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Heat of combustion of $CH_4, C_2H_4$ and $C_2H_6$ are $-890, -1411$ and $-1560 \ kJ/mol$ respectively. Which has the lowest calorific value?

Match the following columns:
Column $I$ Column $II$
$(a)$ Adiabatic process $(1)$ Heat
$(b)$ Isolated system $(2)$ Constant volume
$(c)$ Isothermal change $(3)$ First law of thermodynamics
$(d)$ Path function $(4)$ No exchange of matter and energy
$(e)$ State function $(5)$ No heat exchange
$(f)$ $\Delta U = q$ $(6)$ Constant temperature
$(g)$ Law of conservation of energy $(7)$ Internal energy
$(h)$ Reversible process $(8)$ $p_{ext} = 0$
$(i)$ Free expansion $(9)$ Constant pressure
$(j)$ $\Delta H = q$ $(10)$ Infinitely slow process involving equilibrium states
$(k)$ Intensive property $(11)$ Entropy
$(l)$ Extensive property $(12)$ Pressure
$(13)$ Specific heat

When $1 \ g$ of $NH_4NO_3$ is decomposed in a bomb calorimeter,the temperature of the calorimeter increases by $6.12 \ K$. If the heat capacity of the system is $1.23 \ kJ/K$,the molar enthalpy of decomposition of $NH_4NO_3$ is ........ $kJ/mol$.

Observe the following reactions:
$AB_{(g)} + 25 H_2O_{(l)} \rightarrow AB_{(25 H_2O)} ; \Delta H = x \ kJ \ mol^{-1}$
$AB_{(g)} + 50 H_2O_{(l)} \rightarrow AB_{(50 H_2O)} ; \Delta H = y \ kJ \ mol^{-1}$
The enthalpy of dilution $(\Delta H_{dil})$ in $kJ \ mol^{-1}$ is

$\Delta H_f^o$ of water is $-285.5\, kJ\, mol^{-1}$. If enthalpy of neutralisation of monoacidic strong base is $-57.3\, kJ\, mol^{-1}$,$\Delta H_f^o$ of $OH^{-}$ ion will be $.....\, kJ\, mol^{-1}$.

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