One of the purposes of the kidneys is to transfer useful chemicals from the urine to the

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One of the purposes of the kidneys is to transfer useful chemicals from the urine to the blood, and toxins from the blood to the urine. In the transport of glucose from the urine to the blood, the kidneys are transporting glucose against a concentration gradient (that is, the direction of transport is from a low concentration to a high concentration). This can occur only because the transport is coupled with a chemical reaction, a process called active transport. If the concentration of glucose initially in the urine is 5 × 10−5 mol/kg and after leaving the kidney is 5 × 10−6 mol/kg, and the concentration of glucose in the blood (which has a much larger volume) is approximately constant at 5 × 10−3 mol/kg, compute the minimum work that must be done (or Gibbs energy supplied) per mole of glucose transported across the kidney.

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