + D = E + F, we have the reactants C and D on the left-hand side and the products E and F on the right-hand side. The coefficients of C and D are both 2, while the coefficients of E and F are both 1.
In the rate law rate = k [C]^2 [D]^3, the exponent for C is 2, indicating a second-order dependence on C. Similarly, the exponent for D is 3, indicating a third-order dependence on D.
Since the coefficients of C and D in the equation are both 2, and the exponents in the rate law are 2 and 3 respectively, it is possible for the given equation to have a rate law of rate = k [C]^2 [D]^3. The exponents in the rate law show that the reaction rate is directly proportional to the square of the concentration of C and the cube of the concentration of D.