Question

The rate constant for the decomposition of nitrogen dioxide NO2(g) LaTeX: \longrightarrow⟶ NO (g) + 1/2 O2(g) with a laser beam is 1.95 1/MLaTeX: \cdot⋅ min. Find the time, in seconds, needed to decrease 2.48 M of NO2 to 0.97 M. Hint: What is the order of the reaction? How can you determine that? Units of k?

Answer 1

Answer :

The time taken by the reaction is 19.2 seconds.

The order of reaction is, second order reaction.

Explanation :

The general formula to determine the unit of rate constant is:

$(Concentration)^{(1-n)}(Time)^{-1}$

Unit of rate constant                           Order of reaction

$Concentration/Time$                                        0

$Time^{-1}$                                                              1

$(Concentration)^{-1}Time^{-1}$                                 2

As the unit of rate constant is $M^{-1}min^{-1}$. So, the order of reaction is second order.

The expression used for second order kinetics is:

$kt=\frac{1}{[A_t]}-\frac{1}{[A_o]}$

where,

k = rate constant = $1.95M^{-1}s^{-1}$

t = time = ?

$[A_t]$ = final concentration = 0.97 M

$[A_o]$ = initial concentration = 2.48 M

Now put all the given values in the above expression, we get:

$1.95\times t=\frac{1}{0.97}-\frac{1}{2.48}$

$t=0.32min=0.32\times 60s=19.2s$

Therefore, the time taken by the reaction is 19.2 seconds.

Answer 2

The reaction for the decomposition of nitrogen dioxide follows a second-order reaction. The time for the reaction to complete is 19.2 seconds.

What is the rate constant?

The rate constant is the value of the constant that specifies the relationship between the rate and concentration.

The rate constant for the reaction is $\rm 1.95\;M^{-1}s^{-1}$

The constant value gives the information that the rate of reaction is dependent on the concentration of the reactant in the reaction. The rate followed by the reaction is a second-order reaction.

The rate constant (k) for the second-order reaction is given as:

$kt=\dfrac{1}{A_t}-\dfrac{1}{A^\circ}$

Where, the rate constant for the reaction is, $k=1.951\;\rm M^{-1}s^{-1}$

The initial concentration of nitrogen dioxide is, $A^\circ=2.48\;\rm M$

The final concentration of nitrogen dioxide is, $A_t=0.97\;\rm M$

Substituting the values for the time of reaction:

$1.951t=\dfrac{1}{0.97}-\dfrac{1}{2.48}\\ 1.951t=1.03-0.403\\t=0.32\;\rm min$

The minutes are converted to seconds as:

$\rm 1\;min=60\;sec\\0.32\;min=0.32\;\times\;60\;sec\\0.32\;min=19.2\;sec$

Therefore, the time required for the decomposition of nitrogen dioxide is 19.2 sec.

Learn more about the order of reaction, here:

https://brainly.com/question/8592296