Firefly luciferase is the enzyme that allows fireflies to illuminate their abdomens. because this light generation is an atp-requiring reaction, firefly luciferase can be used to test for the presence of atp. in this way, luciferase can test for the presence of life. the coupled reactions are

Overall DeltaG = -6.40 kJ/mol

Delta G = 31.6 - 6.4 =25.2 KJ

T = 17 + 273.15 =290.15 K

Delta G = -RT * Ln (K)

25.2 * 10^3 J = -(8.314 J/moles*k)(290.15K) * Ln (K)

So (Delta G)/(-RT) = Ln (K)

Ln K = -10.44643114

Thus k = 2.905 *10^-5

Luciferase is an enzyme that belongs to the oxidative enzyme set of some bioluminescence reactions. This phenomenon was discovered by Rafaël Dubois, who detected the emission of light in some living things was nothing more than an enzymatic oxidation, in which luciferase was the catalyst, and luciferin the substrate. This phenomenon was frequently detected in fireflies and in the Pholas dactylus mollusk, and later in Cnidarians (Renilla reniformis), marine copepods (Gaussia princeps), abyssal molluscs (Oplophorus gracilirostris), bacteria, etc.

Explanation:

The biological role of luciferase lies in its quality as a catalyst for some types of bioluminescence. Bioluminescence is a type of chemiluminescence, it consists of the oxidation of luciferin, a luminescent substance, catalyzed by luciferase. Said reaction begins with luciferin whose carboxylic group reacts with the phosphate group of ATP, forming luciferyl adenylate. This molecule is oxidized (a process catalyzed by luciferase), resulting in an intermediate peroxide (luciferase-luciferin-AMP-O2 complex) which, upon releasing a molecule of carbon dioxide, results in a ketoderivative, the oxyluciferin, which is excited, returning to its normal state by releasing a photon of light:

Luciferin + O2 → Peroxidic intermediary (luciferase-luciferin-AMP-O2 complex) → [oxyluciferin] → oxyluciferin → light

we would need to see the picture to answer it