Calculating Rate Constant for 2N2O5 Reaction

[parwana]

At a certain temperature the reaction

2N2O5 --> 4NO2 + O2

is a first order reaction with t1/2 = 153.0 sec

What is the rate constant for this reaction (1/sec) ?

Enter a numeric answer only, do not include units in your answer


Ok I know the equation is t1/2= ln2/k

so isn't k the rate constant, and wouldn't the answer be ln2/153 sec= .0045??

 

[Astronuc]

The first order equation is -

$\frac{d [A]}{dt} = - k [A]$

where k is the rate constant.

The solution, as you correctly mentioned, is -

$ln \frac{[A]}{[A_o]} = - k t$, where [A] is the concentration at time t, and A_o is the initial concentration, at t=0.

The definition of half-life is-

$ln \frac{[A_o]/2}{[A_o]} = - k t_{1/2}$, or

ln 2 = k t_1/2

 

[ravenprp]

Yes, you are correct. The rate constant (k) can be calculated using the half-life (t1/2) and the equation t1/2 = ln2/k. Therefore, the rate constant for this reaction would be ln2/153 sec = 0.0045 1/sec. This means that at this particular temperature, the reaction rate is 0.0045 moles per liter per second.