For a reaction $aA_{(g)} \rightleftharpoons bB_{(g)}$ at equilibrium,the heat of reaction at constant volume is $1500 \text{ cal}$ more than that at constant pressure. If the temperature is $27^\circ\text{C}$,then:

Given the equilibria:
$I: A + 2B \rightleftharpoons C ; K_{eq} = K_1$
$II: C + D \rightleftharpoons 3A ; K_{eq} = K_2$
$III: 6B + D \rightleftharpoons 2C ; K_{eq} = K_3$
Which of the following relations is correct?

For the reaction $AB_{(g)} \rightleftharpoons A_{(g)} + B_{(g)}$,$AB$ is $33.3\%$ dissociated at a total equilibrium pressure of $P$. Therefore,$P$ is correctly related to $K_p$ by which of the following options?

The rate constant for forward and backward reactions of hydrolysis of ester are $1.1 \times 10^{-2} \text{ min}^{-1}$ and $1.5 \times 10^{-3} \text{ min}^{-1}$ respectively. The equilibrium constant for the reaction $CH_3COOC_2H_5 + H_2O \rightleftharpoons CH_3COOH + C_2H_5OH$ is: (in $.33$)

One mole of $PCl_5$ is heated in a closed container of $1 \ L$ capacity. At equilibrium,$20\%$ of $PCl_5$ is not dissociated. What should be the value of $K_C$?

For which of the following reactions is the relation $\frac{K_p}{K_c} + \log(RT) = 0$ correct?