Question

If $K_p$ of an equilibrium $CaC{O}_3\left(s\right)\rightleftharpoons CaO\left(s\right)+C{O}_2\left(g\right)$ is 1.5 atm at ${29}^{0}C$ then the moles of CaO formed if excess $CaC{O}_2\left(S\right)$ is being placesd in a 1 L of closed container containing $C{O}_2$ gas at 0.5 atm pressure at same temperature is:

• A. $\frac{1}{56}$
• B. $\frac{1}{24}$
• C. $\frac{1}{21}$
• D. $\frac{1}{13}$

Answer 1

Answer: (B)

$\frac{1}{24}$

$CaCO\left(s\right)\rightleftharpoons CaO\left(s\right)+{CO}_2\left(g\right)K_P=1.5atm$

$t=0$ $a$ $0$ $a^1$

$t=$ $a-x$ $x$ $x+a^1$

$t_{eq}$

Initially $a^1$ moles make pressure of $0.5$ atm at ${29}^{0}C$

So from $PV=nRT$

$\left(0.5\right)\left(1\right)=\left(a^1\right)\left(0.0821\right)\left(302\right)$

$a^1=0.0202$

At equilibrium $K_P=P^{{CO}_2}=1.5atm$

$a^1$$+x$ moles from $1.5$atm at ${29}^{0}C$

$\left(1.5\right)\left(1\right)=(a^1+x)\left(0.0821\right)\left(302\right)$

$a^1+x=0.0605$

$x=0.0403=$ also equal to no. of moles of $CaO$ formed $\approx \frac{1}{24}$