A leaf cell transports glucose from the cytosol (concentration 5 mM) to the vacuole (concentration 1 mM) by (i) passive diffusion through channels with permeability $P = 1.2\times10^{-6}\;\text{m\,s}^{-1}$ across a membrane area of $2\times10^{-9}\;\text{m}^{2}$, and (ii) active transport via a proton‑glucose symporter that moves glucose against the gradient at a rate of $2\times10^{-9}\;\text{mol\,s}^{-1}$ per cell, consuming one ATP per glucose molecule ($\Delta G_{\text{ATP}} = 30.5\;\text{kJ\,mol}^{-1}$). (a) Calculate the net molar flux of glucose into the vacuole by passive diffusion (in mol\,s⁻¹). (b) Determine the energy cost per second (in kJ\,s⁻¹) for the active transport pathway. (c) If the cell requires a total glucose import rate of $5\times10^{-9}\;\text{mol\,s}^{-1}$, what proportion of this must be supplied by active transport?

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(a) 9.6×10⁻¹⁵ mol s⁻¹; (b) 6.1×10⁻⁸ kJ s⁻¹; (c) ≈ 99.9998 % of the required import must be provided by active transport.

Gce Model Questions Vol1 2017 Biology Question 20

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