What is the substrate concentration [S] when the Vo is 1/4 Vmax? Hint: start with Vo = (Vmax * [S]) / (Km + [S]) substitute in for the Vo and solve for [S]

Step-by-step explanation:

Given that,

Vo = ¼ Vmax

We are given the equation

Vo = (Vmax × [S]) / (Km + [S])

We want to find substrate [S]

Let substitute Vo = ¼Vmax into the given equation, so we have

Vo = (Vmax × [S]) / (Km + [S])

¼ Vmax = (Vmax × [S]) / (Km + [S])

Cross multiply

Vmax × (Km + [S]) = 4 × Vmax × [S] Divide both side by Vmax

(Km + [S]) = 4 × [S]

Km + [S] = 4•[S]

Make [S] subject of formula

4•[S] — [S] = Km

3•[S] = Km

Divide both sides by 3

[S] = Km / 3

[S] = ⅓ Km

So the substrate [S] is ⅓ Km when Vo is ¼Vmax