Question

Assume that the complete combustion of one mole of glucose, a monosaccharide, to carbon dioxide and water liberates 2870 kJ2870 kJ of energy (ΔG°′=−2870 kJ/mol(ΔG°′=−2870 kJ/mol ). If the energy generated by the combustion of glucose is entirely converted to the synthesis of a hypothetical compound X, calculate the number of moles of the compound that could theoretically be generated. Use the value ΔG°′compound X=−54.1 kJ/molΔG°′compound X=−54.1 kJ/mol . Round your answer to two significant figures.

Answer 1

number of moles of the compound
`\approx` 53 mole

Step-by-step explanation:

Given that:

The total energy liberated = - 2870 kJ ( here , the negative sign typical implies the release of energy due to the combustion reaction)

The equation of the reaction can be represented as:

`\mathbf{C_6H_(12)O_6_((s)) + 6O_(2(g)) \to 6CO_(2(g))+6H_2O_((l))}`

The energy needed to synthesize 1 mole of compound X = - 54.1 kJ.mol

Thus;

The total energy = numbers of moles of compound × Energy needed to synthesize 1 mole of compound X

Making the numbers of moles of the compound the subject; we have;

numbers of moles of compound =
`numbers \ of \ moles \ of \ compound = (total \ energy )/(Energy \ needed \ to \ synthesize \ 1 \ mole \ of \ compound \ X)`
`numbers \ of \ moles \ of \ compound = (-2870 \ kJ )/(-54.1 \ kJ/mol)`

number of moles of the compound = 53.04990 mole

number of moles of the compound
`\approx` 53 mole to two significant figure