Question

The incredible catalytic power of enzymes can perhaps best be appreciated by imagining how challenging life would be without just one of the thousands of enzymes in the human body. For example, consider life without fructose-1,6-bisphosphatase, an enzyme in the gluconeogenesis pathway in liver and kidneys, which helps produce new glucose from the food we eat:
Fructose-1,6-bisphosphate + H2O → Fructose-6-phosphate + Pi
The human brain requires glucose as its only energy source, and the typical brain consumes about 120. g (or 480. calories) of glucose daily. Ordinarily, two pieces of sausage pizza could provide more than enough potential glucose to feed the brain for a day. According to a national fast-food chain, two pieces of sausage pizza provide 1260 calories, 49.0 % of which is from fat. Fats cannot be converted to glucose in gluconeogenesis, so that leaves 615 calories potentially available for glucose synthesis. The first-order rate constant for the hydrolysis of fructose-1,6-bisphosphate in the absence of enzyme is 2.00×10-20 sec-1.Calculate how long it would take to provide enough glucose for one day of brain activity from two pleces of sausage pizza without the enzyme.

Answer 1

Answer:

t = 7.58 * 10¹⁹ seconds

Explanation:

First order rate constant is given as,

k =  (2.303 /t) log  [A₀] /[Aₙ]

where  [A₀]  is the initial concentraion of the reactant; [Aₙ] is the concentration of the reactant at time, t

[A₀]  = 615 calories;

[Aₙ] = 615 - 480 = 135 calories

k = 2.00 * 10⁻²⁰ sec⁻¹

substituting the values in the equation of the rate constant;

2.00 * 10⁻²⁰ sec⁻¹ = (2.303/t) log (615/135)

(2.00 * 10⁻²⁰ sec⁻¹) / log (615/135) = (2.303/t)

t = 2.303 / 3.037 * 10⁻²⁰

t = 7.58 * 10¹⁹ seconds