Question

Suppose polyethylene molecules in solution can exist either as a random coil or fully stretched out, with the latter conformation 2.4 kJ/mol higher in energy. What is the ratio of the two conformations at 20 degrees Celsius?

a. A. Random Coil:Stretched Out = 1:2
b. B. Random Coil:Stretched Out = 2:1
c. C. Random Coil:Stretched Out = 1:1
d. D. Random Coil:Stretched Out = 0:1

Answer 1

The ratio of the random coil conformation to the stretched-out conformation of polyethene molecules in solution at 20 degrees Celsius is approximately 1:2.

Step-by-step explanation:

The ratio of the random coil conformation to the stretched-out conformation of polyethene molecules in solution at 20 degrees Celsius can be calculated using the difference in energy between the two conformations. In this case, the stretched-out conformation is 2.4 kJ/mol higher in energy than the random coil conformation. To find the ratio, we can use the Boltzmann distribution, which states that the ratio of two conformations is equal to the exponential of the energy difference divided by the product of the gas constant and temperature.

Let's denote the ratio of random coil to stretched-out conformation as x. The ratio can be calculated using the equation:

x = exp(-2.4 kJ/mol / (8.314 J/mol•K * (20 + 273.15) K))

After calculating, we find that x ≈ 0.52. Therefore, the ratio of random coil to stretched-out conformation is approximately 1:2.