These data pertain to questions 1 and 2. Consider the decomposition of hydrogen

Question

These data pertain to questions 1 and 2. Consider the decomposition of hydrogen peroxide. 2 H_2 O_2 rightarrow 2 H_2 O + O_2 The value of the rate constant k for the reaction was determined at several temperatures. K_1 = 7.77 times 10^-6 s^-1 T_1 = 298 K k_2 = 7.45 times 10^-4 s^-1 T_2 = 348 K k_3 = 0.0227 s^-1 T_3 = 398 K Which statements about this reaction are true? The reaction is first order. The reaction is second order. The rate of reaction decreases as the temperature increases. The rate of reaction increases as temperature increases. A plot of the rate constant versus temperature (K vs. T) will yield a line. Consider the decomposition of hydrogen peroxide. 2H_2 rightarrow 2H_2 + O_2 The value of the rate constant k for the reaction was determine at several temperatures.

Explanation / Answer

a.   Since the rate constants are given we can find the order of the reaction from the unit of the rate constant. In our case it is s-1 that is reaction is first order.
We know rate of reaction = change in concentration/time
Thus the unit of rate of a reaction is M s-1
As per rate law
Rate = k [reactant], since the concentration is in M, the concentration term in units cancel each other and you will get the unit as s-1, for a first order reaction.
Thus the first option is correct and second is wrong.
b.
Rate = k [reactant]
As temperature increases, k is increasing. It is very much clear from the given values.
At 298 K , k= 7.77 x 10-6, at 348 K, k = 7.45 x 10-5 and at 398 K, k= 0.0227 s-1.
Thus 3rd option is wrong and fourth one is correct

C
As per Arrhenius equation
k= A e-Ea/RT
Where A is the pre-exponential factor, Ea is activation energy, R is gas constant and T is temperature.
k is related to 1/T, exponentially. Thus a plot between k and T won’t be straight line
if we are taking natural logarithm on above equation
ln k = ln A – (Ea/RT)
Then a plot between ln k vs 1/T will be a straight line with slope –Ea/R and intercept ln A.
If a plot of k vs 1/T is straight line a lot of k vs T also will be straight-line
5th option is wrong and 6th option correct

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