During the complete combustion of one mole of butane, 2658 kJ of heat is released. The thermochemical reaction for this change is:

${∆}_{\mathrm{f}}{\mathrm{U}}^{⊝}$ of formation of ${\mathrm{CH}}_4\left(\mathrm{g}\right)$ at certain temperature is $-393$ $\mathrm{kJ}$ ${\mathrm{mol}}^{-1}$. The value of ${∆}_{\mathrm{f}}{\mathrm{H}}^{⊝}$ is-

1. Zero

2. $<{∆}_{\mathrm{f}}{\mathrm{U}}^{⊝}$

3. $>{∆}_{\mathrm{f}}{\mathrm{U}}^{⊝}$

4. Equal to ${∆}_{\mathrm{f}}{\mathrm{U}}^{⊝}$

Based on the reactions, ascertain the valid algebraic relationship:
$\left(i\right)$ $C\left(g\right)$ $+4H$ $\left(g\right)$ $\to C{H}_4\left(g\right);$ $$
$∆H_r$ $=x$ $kJ$ $mo{l}^{-1}$
$\left(ii\right)$ $C\left(graphite\right)$ $+$ $2H_2$ $\left(g\right)$ $\to$ $$ $C{H}_4;$ $$
$∆H_r$ $$ $=$ $y$ $kJ$ $mo{l}^{-1}$

In an exothermic reaction, heat is evolved, and the system loses heat to the surrounding. The correct choice among the following for such a system are-

(a) q_p will be negative

(b) ${∆}_{\mathrm{r}}\mathrm{H}$ will be negative

(c) q_p will be positive

(d) ${∆}_{\mathrm{r}}\mathrm{H}$ will be positive

1. (a, b)

2. (b, c)

3. (c, d)

4. (a, d)