What is the rate law expression for a reaction, A + B rightarrow product based o

Question

What is the rate law expression for a reaction, A + B rightarrow product based on the initial rate data: rtate = k[A]^2 rate = k[B]^2 rate = k[A][B] rate = k[A][B]^2 Calculate the value of the rate constant, k, with the correct units with your results of the previous question: 1.5 M^-1 s^-1 0.30 M^-1 s^-1 0.67 M^-1 s^-1 0.15 M^-1 s^-1 Which of the following liquid systems would be expected to have the lowest vapor pressure at room temperature? 1.00 m solution of ethanol in water 1.00 m solution of sucrosein water 1.00 m solution of acetone (CH_3C(O)CH_3) in water 1.00 m solution of NaCl in water all are the same A 10.0% by weight solution of NaCl in water has a molality of 0.127 m 1.42 m 1.50 m 7.85 m impossible to determine unless you know the density of the solution If freezing point depression was used to determine the molecular weight of a strong acid dissolved in water, and the dissociation of the acid wasn't taken into account, the determined value of the molecular weight of the acid would be: accurate too high too low inaccurate, but in a direction that cannot be predicted.

Explanation / Answer

Q8

In order to calculate the rate law expression for a A+B reaction, we need to apply Initial Rates Method.

Note that the generic formula goes as follows:

r = k [A]^a [B]^b

Note that if we got at least 3 sets of point, in which we have A and B constant, then we could use:

r1 / r2 = (k1 [A]1^a [B]1^b) / (k2 [A]2^a [B]2^b)

If we assume K1 and K2 are constant, then K1= K2 cancel each other

r1 / r2 = ([A]1^a [B]1^b) / ( [A]2^a [B]2^b)

Then, order according to [A] and [B]

r1 / r2 = ([A]1/[A2])^a * ([B]1/[B]2)^b

If we get two points in which A1 = A2, then we could get B, and vise versa for A...

From the data shown in YOUR table

Choose point 1 and 2...

r1 / r2 = ([A]1/[A2])^a * ([B]1/[B]2)^b

substitute

(1.5 * 10^-2) / (6*10^-2) = (0.15/0.15)^a * (0.10/0.20)^b

Cleary, the coefficient cancels:

0.25 = 1 * (0.5)^b

solve,

ln(0.25) / ln(0.5) = b

b = 2

Choose now points 2 and 3:

r3 / r3 = ([A]2/[A]3)^a * ([B]2/[B]3)^b

substitute

(6*10^-2)/(6*10^-2) = (0.15/0.30)^a * (0.20/0.20)^b

Cleary, the coefficient cancels:

1= (0.5)^a * 1

solve,

ln(1) / ln(0.5) = a

a = 0

so...

a = 0, b = 2

then

r = k [A]^a [B]^b

so

r = k [A]^0 [B]^2

r = k*[B]^2

For "k" value... choose any point in your set of data, I will choose 1 for simplicity

substitute data

r = k*[B]^2

1.5*10^-2 = k*(0.1^2)

K = (1.5*10^-2)/(0.1^2) = 1.5

units are according to order.. that is, second order, so choose 1.5 (M^-1 s^-1)

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