Problem on MM equation

Question

How to obtain relation between Vm and Km,given k(sec^-1) = Vmax/mg of enzyme x molecular weight x 1min/60 sec S* = 4.576(log K -10.753-logT+Ea/4.576T).

Answer 1

According to M.M Equation,
                                
                           V = Vmax x {S]/Km + {S]
                
Since Vmax = ksec^-1 {Et}

V = Ksec^-1{Et} x {S}/Km + {S}

Substituting the given value of Ksec^-1 in the above equation,we get
 
V = Vmax x mol.wt x 1min/60 sec x {S}/mg of enzyme / Km +{S]

V = Vmax x mol.wt x {S}/mg of enzyme/Km +{S}

Substituting the given value of {S}

V = Vmax x mol.wt x 4.576(log K -10.753-logT+Ea/4.576T)/mg of enzyme/ Km +  4.576(log K -10.753-logT+Ea/4.576T)