Question

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

2. same question but when km = 30[s]​

Answer 1

(a)96.77%

(b)3.23%

Explanation:

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

Dividing both sides by
`V_(\max )}`

`(v)/(V_(max))=([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`

`(v)/(V_(max))=([S])/(K_M + [S])\\(v)/(V_(max))=(30K_M)/(K_M + 30K_M)\\(v)/(V_(max))=(30)/(1 + 30)\\(v)/(V_(max))=(30)/(31)\\$Expressed as a percentage\\(v)/(V_(max))=(30)/(31)X100=96.77\%`

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

`(v)/(V_(max))=([S])/(K_M + [S])\\(v)/(V_(max))=([S])/(30[S] + [S])\\\\=(1[S])/(30[S] + 1[S])\\=(1)/(30 + 1)\\(v)/(V_(max))=(1)/(31)\\$Expressed as a percentage\\(v)/(V_(max))=(1)/(31)X100=3.23\%`