Question

A homogeneous ideal gaseous reaction $A{B}_{2\left(g\right)}\rightleftharpoons A_{\left(g\right)}+2B_{\left(g\right)}$ is carried out in a $25L$ flask at ${27}^{o}C$. The initial amount of $A{B}_2$ was $1mol$ and the equilibrium pressure was $1.9atm$. The value of $K_P$ is $x\times {10}^{-2}$. The value of $x$ is ______. $[R=0.08206d{m}^{3}atm{K}^{-1}mo{l}^{-1}]$

Answer 1

$A{B}_{2\left(g\right)}\rightleftharpoons A_{\left(g\right)}+2B_{\left(g\right)}$
Initial mole $100$
At eq. $1-xx2x$
At equilibrium,
$n_T=\frac{PV}{RT}{n}_T=\frac{1.9\times 25}{0.08206\times 300}=1.93\text{Total number of moles at equilibrium:}{n}_T=1-x+x+2x=1+2x1+2x=1.93\therefore x=0.465$

$K_P=\frac{P_A{P}_B^2}{P_{A{B}_2}}{P}_A=X_A{P}_{total}{K}_P=\frac{(\frac{0.465}{1.93}\times 1.9){(\frac{0.93}{1.93}\times 1.9)}^2}{(\frac{0.535}{1.93}\times 1.9)}\therefore K_P=73\times {10}^{-2}at{m}^2$