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Consider the equilibrium SO(3) (g) hAr...

Consider the equilibrium
`SO_(3) (g) hArr SO_(2) (g) + (1)/(2) O_(2) (g) " " K_(C ) = 1`
What should be the initial concentration so that at equilibrium `[SO_(3)] = [O_(2)]`

A

`(4)/(3) M`

B

`(1)/(3)M`

C

`(1)/(4)M`

D

`(3)/(4)M`

Text Solution

Verified by Experts

The correct Answer is:
D
`{:(,SO_(3) (g),hArr,SO_(2) (g),+,(1)/(2) O_(2) (g),K_(C) = 1,),(t = 0,C_(0),,0,,0,,),("conc.",,,,,,,),(t = t_("eqm"),C_(0) - x,,x,,(x)/(2),,),("conc.",,,,,,,):}`
Given `[SO_(3)] = (O_(2)]`
`C_(0) - x = (x)/(2)`
`(3x)/(2) = C_(0) rArr x = (2C_(0))/(3)`
at equilibrium `[O_(2)] = (x)/(2) = (C_(0))/(3), [SO_(2)] = x = (2C_(0))/(3), [SO_(3)] = C_(0) - x`
`[SO_(3)] = C_(0) - (2C_(0))/(3)`
`[SO_(3)] = (C_(0))/(3)`
`K_(C) = 1 = ([SO_(2)] [O_(2)]^(1//2))/([SO_(3)]) = ((2C_(0))/(3) xx ((C_(0))/(3))^(1//2))/((C_(0))/(3))`
`1 = 4 (C_(0))/(3)`
`C_(0) = (3)/(4) M`
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