code: def ANC_closed(pH, total_carbonates):
      
      return (total_carbonates * (u.eq/u.mol * alpha1_carbonate(pH) +
              2 * u.eq/u.mol * alpha2_carbonate(pH)) +
              1 * u.eq/u.mol * Kw/invpH(pH) - 1 * u.eq/u.mol * invpH(pH))
docs: Calculate the acid neutralizing capacity (ANC) under a closed system
      in which no carbonates are exchanged with the atmosphere during the
      experiment. Based on pH and total carbonates in the system.
  
      :param pH: pH of the system
      :type pH: float
      :param total_carbonates: Total carbonate concentration in the system (mole/L)
      :type total_carbonates: float
  
      :return: The acid neutralizing capacity of the closed system (eq/L)
      :rtype: float
  
      :Examples:
  
      >>> from aguaclara.research.environmental_processes_analysis import ANC_closed
      >>> from aguaclara.core.units import unit_registry as u
      >>> round(ANC_closed(10, 1*u.mol/u.L), 7)
      <Quantity(1.359831, 'equivalent / liter')>