In the first step of glycolysis, the given two reactions are coupled. reaction 1:reaction 2:glucose+Pi⟶glucose-6-phosphate+H2 OATP+H2O⟶ADP+PiΔG=+13.8 kJ/molΔG=−30.5 kJ/mol reaction 1:glucose+Pi⟶glucose-6-phosphate+H2 OΔG=+13.8 kJ/molreaction 2:ATP+H2O⟶ADP+PiΔG=−30.5 kJ/mol Answer the four questions about the first step of glycolysis. Is reaction 2 spontaneous or nonspontaneous?

Answer : The reaction 2 is spontaneous.

Explanation :

As we know that:

= +ve, reaction is non spontaneous

= -ve, reaction is spontaneous

= 0, reaction is in equilibrium

For the reaction to be spontaneous, the Gibbs free energy of the reaction must come out to be negative.

Reaction 1:

Glucose + Pi glucose-6-phosphate + H₂O,   ΔG = +13.8 kJ/mol

Reaction 2:

ATP + H₂O ADP + Pi,   ΔG = -30.5 kJ/mol

From this we conclude that the value of ΔG is negative. So, reaction 2 is a spontaneous reaction.

part 1: the half-life of the element is 22 years.

part 2: it will take 132.02 year for the sample to decay from 308.0 g to 4.8125 g.

explanation:

part 1: there are two ways to determine the half life time.

first way: the half life time can be determined directly from its definition as it is the time required for the sample to decay to its half concentration.

from the data the initial concentration was 45.0 g and decayed to its half value (22.5 g) in 22.0 years.

second way: the radio active decay is considered first order reaction so we can use the laws of first order reactions.

k = (1/t) ln (a/a-x), where k is the rate constant of the reaction,

t is the time of the reaction

a is the initial concentration of the reactant

a-x is the remaining concentration at time (t)

a = 45.0 g the initial concentration at t = 0 year.

at t = 22 year, a-x = 22.5 g

then k = (1/22 year) ln (45.0 g/ 22.5 g) = 0.0315 year-1.

the half-life time (t1/2) = ln 2/ k = 0.693/ k =0.693/ 0.0315 = 22 years.

part 2:

using the same law k = (1/t) ln (a/a-x),

using the given data; a = 308.0 g and a-x = 4.8125 g and the calculated k from the part 1 (k = 0.0315 year-1)

t = (1/k) ln (a/a-x) = (1/0.0315) ln (308.0/ 4.8125) = 132.02 years