Calculating Fraction of A Dissociated at 1000K with 1 atm and 10^-3 atm Pressure

[cantgetno]

Homework Statement

The Equilibrium constant for A(g) -> 2B(g)
is 1x10^-2 at 1000k. Calculate the fraction on A which is dissociated at 1000k if the total pressure is
1 atm
10^-3 atm

Homework Equations

PV=nRT
B^2 / A = Ke (1x10^-2)

The Attempt at a Solution

for A PV=1x8.714x1000 = 8.714x10^3
for B PV=2x8.714x1000 = 17.428



All i can work out from this is that there's gunna be a 1:2 ratio? I am completely lost and my minds gone blank. Thanks in advance for the help

 

[Borek]

Solve in terms of partial pressures. What is sum of pA and pB?

 

[cantgetno]

surely it would be pA+2pB=1atm ?
and I am not very sure how to solve in terms of partial pressures

would i have
kp= pB^2 / pA
so 0.01 = pB^2 / pA

I've tried using a simultaneous equation with pA+2pB=1
and just end up with rubbish

 

[Borek]

Why pA + 2 pB? Do you know definition of partial pressure?

 

[cantgetno]

because there's 2 moles of it? i thought that was right, my bad.

pA+pB=1atm that right?
would i be right to use a simlt equ then?

 

[Borek]

2*yes.

 

[cantgetno]

ok using the equations i end up with the quadratic:
pB^2 + 0.01pB-0.01=0 so pB=0.095atm
so pA=0.905atm
and i can work out for the other atmthanks