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In a closed cylinder of capacity 24.6 L,...

In a closed cylinder of capacity 24.6 L, the following reaction occurs at` 27^(@) C.`
`A _(2) (s) hArr B _(2) (s) + 2 C (g)`
At equilibrium, 1g of` B_(2)` (s) (molar mass `= 50 g mol^(-1)) `is present. The equilibrium constant `K_(p)` for the equilibrium in `atm^(2)` unit
`(R = 0.082 L atm K ^(-1) mol ^(-1))`

A

a)`1.6 xx 10 ^(-3)`

B

b)`1. 6 xx 10 ^(-5)`

C

c)`1.6 xx 10 ^(-2)`

D

d)`1.6 xx 10 ^(-4)`

Text Solution

Verified by Experts

The correct Answer is:
C
Equilibrium concentration of `B_(2)`
`[B_(2)] _("equilibrium") = ("mass")/( "molar mass " xx "volume") = (1)/( 50 xx 24.0) = 8.13 xx 10 ^(-4)`
For the reaction,
`{:(A _(2) (s) hArr B _(2) (s) + 2 C(g)), ( "Initial" a " "0 " "0), ( "at equilibrium" a-x " "x 2x):}=8.13 xx 10 ^(-3)`
`therefore [C] = 2 xx 8.13 xx 10 ^(-4) = 1. 63 xx 10 ^(-3)`
`K _(c) = [C] ^(2) = [ 1. 63 xx 10 ^(-3)) ^(2) = 2. 66 xx 10 ^(-6)`
Again from, `K _(p) = K _(c) (RT) ^(Delta ng)`
Here, `Delta n _(g) = 2 - 0 =2`
`K_(p) = 2. 66 xx 10 ^(-6) xx (0.082 xx 300) ^(2)`
`~~1.6 xx 10 ^(-3)`
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