Chemistry extended problems (resonance framework)

Problem 4 – Activation resonance barrier#

A reaction’s activation energy is modeled as

$$ E_a = \frac{D_6}{τ_r} + ΛΘ. $$

1. If $$τ_r$$ increases, how does the first term change?
2. If the chemist wants to lower $$E_a$$, which parameter is most effective to adjust?

Problem 5 – Resonant catalysis efficiency#

Catalytic efficiency is given by

$$ η = \frac{X τ_r}{1 + e^{-D_3}}. $$

If $$τ_r$$ is doubled while $$X$$ and $$D_3$$ remain fixed, by what factor does $$η$$ change?

Problem 6 – Molecular orbital resonance#

A simplified orbital energy level is modeled as

$$ E_{\text{orb}} = D_9 - X \sqrt{τ_r}. $$

1. If $$τ_r$$ quadruples, how does the second term change?
2. Does the orbital energy increase or decrease?

Problem 7 – Temperature-driven equilibrium shift#

An equilibrium constant is modeled as

$$ K = e^{ΛΘ / D_3}. $$

If $$Θ$$ increases by 10% and $$Λ$$ decreases by 5%, what is the net percent change in the exponent?

Problem 8 – Resonant diffusion coefficient#

A diffusion coefficient under triadic resonance is

$$ D = \frac{T_f^2}{D_6 + τ_r}. $$

1. If $$T_f$$ increases by 20%, how does the numerator change?
2. If $$τ_r$$ also increases by 20%, how does the denominator change?
3. What is the qualitative net effect on $$D$$?