Question

From the following data for the first-order gas-phase isomerization of CH3NC at 215 C, calculate the first-order rate constant and half-life for the reaction:
Time (s) Pressure CH3NC(torr)
0 502
2000 335
5000 180
8000 95.5
12000 41.7
15000 22.4

k = ?
t1/2 = ?

Answer 1

Where.. 
[At] = concentration of component "A" after time = t has elapsed 
k = rate constant 
t = time elapsed 
[Ao] = concentration at time = 0.. i.e.. the concentration you started with. 

************ 
now... you have pressure.. not concentration right? 

if your gas is an ideal gas, then 
PV = nRT 
P = (n/V) x (RT) 

and since "concentration" = moles / volume.. i.e.. [A] = n/v 
and since "R" is a constant 
and since "T" is a constant 

[A] = P / (RT) 

***** 
so we can either do this.. 
ln( Pt/(RT) ) = -kt + ln( Po/(RT)) 

and since Pt and "t" vary and Po and R and T are constant 

this is of the form 
y = mx + b 

if we let 
.. y = ln( Pt / (RT) ) 
.. m = -k 
.. .x = time 
.. b = ln( Po / (RT)) 

i.e.. a plot of ln(P / RT) on the y-axis versus time on the x-axis will have a slope = -k 

so.. 
open up an excel spreadsheet 
make three columns starting with T = 

.. .. .. .. ..col A.. . .col B.. .. ,.Col C 
row 1.... . t.. ... .P(torr)... . .ln[P/RT (M)]. 
row 2.. ....0... .. . .502... .. .+ln(B2/760/0.08206/(273.15+215)) 
row 3.. ....2000 . .335... .. .+ln(B3/760/0.08206/(273.15+215)) 
etc.. 

mouse to A2 
left click and hold 
drag highlight to A7 
press and hold ctrl 
release mouse (keep holding ctrl 
mouse to c2 
left click and hold 
drag to c7 
release ctrl 
release mouse 
left click insert 
left click scatter 
choose the upper left one with just the data points by left clicking on it 
right click on any data point on the plot 
left click add trendline 
left click the two boxes to display equation on chart and display r^2 
close 
right click on the equation that appeared on the plot 
left click format trendline label 
sent number format to display 8 decimal points 

and... TADA.. you have.. 
(1).. plotted ln(P/RT) vs time 
(2).. fitted the data points with the equation y = -0.00020775x - 4.0986 

meaning.. 
k in your rate equation 
ln[At] = -kt + ln[Ao] 
is... 
k = +0.00020775 /s