EG-203 Equations

Question 1

(Active Enzyme) [E]_active =

Answer 1

[E]_active = ([E]_0)(e^(-kdt))

Question 2

(Half Life) t_1/2 =

Answer 2

t_(1/2) = ln(2) / k_d

Question 3

rate, r

Answer 3

r = ((V_m)*[S]) / ((K_m) + [S])

Question 4

k =

Answer 4

k = A * e^(-E_a/RT)

Question 5

V_m =

Answer 5

V_m = (k_2) * [E]_0

Question 6

K_m =

Answer 6

K_m = ((k_-1) + (k_2)) / (k_1)

Question 7

X =

Answer 7

X = (X_0) * (e^(μ*t))

Question 8

t_d =

Answer 8

t_d = ln2 / μ

Question 9

μ =

Answer 9

μ = ((μ_m) * [S]) / (k_s + [S])

Question 10

Y_x/s =

Answer 10

Y_x/s = (-)(X - X_0) / ([S] - [S]_0)

Question 11

(batch) (n_t) / (n_0) =

Answer 11

(batch) (n_t) / (n_0) = e^((-k_d) * (t))

Question 12

(continuous) (n_t) / (n_0) =

Answer 12

(continuous) (n_t) / (n_0) = e^((-k_d) * (τ_hold))

Question 13

dV_f / dt =

Answer 13

dV_f / dt = (A * ∆P) / (μ_f (r_c + r_m))

Question 14

r_c =

Answer 14

r_c = (α) * ((c * V_f) / (A))

Question 15

α =

Answer 15

α = (α’) * (∆P)^(S)

Question 16

OTR =

Answer 16

OTR = (k_La) * ((C*) - (C_L))

Question 17

OUR =

Answer 17

OUR = (q_o2) * (X) = (μ * X) / (Y_x/o2)

Question 18

Y_x/o2 =

Answer 18

Y_x/o2 = (-) ((X) - (X_0)) / ([O2] - [O2]_0)

Question 19

(Integration) ∫ x^(n) dx =

Answer 19

∫ x^(n) dx = (1 / (n + 1)) * (x^(n+1))

Question 20

(Integration) ∫ (1 / x) dx =

Answer 20

∫ (1 / x) dx = ln ( x )

Question 21

(Integration) ∫ e^(ax) dx =

Answer 21

∫ e^(ax) dx = (1 / a) * (e^(ax))

Question 22

(Integration) ∫ 1 / (ax + b) dx =

Answer 22

∫ 1 / (ax + b) dx = (1 / a) * (ln(ax+b))

Question 23

Circumference of a Circle

Answer 23

pi * Diameter

Question 24

Area of Circle

Answer 24

pi * Radius^2

Question 25

Volume of Cylinder

Answer 25

pi * Radius^2 * Height

Question 26

(scale up/ down) - Constant mixing time

Answer 26

Constant Parameter = N

Question 27

(scale up/ down) - Constant shear (tip speed)

Answer 27

Constant Parameter = (N) (D_i)

Question 28

(scale up/ down) - Constant Re number

Answer 28

Constant Parameter = (N) (D_i)^2

Question 29

(scale up/ down) - Constant Oxygen Transfer Rate

Answer 29

Constant Parameter = (N)^3 (D_i)^2