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IgorC [24]
3 years ago
8

From the following data for the first-order gas-phase isomerization of CH3NC at 215 C, calculate the first-order rate constant a

nd 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 = ?
Chemistry
1 answer:
olganol [36]3 years ago
4 0
Where.. 
<span>[At] = concentration of component "A" after time = t has elapsed </span>
<span>k = rate constant </span>
<span>t = time elapsed </span>
<span>[Ao] = concentration at time = 0.. i.e.. the concentration you started with. </span>

<span>************ </span>
<span>now... you have pressure.. not concentration right? </span>

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

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

<span>[A] = P / (RT) </span>

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

<span>and since Pt and "t" vary and Po and R and T are constant </span>

<span>this is of the form </span>
<span>y = mx + b </span>

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

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

<span>so.. </span>
<span>open up an excel spreadsheet </span>
<span>make three columns starting with T = </span>

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

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

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

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