Solution for this half life question

Question

The reaction: I2(g)----> 2I (g) is first order with a rate constant of 16.3 min-1at 625 K. If the initial concentration of I2 is 0.086 M, determine the concentration of I2 that remains after 12 s.

Answer 1

Hello Divine

 

The equation to use is:

 

ln[A_t] = ln[A_o] – kt

 

[A_t] = ?

[A_o] = 0.086 M

k = 16.3 min^-1

t = 12 s

 

Note that the unit for k is min^-1 and t is in seconds (s).  We need to convert unit of time from seconds to minutes (you can also convert min^-1 to s^-1 if you prefer) so that when we multiply "kt", the units will cancel.

 

t = 12 s x (1 min / 60 s) = 0.20 min

 

Now plug in the numbers into the above equation and solve for [A_t].

 

ln[A_t] = ln[A_o] – kt

 

ln[A_t] = ln[0.086] – (16.3 x 0.20)

 

ln[A_t] = –2.5 – 3.26

 

ln[A_t] = –5.76

 

Take the antilog (e^x) of both sides of the equation.

 

[A_t] = e^–5.76 = 0.0032 M (rounded to 2 significant figures)