Final - Help Sheet

Reaction Velocity

v = \frac{k_{c a t} * [E_{T}] * [S]}{K_{M} + [S]}

v = \frac{v_{m a x} * [S]}{K_{M} + [S]}

α * K_{m} = K_{M}^{a p p}

V_{m a x} = k_{c a t} * [E_{T}]

α = 1 + \frac{[I]}{K_{I}}

Rate Equations

Zero Order : [A] = [A_{0}] * - k * t

1st Order : l n ([A]) = l n ([A_{0}]) * - k * t

2nd Order : \frac{1}{[A]} = \frac{1}{[A_{0}]} + (k * t)

Half Life Equations

t_{\frac{1}{2}} = \frac{1}{2} * \frac{[A_{0}]}{k}

t_{\frac{1}{2}} = \frac{l n (2)}{k}

t_{\frac{1}{2}} = \frac{1}{k * [A_{0}]}

Misc

Rate Enhancement (R E) = \frac{k_{c a t a l y z e d}}{k_{n o n - c a t a l y z e d}}

Rate Enhancement (R E) = e^{(\frac{Δ Δ G^{‡}}{R * T})}

Catalytic Efficiency = \frac{k_{c a t}}{K_{M}}

X - I n t e r c e p t = \frac{- 1}{K_{m}}

Y - I n t e r c e p t = \frac{1}{V_{m a x}}

S l o p e = \frac{K_{m}}{v_{m a x}}

Definitions

$\Delta G^{\circ \ddagger}$ = energy of the transition state

K_{I} = \frac{[E] * [I]}{[E I]}

K_{I}^{^{'}} = \frac{[E S] * [I]}{[E S I]}

α^{^{'}} = 1 + \frac{[I]}{K_{I}^{^{'}}}

Gas Constant = \frac{8.314 J}{K \cdot m o l}

Δ Δ G^{\circ ‡} = Δ G_{n o n - c a t a l y z e d}^{^{\circ} ‡} - Δ G_{c a t a l y z e d}^{^{\circ} ‡}

$\Delta \Delta G^{\circ \ddagger}$ = the difference in activation energies between the noncatalyzed and catalyzed reactions
- indicates by how many kJ/mol the transition state is stabilized in the catalyzed reaction

Competitive Inhibition :
- $K_M$ = increased
- $V_{max}$ = unchanged
- Lines = intersect on y-axis
Uncompetitive Inhibition :
- $K_M$ = decreased
- $V_{max}$ = decreased
- Lines = Parallel
Mixed Inhibition :
- $K_M$ = increased
- $V_{max}$ = decreased
- Lines = Intersect near the x-intercept