Assume that a human body requires $2500 \, kcal$ of energy each day for metabolic activity and sucrose is the only source of energy,as per the equation $C_{12}H_{22}O_{11(s)} + 12 \, O_{2(g)} \longrightarrow 12 \, CO_{2(g)} + 11 \, H_2O_{(l)};$ $\Delta H = -5.6 \times 10^6 \, J$. (Fill in the blanks) $(a)$ The energy requirement of the human body per day is $.... \, kJ$. $(b)$ The mass of sucrose required to provide this energy is $........ \, g$ and the volume of $CO_2$ (at $STP$) produced is $......... \, litres.$

(A) Given $1 \, kcal = 4.184 \, kJ$. Therefore,$2500 \, kcal = 2500 \times 4.184 \, kJ = 10460 \, kJ$. The energy requirement is $10460 \, kJ$.
$(b)$ Molar mass of sucrose $(C_{12}H_{22}O_{11})$ = $(12 \times 12) + (22 \times 1) + (11 \times 16) = 342 \, g/mol$.
Energy released per mole of sucrose = $5.6 \times 10^6 \, J = 5600 \, kJ/mol$.
Moles of sucrose required = $\frac{10460 \, kJ}{5600 \, kJ/mol} \approx 1.8679 \, mol$.
Mass of sucrose = $1.8679 \, mol \times 342 \, g/mol \approx 638.82 \, g$.
From the equation,$1 \, mol$ of sucrose produces $12 \, mol$ of $CO_2$.
Moles of $CO_2$ produced = $1.8679 \times 12 = 22.4148 \, mol$.
Volume of $CO_2$ at $STP$ = $22.4148 \, mol \times 22.4 \, L/mol \approx 502.09 \, L$.