At 300K ,a gaseous reaction A---->B C was found to follow 1st order ki...
At 300K ,a gaseous reaction A---->B C was found to follow 1st order ki...
Partial Pressure of A in the Reaction A ----> B + C
Given:
Temperature (T) = 300 K
Time (t) = 20 minutes
Total Pressure at t = 100 mm Hg
Total Pressure after completion of the reaction = 180 mm Hg
To find: Partial Pressure of A
1. Conversion of Time to Seconds:
20 minutes = 20 × 60 seconds = 1200 seconds
2. Calculating Rate Constant (k):
The reaction is said to follow first-order kinetics, which means the rate of the reaction is directly proportional to the concentration of the reactant A.
The integrated rate law for a first-order reaction is given by:
ln([A]t/[A]0) = -kt
Where [A]t is the concentration of A at time t, [A]0 is the initial concentration of A, k is the rate constant, and t is the time.
At the start of the reaction, t = 0, [A]t = [A]0, so the equation becomes:
ln(1) = -k(0)
0 = 0
This equation shows that at the start of the reaction, the concentration of A remains the same.
At time t = 1200 seconds, [A]t = 0 (as the reaction is completed), so the equation becomes:
ln(0) = -k(1200)
This equation is undefined as the natural logarithm of zero is not defined.
Therefore, we cannot directly use the integrated rate law to find the rate constant.
3. Using the Equation for Partial Pressure:
The total pressure at the end of 20 minutes is given as 100 mm Hg, which can be written as the sum of the partial pressures of A, B, and C.
Ptotal = PA + PB + PC
100 = PA + PB + PC
The total pressure after completion of the reaction is given as 180 mm Hg, which can also be written as the sum of the partial pressures of B and C.
Ptotal = PB + PC
180 = PB + PC
We can subtract the second equation from the first equation to eliminate PB and PC:
100 - 180 = (PA + PB + PC) - (PB + PC)
-80 = PA
Therefore, the partial pressure of A is -80 mm Hg.
However, this is not a physically meaningful result, as pressure cannot be negative.
Hence, there might be a mistake or inconsistency in the given data or calculations.
The correct answer cannot be determined with the given information.
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