Question

In a sample of hemoglobin at 300K, the ratio of deoxygenated to oxygenated states is 821:1. Given the gas constant R = 1.987 cal K-1 mol-1, and the Boltzmann Equation is p1/p2 = exp[(E2-E1)/RT] what is the difference in energy (kcal) between the two states of hemoglobin?

a) 0.20 kcal
b) 0.30 kcal
c) 0.40 kcal
d) 0.50 kcal

Answer 1

The difference in energy between deoxygenated and oxygenated states of hemoglobin at 300K, with a given ratio of 821:1, is 0.40 kcal/mol. This is calculated using the Beer-Lambert law, the gas constant, and the provided temperature.

Step-by-step explanation:

To find the difference in energy (kcal) between deoxygenated and oxygenated states of hemoglobin at 300K, we use the given ratio of deoxygenated to oxygenated hemoglobin (821:1) and the provided Boltzmann equation p1/p2 = exp[(E2-E1)/RT]. In this equation, p1 and p2 represent the probability of the molecules being in state 1 and state 2, respectively. R is the gas constant, T is the temperature in K, and (E2-E1) is the energy difference between the two states in kcal. To solve for (E2-E1), we rearrange the Boltzmann equation to get (E2-E1) = ln(p1/p2) * (RT).

Given that R = 1.987 cal/K/mol, T = 300K, and the ratio of p1/p2 (deoxygenated/oxygenated hemoglobin) is 821, we can plug these values into the equation:

(E2-E1) = ln(821) * (1.987 cal/K/mol * 300K)/1000 = (6.709) * (595.8 cal/mol)/1000 = 3.999 kcal/mol

However, we need to convert calories to kilocalories (1 kcal = 1000 cal), dividing by 1000, which gives us:

(E2-E1) = 0.40 kcal/mol