    Question

# For first order homogeneous gaseous reaction A → 2B + C, the initial pressure was P0 while total pressure at time 't' was Pt. The expression for the rate constant k in terms of P0, Pt & t is:

A
k=2.303tlog(2P03P0Pt)
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B
k=2.303tlog(2P02PtPt)
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C
k=2.303tlog(P0P0Pt)
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D
None of these
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Solution

## The correct option is A k=2.303tlog(2P03P0−Pt)Progress of gaseous reaction can be monitored by measuring total pressure at a fixed volume & temperature. We know, PV=nRT V : Volume n : No. of moles P : Pressure R : Gas constant T : Temperature So, P=nVRTP∝nVP∝Concentration So, for gaseous reactions, pressure is considered to monitor the reaction instead of concentration. The first-order reaction is A(g)→2B(g)+C(g) At t=0: P0 0 0 At t=t: P0−Pr 2Pr Pr P0 is initial pressure Pr is pressure of reactant which is already converted to product Total pressure, Pt=(P0−Pr)+2Pr+Pr Pt=P0+2Pr Pr=12(Pt−P0) So, pressure of A after time t, PA=P0−Pr PA=P0−12(Pt−P0) PA=12(3P0−Pt) Hene, the expression for the rate constant will be: k=2.303tlog(aa−x) Since, P∝Concentration aa−x = P0P0−Pr k=2.303tlog(P0P0−Pr) Thus the expession for the rate constant becomes k=2.303tlog(2P03P0−Pt) Hence, the correct option is A  Suggest Corrections  5      Similar questions  Related Videos   Rate of Reaction
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