If for a certain reaction $\Delta_r H$ is $30\text{ kJ mol}^{-1}$ at $450\text{ K}$, the value of $\Delta_r S$ (in $\text{J K}^{-1}\text{ mol}^{-1}$) for which the same reaction will be spontaneous at the same temperature is:

For the gas phase reaction, $\text{PCl}_5\text{(g)} \rightleftharpoons \text{PCl}_3\text{(g)} + \text{Cl}_2\text{(g)}$, which of the following conditions is correct?

One mole of an ideal gas at $300\text{ K}$ is expanded isothermally from an initial volume of $1\text{ litre}$ to $10\text{ litres}$. The $\Delta E$ for this process is: ($R = 2\text{ cal mol}^{-1}\text{K}^{-1}$)

What is the amount of work done by an ideal gas, if the gas expands isothermally from $10^{-3} \text{ m}^3$ to $10^{-2} \text{ m}^3$ at $300 \text{ K}$ against a constant pressure of $10^5 \text{ N m}^{-2}$?

Match List-I (Equations/Conditions) with List-II (Type of processes) and select the correct option. **List-I (Equations)** (a) $K_p > Q$ (b) $T < \frac{\Delta H}{\Delta S}$ (for $\Delta H > 0$) (c) $K_p = Q$ (d) $T > \frac{\Delta H}{\Delta S}$ (for $\Delta H > 0$) **List-II (Type of processes)** (i) Non-spontaneous (ii) Equilibrium (iii) Spontaneous and endothermic (iv) Spontaneous

The enthalpy of neutralization of which of the following acids and bases is nearly –13.6 Kcal [Roorkee 1999]

The heat of combustion of carbon to $\text{CO}_2$ is $-393.5 \text{ kJ/mol}$. The heat released upon the formation of $35.2 \text{ g}$ of $\text{CO}_2$ from carbon and oxygen gas is:

A system is changed from state A to state B by one path and from B to A by another path. If $E_{1}$ and $E_{2}$ are the corresponding changes in internal energy, then [Pb. PMT 2001]:

The work done to contract a gas in a cylinder is 462 joules. 128 joule energy is evolved in the process. What will be the internal energy change in the process? [MP PMT 2003]