Problem 1 What is the concentration ratio ... [FREE SOLUTION]

Chapter 18: Problem 1

What is the concentration ratio between the lowest energy and next best predicted RNA secondary structure if they differ by \(\Delta \Delta G=5.7 \mathrm{~kJ} \mathrm{~mol}^{1}\) at \(37^{\circ} \mathrm{C}\) ?

Short Answer

Expert verified

The concentration ratio between the lowest energy and next best predicted RNA secondary structure is obtained by evaluating the expression exp(-5700/(8.314*310.15)).

Step by step solution

Understand thermodynamic principles

The concentration ratio between different states of a molecular system at thermal equilibrium is described by the Boltzmann distribution. In terms of energy difference \(\Delta G\) between two states, it calculates the ratio as \(\frac{[RNA']}{[RNA]}\) = exp(-\(\Delta G\)/RT), where R is the gas constant (8.314 J/mol K), T is the temperature in Kelvin, and \(\Delta G\) is the difference in the Gibbs free energy between the two states. The ratio effectively reflects the relative populations of the two states at equilibrium.

Convert thermal units

Firstly, we need to make sure that the units we're using are consistent. The value of energy difference is given in kJ/mol, while the gas constant R is in J/mol K. Therefore, we should convert the energy difference from kJ/mol to J/mol by multiplying it by 1000. Thus, \(\Delta \Delta G\) = 5.7 * 1000 = 5700 J/mol.

Convert temperature to Kelvin

The temperature given is in Celsius. However, in the equation, the temperature must be in Kelvin. We can convert from Celsius to Kelvin by adding 273.15 to the Celsius measurement. Thus, the temperature T = 37掳C + 273.15 = 310.15 K.

Plug into formula and compute

We now have all of the values in the appropriate units to plug into the formula \(\frac{[RNA']}{[RNA]}\) = exp(-\(\Delta G\)/RT). After substituting R = 8.314 J/mol K, T = 310.15 K, and \(\Delta \Delta G\) = 5700 J/mol, we find that \(\frac{[RNA']}{[RNA]}\) = exp(-5700/(8.314*310.15)). Evaluating the exponential function gives the final concentration ratio.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Gibbs free energy

Gibbs free energy is a key concept in thermodynamics that tells us about the maximum amount of work that can be done by a system at constant temperature and pressure. It is denoted by the symbol \(G\) and is calculated with the formula: \( G = H - TS \), where \( H \) is enthalpy (total heat content), \( T \) is temperature in Kelvin, and \( S \) is entropy (measure of disorder).

Gibbs free energy helps predict chemical reactions and equilibrium

A negative change in Gibbs free energy (\( \Delta G < 0 \)) indicates that a process is spontaneous.
When \( \Delta G = 0 \), the system is in equilibrium.
If \( \Delta G > 0 \), the process is non-spontaneous under those conditions.

In the context of RNA secondary structure, differences in Gibbs free energy (like the \( \Delta \Delta G \) given in the exercise) can help us determine which structure is more stable under given conditions.

RNA secondary structure

RNA secondary structure refers to the set of base pairs that form within an RNA molecule, giving it a particular shape. This structure is crucial as it determines the function of the RNA.

Key elements of RNA secondary structure include:

Stems: These are formed from base pairs and provide stability.
Loops: These unpaired sections connect different stems, affecting the 3D shape.
Bulges and junctions: Regions where the expected pairing deviates, affecting folding.

Predicting RNA secondary structure involves computational models

These models help determine the most likely configuration, often the one with the lowest Gibbs free energy.
Stable structures have lower free energy, making them more prevalent at equilibrium.
Understanding RNA structures is essential in fields such as genetics and medicine, particularly in devising antiviral strategies.

Thermal equilibrium

Thermal equilibrium is a state where different parts of a system are at the same temperature, with no net energy flow between them. At this point, the system's properties, including temperature, distribute uniformly across it.

In thermodynamics, reaching thermal equilibrium is crucial for understanding distribution laws like Boltzmann distribution

Boltzmann distribution describes how energy states are populated in such a system.
While energy varies with temperature, at thermal equilibrium the probability of finding a system in a specific energy state is predictable.
This predictability aids in calculating concentration ratios, such as seen in different RNA structures under certain conditions.

Achieving thermal equilibrium ensures calculations, like those involving Gibbs free energy, are accurate and reflective of real biological systems.

91影视

What is the concentration ratio between the lowest energy and next best predicted RNA secondary structure if they differ by \(\Delta \Delta G=5.7 \mathrm{~kJ} \mathrm{~mol}^{1}\) at \(37^{\circ} \mathrm{C}\) ?

Short Answer

Step by step solution

Understand thermodynamic principles

Convert thermal units

Convert temperature to Kelvin

Plug into formula and compute

Key Concepts

Gibbs free energy

RNA secondary structure

Thermal equilibrium

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