A certain reaction X + Y → Z is described as being first order in [X] and third order overall. Which of the following statements is or are true?: The rate law for the reaction is: Rate = k[X][Y]2. If the concentration of X is increased by a factor of 1.5, the rate will increase by a factor of 2.25. If the concentration of Y is increased by a factor of 1.5, the rate will increase by a factor of 2.25.

The second statement is true: If the concentration of Y is increased by a factor of 1.5, the rate will increase by a factor of 2.25.

Explanation:

Hi there!

Let's write the rate law for the original reaction and the reaction with X increased by 1.5:

rate 1 = k [X][Y]²

rate 2 = k[1.5 X][Y]²

Now we have to demonstrate if rate 2 = 2.25 rate 1

Let's do the cocient between the two rates:

rate 2 / rate 1

if rate 2 = 2.25 rate 1

Then,

rate 2 / rate 1 = 2.25 rate 1 / rate 1 = 2.25

Let's see if this is true using the expressions for the rate law:

rate 2 / rate 1

k[1.5 X][Y]² / k [X][Y]² = 1.5 k [X][Y]² / k[X][Y]² = 1.5

2.25 ≠ 1.5

Then the first statement is false.

Now let's write the two expressions of the rate law, but this time Y will be increased by 1.5:

rate 1 = k[X][Y]²

rate 2 = k[X][1.5Y]²

Again let's divide both expressions to see if the result is 2.25

rate 2 / rate 1

k[X][1.5Y]² / k [X][Y]²

(distributing the exponent)

(1.5) ²k [X][Y]² / k [X][Y]² = (1.5) ² = 2.25

Then the second statement is true!

a) True

b) False

c) True

Explanation:

The order of reactants decides the exponents of respective reactant concentrations.

Since X is first order, exponent is = 1

Overall third order, Exponent X + Exponent Y = 3

Hence, exponent Y = 2.

Hence,

Rate = k[X][Y]^2

b)

If X conc is increased by 1.5 Rate should increase by 1.5 because k proportional to [X]. Hence, statement is False

c)

If Y conc is increased by 1.5 Rate should increase by 2.25 because k proportional to [Y]^2 = (1.5) ^2 = 2.25. Hence, statement is True