$A$ $4.50 \ g$ sample of methane occupies $12.7 \ L$ at $310 \ K$. Calculate the work done in $J$ when the gas undergoes isothermal expansion against a constant external pressure of $200 \ torr$ until the volume increases by $3.3 \ L$. (in $.99$)

Assertion: Many endothermic reactions that are not spontaneous at room temperature become spontaneous at high temperature.
Reason: Entropy of the system increases with increase in temperature.

For the conversion of limestone to lime,$CaCO_{3(s)} \rightarrow CaO_{(s)} + CO_{2(g)}$,the values of $\Delta H^{\circ}$ and $\Delta S^{\circ}$ at $298 \, K$ and $1 \, bar$ pressure are $+179.1 \, kJ \, mol^{-1}$ and $160.2 \, J \, K^{-1} \, mol^{-1}$ respectively. Assuming $\Delta H^{\circ}$ and $\Delta S^{\circ}$ do not change with temperature,at what temperature (in $K$) will the conversion of limestone to lime become spontaneous (in $, K$)?

$A$ chemical reaction cannot occur at all if

If $\Delta_r H^{\ominus}$ and $\Delta_r S^{\ominus}$ are standard enthalpy change and standard entropy change respectively for a reaction,the incorrect option is

Identify from the following the correct set of thermodynamic conditions for the reaction to be spontaneous at all temperatures.