Question

A) What is the order of reaction for the plot above?

(The plot of ln[NO₂Cl] vs. time in seconds gave a straight line with the equation y = −3.250 × 10⁻³ x − 2.947).

B) What was the initial concentration of NO₂Cl?

(The plot of ln[NO₂Cl] vs. time in seconds gave a straight line with the equation y = −3.250 × 10⁻³ x − 2.947).

C)

Write the rate law expression. (For example: Rate=k[A][B]² [C]³ )

Note: For exponents, write [B]^2 to represent [B]²

Remember: (The plot of ln[NO₂Cl] vs. time in seconds gave a straight line with the equation y = −3.250 × 10⁻³ x − 2.947)

D) What is the value of the rate constant?  
(The plot of ln[NO₂Cl] vs. time in seconds gave a straight line with the equation y = −3.250 × 10⁻³ x − 2.947).

E) How long would it take (in seconds) for concentration for NO₂Cl to be 25% of the initial concentration?

(The plot of ln[NO₂Cl] vs. time in seconds gave a straight line with the equation y = −3.250×10⁻³ x − 2.947).

Thank You!

Answer 1

For a first order reaction:

A P

rate of reaction, r_t = k[A]_t   , where k = rate constant of the reaction

concentration of reactant at time t = [A]_t

And   [A]_t = [A]₀ exp (-kt)

So, ln [A]_t = ( -k) t + ln [A]₀

where slope of the line is -k and intercept on y-axis is ln [A]₀

The plot of ln[NO₂Cl] vs. time in seconds gave a straight line with the equation y = −3.250 × 10⁻³ x − 2.947

ln [NO2Cl]_t = (−3.250 × 10⁻³) t + ln [NO2Cl]₀

The slope is - 3.250 × 10⁻³    and   Intercept = -2.947

Hence, a) the reaction is first order with respect to NO2Cl.

              b) initial concentration of NO₂Cl , that is [NO2Cl]₀

ln [NO2Cl]₀ = -2.947

Or,             [NO2Cl]₀   = exp (-2.947) = 0.0525 M

c) the rate law expression:

Rate=k [NO2Cl]^1

d) value of the rate constant k , that is the slope of the straight line = 3.250 × 10⁻³ s^-1

e) for concentration for NO₂Cl to be 25% of the initial concentration:

It means [NO2Cl]_t = 0.25 [NO2Cl]₀

[NO2Cl]_t = [NO2Cl]₀ exp (-kt)

0.25 = exp (-kt)

Or, t = -(1/k) ln (0.25) = -ln (0.25) / (3.250 × 10⁻³ s^-1) = 426.5 s