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Concentrations Replaced by Other Quantities in First-Order Integrated Rate Law

Case I: Let there be a first-order reaction of the type A B + C. Let us assume that all the three species are gases. We are required to calculate the value of rate constant based on the following data.
Time
0
T
Partial pressure of A
P0
Pt
 
Rate constant for this case is given as
 
Description: 34818.png
Description: 34827.png
 
Case II:
 
A(g) B(g) + C(g)
 
Time
0
T
Partial pressure of A + B + C
Pt
P
 
Rate constant for this case is given as
 
Description: 34834.png
 
Case III: Now, let us assume a first-order reaction A B + C such that A, B, and C are in solution. At time zero, a small amount of the solution is taken, cooled (to stop the reaction from proceeding), and titrated with a suitable reagent. Let us assume that the reagent reacts only with A and not with B and C. The same process is repeated at time t.
 
Time
0
t
Volume of reagent
V0
Vt
 
Rate constant for this case is given as
 
Description: 34845.png
 
Case IV: Now, let us assume that A, B, and C are optically active compounds, which rotate the plane polarized light in the clockwise or anticlockwise direction.
 
A(soln.) B(soln.) + C(soln.)
 
Time
0
t
Total rotation in degrees
r0
rt
r
 
Rate constant for this case is given as
 
Description: 34854.png




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