The heat evolved in the combustion of methane is given by the following equation: $CH_{4(g)} + 2O_{2(g)} \to CO_{2(g)} + 2H_2O_{(l)}$; $\Delta H = -890.3 \ kJ$. How many grams of methane would be required to produce $445.15 \ kJ$ of heat of combustion?

$A$ gas expands from $3\, dm^3$ to $5.8\, dm^3$ against a constant external pressure of $3\, bar$. The work done during expansion is used to heat $2\, moles$ of water from $290\, K$ to a final temperature of $T\, K$. If the specific heat of water is $4.2\, J\, g^{-1}\, K^{-1}$,then $T = ......\, K$. (in $.6$)

For the combustion of one mole of acetic acid,the work done at $298 \ K$ is (in $J$)

Match the conditions and the temperature for the 'fusion' process of $H_2O_{(s)}$ at $1 \ atm$ pressure.

Condition	Temperature
$(1)$. Spontaneous	$(p)$. $273 \ K$
$(2)$. At equilibrium	$(q)$. $260 \ K$
$(3)$. Non-spontaneous	$(r)$. $280 \ K$

One mole of an ideal monoatomic gas is subjected to changes as shown in the graph. The magnitude of the work done (by the system or on the system) is $...........J$ (nearest integer). Given: $\log 2=0.3, \ln 10=2.3$

$28.0 \, L$ of $CO_2$ is produced on complete combustion of $16.8 \, L$ gaseous mixture of ethene $(C_2H_4)$ and methane $(CH_4)$ at $25^{\circ}C$ and $1 \, atm$. Heat evolved during the combustion process is $......... \, kJ$.
Given :
$\Delta H_C(CH_4) = -900 \, kJ \, mol^{-1}$
$\Delta H_C(C_2H_4) = -1400 \, kJ \, mol^{-1}$