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The molecular biology of the cell (6 ed) claims that:

"Another [antiporter] [...] is a $Na^+$-driven$Cl^--HCO_3$-exchanger hat couples an influx of $Na^+$ to an efflux of $Cl^-$ and $H^+$. (so that $NaCO_3$ comes in and HCl gets out)"

In the next paragraph, (regarding a transporter with an opposite direction) we can read that:

"The movement of $HCO_3$ in this case is normally out of the cell, down its elecrochemical gradient, which decreases the pH of the cytosol".

Meaning that intracellular concentrations of $HCO_3$ typically must be higher thatn extracellular concentrations. In addition, Khan academy (among other sources) tell us that the extracellular concentration of $Cl^-$ is higher than intracellular concentration.

This means that for the price of one $Na^+$, the pump is moving two molecules ($HCO_3$ and $Cl^-$) against their gradients. How is this possible?

Is the $Na^+$-gradient really so strong that it can power this simultanous unfavourable transport? Or are multiple $Na^+$ ions used? Have I misinperpreted the intracellular/extracellular concentrations of $Cl^-$ and $HCO_3$?

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