If a rocket runs on a fuel ($$C_{15}H_{30}$$) and liquid oxygen, the weight of oxygen required and $$CO_2$$ released for every litre of fuel respectively are :
(Given : density of the fuel is $$0.756$$ g/mL)

The fuel is $$C_{15}H_{30}$$ with density $$0.756$$ g/mL. We need to find the weight of $$O_2$$ required and $$CO_2$$ released for every litre of fuel.

The balanced combustion reaction is:

$$ C_{15}H_{30} + \frac{45}{2}O_2 \rightarrow 15CO_2 + 15H_2O $$

Verification: C: 15 = 15 ✓; H: 30 = 30 ✓; O: 45 = 30 + 15 = 45 ✓

The mass of 1 litre of fuel is: $$ \text{Mass} = 1000 \text{ mL} \times 0.756 \text{ g/mL} = 756 \text{ g} $$ The molar mass of $$C_{15}H_{30}$$ is: $$ M = 15 \times 12 + 30 \times 1 = 180 + 30 = 210 \text{ g/mol} $$ so the number of moles of fuel in 1 litre is: $$ n = \frac{756}{210} = 3.6 \text{ mol} $$

Each mole of fuel requires $$\frac{45}{2} = 22.5$$ moles of $$O_2$$, so the mass of $$O_2$$ required is: $$ \text{Mass of } O_2 = 3.6 \times 22.5 \times 32 = 3.6 \times 720 = 2592 \text{ g} $$

Each mole of fuel produces 15 moles of $$CO_2$$, so the mass of $$CO_2$$ released is: $$ \text{Mass of } CO_2 = 3.6 \times 15 \times 44 = 3.6 \times 660 = 2376 \text{ g} $$

The weight of oxygen required is 2592 g and $$CO_2$$ released is 2376 g. The correct answer is Option C: 2592 g and 2376 g.