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Question

Mathematics Question on homogeneous differential equation

For the reaction CO(g)+(12)O2(g)⟶CO2(g),Kp/KcCO ( g )+\left(\frac{1}{2}\right) O _{2}( g ) \longrightarrow CO _{2}( g ), K _{ p } / K _{ c } is

A

RTRT

B

(RT)−1(RT)^{-1}

C

(RT)−1/2(RT)^{-1/2}

D

(RT)1/2(RT)^{1/2}

Answer

(RT)−1/2(RT)^{-1/2}

Explanation

Solution

Kp=Kc(RT)Δn;Δn=1−(1+12)K_{p}=K_{c}(R T)^{\Delta n} ; \Delta n=1-\left(1+\frac{1}{2}\right)
=1−32=−12=1-\frac{3}{2}=-\frac{1}{2}
∴KpKc=(RT)−1/2\therefore \frac{K_{p}}{K_{c}}=(R T)^{-1 / 2}