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Question
Consider a first order gas phase decomposition reaction given below :
\[\ce{A(g) -> B(g) + C(g)}\]
The initial pressure of the system before decomposition of A was pi. After lapse of time ‘t’, total pressure of the system increased by x units and became ‘pt’ The rate constant k for the reaction is given as ______.
Options
`k = 2.303/t log p_i/(p_i - x)`
`k = 2.303/t log p_i/(2p_i - p_t)`
`k = 2.303/t log p_i/(2p_i + p_t)`
`k = 2.303/t log p_i/(p_i + x)`
Solution
The initial pressure of the system before decomposition of A was pi. After lapse of time ‘t’, total pressure of the system increased by x units and became ‘pt’ The rate constant k for the reaction is given as `k = 2.303/t log p_i/(2p_i - p_t)`.
Explanation:
Consider a first order gas phase decomposition reaction:
\[\ce{A_{(g)} -> B_{(g)} + C_{(g)}}\]
The initial pressure of the system before decomposition of A was Pi.
After lapse of time (t), total pressure of the system increased by x units and became 'Pt'.
In other words, the pressure of A decreased by x atom.
\[\ce{A_{(g)} -> B_{(g)} + C_{(g)}}\]
Initial pressure: Pi atm
Pressure after time t: (Pi – x) atm x atm x atm
Pt = (Pi – x) + x + x = Pi + x atm
x = Pt – Pi
PA = Pressure of A after time t = Pi - x = Pi - (Pi - Pi) = 2Pi - Pt
`k = 2.303/t log (["A"]_0)/(["A"])`
= `k = 2.303/t log p_i/(2p_i - p_t)`
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