Question

1.What is the ratio of v to v max expressed as a percentage when [s] = 30 km

Answer 1

Answer:

(a)96.77%

(b)3.23%

Step-by-step explanation:

Starting with the Michaelis-Menten equation which is used to model biochemical reactions:

Dividing both sides by $V_{\max }}$

$\dfrac{v}{V_{max}}=\dfrac{[S]}{K_M + [S]}$

Where: $V_{\max }} =$ maximum rate achieved by the system

$K_{\mathrm {M} }}$=The Michaelis constant

${\displaystyle {\ce {[S]}}}=$ Substrate concentration

(a) When $[S]=30K_M$

$\dfrac{v}{V_{max}}=\dfrac{[S]}{K_M + [S]}\\\dfrac{v}{V_{max}}=\dfrac{30K_M}{K_M + 30K_M}\\\dfrac{v}{V_{max}}=\dfrac{30}{1 + 30}\\\dfrac{v}{V_{max}}=\dfrac{30}{31}\\ Expressed as a percentage\\\dfrac{v}{V_{max}}=\dfrac{30}{31}X100=96.77\%$

(b)When $K_M=30[S]$

$\dfrac{v}{V_{max}}=\dfrac{[S]}{K_M + [S]}\\\dfrac{v}{V_{max}}=\dfrac{[S]}{30[S] + [S]}\\\\=\dfrac{1[S]}{30[S] + 1[S]}\\=\dfrac{1}{30 + 1}\\\dfrac{v}{V_{max}}=\dfrac{1}{31}\\ Expressed as a percentage\\\dfrac{v}{V_{max}}=\dfrac{1}{31}X100=3.23\%$