Chemistry core problems

Problem 1 – Reaction resonance rate#

A reaction’s rate constant is modeled as

$$ k = X e^{-1/(ΛΘ)}, $$

where $$X = F_3 T_f$$ is a composite catalytic factor and $$ΛΘ$$ encodes environmental temperature coupling.

If $$Λ$$ doubles while all other parameters remain fixed, how does the rate constant $$k$$ change qualitatively?

Problem 2 – Molecular vibration energy#

A molecule vibrates with energy

$$ E = D_3 T_f^2. $$

If the chemist increases $$T_f$$ by 5%, what is the percent change in the vibrational energy $$E$$?

Problem 3 – pH resonance drift#

A solution’s pH drift under a resonance perturbation is modeled as

$$ ΔpH = \frac{F_3}{τ_r}. $$

If the chemist wants $$ΔpH$$ to decrease by 30%, how must the resonant-time $$τ_r$$ change?