# Vmax, Km: Calculation of Kinetic Constants, first order

The initial velocity of an enzyme catalyzed reaction was measured at a serious of different initial substrate concentrations in the table. Find Km (sometimes called Ks)(the half velocity constant) and ...there is moreshow problemThe initial velocity of an enzyme catalyzed reaction was measured at a serious of different initial substrate concentrations in the table. Find Km (sometimes called Ks)(the half velocity constant) and max velocity Vmax. Over what substrate concentration rane would you expect reaction to approximately follow first order kinetics (i.e) V=(k first order) [S] and estimate k-first order

Units of [S] is M Velocity (V) in micromoles/liter-min

8.35 E-6 13.8

1.0E-5 16.0

1.25 E-5 19.1

1.67 E-5 23.8

2.0 E-5 26.7

2.5 E-5 30.8

3.3 E-5 36.2

5.0 E+5 44.5

1.0 E-4 57.2

2.0 E-4 66.7

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I know that at lower substrate concentrations, the reaction follows first order kinetics.

V= (Vmax[S])/(Km+[S])

Linearizing,

1/V= (Km/Vmax)(1/[S])+1/Vmax, this is Lineweaver Burk Double Reciprocal Plot

This is of form y=mx+b

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Please show a detailed solution, even the minor math. Thank you Mr. Allen.

#### Solution Preview

The first thing we do is transfer the data into Excel.

Please see attached Excel file.

Make sure that all of your numbers are transferred correctly and you haven't transposed the numbers wrong. For example, one of your data points is incorrect (the number 5.0 E+5 should be 5.0 E-5.) What I did was transfer the [S] data as regular numbers and then told Excel to format those cells so that the numbers would be displayed using scientific notation. That way I ensure I have transferred the data correctly.

Next thing you do is create columns B and D which will invert the data so you end up with reciprocal, i.e. 1/[S] and 1/Vo. I am using the variable Vo to indicate "initial velocity."

Once you've gotten reciprocal data (click on cell B2 to see how you can have Excel calculate reciprocal data automatically), then you highlight columns B1-11 and D1-11. You do this by highlight B1-11 first and then hold the Ctrl key down to highlight D1-11. If you do it correctly, you will only have highlighted the data in columns B and D. This is your "double ...

#### Solution Summary

The initial velocity of an enzyme catalyzed reaction was measured at a serious of different initial substrate concentrations in the table. Find Km (sometimes called Ks)(the half velocity constant) and ...there is moreshow problemThe initial velocity of an enzyme catalyzed reaction was measured at a serious of different initial substrate concentrations in the table. Find Km (sometimes called Ks)(the half velocity constant) and max velocity Vmax. Over what substrate concentration rane would you expect reaction to approximately follow first order kinetics (i.e) V=(k first order) [S] and estimate k-first order