## Abstract

When the only solute present is a weak acid, H*A*, which penetrates as molecules only into a living cell according to a curve of the first order and eventually reaches a true equilibrium we may regard the rate of increase of molecules inside as

See PDF for Equation

where *P _{M}* is the permeability of the protoplasm to molecules,

*M*, denotes the external and

_{o}*M*the internal concentration of molecules,

_{i}*A*denotes the internal concentration of the anion A

_{i}^{-}and

See PDF for Equation

(It is assumed that the activity coefficients equal 1.) Putting *P _{M}F_{M}* =

*V*, the apparent velocity constant of the process, we have

_{M}See PDF for Equation

where *e* denotes the concentration at equilibrium. Then

See PDF for Equation

where *t* is time.

The corresponding equation when ions alone enter is

See PDF for Equation.

where *K* is the dissociation constant of H*A*, *P _{A}* is the permeability of the protoplasm to the ion pair H

^{+}+ A

^{-}, and

*A*denotes the internal concentration of

_{ie}*A*at equilibrium. Putting

_{i}*P*=

_{A}KF_{M}*V*, the apparent velocity constant of the process, we have

_{A}See PDF for Equation

and

See PDF for Equation

When both ions and molecules of H*A* enter together we have

See PDF for Equation

where *S _{i}* =

*M*+

_{i}*A*and

_{i}*S*is the value of

_{ie}*S*at equilibrium. Then

_{i}See PDF for Equation

*V _{M}, V_{A}*, and

*V*depend on

_{MA}*F*and hence on the internal pH value but are independent of the external pH value except as it affects the internal pH value.

_{M}When the ion pair Na^{+} + A^{-} penetrates and Na_{i} = *BA _{i}*, we have

See PDF for Equation

and

See PDF for Equation

where *P*_{NaA} is the permeability of the protoplasm to the ion pair Na^{+} + A^{-}, Na_{o} and Na_{i} are the external and internal concentrations of Na^{+},

See PDF for Equation,

and *V*_{Na} is the apparent velocity constant of the process.

Equations are also given for the penetration of:

(1) molecules of H*A* and the ion pair Na^{+} + A^{-},

(2) the ion pairs H^{+} + A^{-} and Na^{+} + A^{-},

(3) molecules of H*A* and the ion pairs Na^{+} + A^{-} and H^{+} + A^{-}.

(4) The penetration of molecules of H*A* together with those of a weak base *Z*OH.

(5) Exchange of ions of the same sign.

When a weak electrolyte H*A* is the only solute present we cannot decide whether molecules alone or molecules and ions enter by comparing the velocity constants at different pH values, since in both cases they will behave alike, remaining constant if *F _{M}* is constant and falling off with increase of external pH value if

*F*falls off. But if a salt (

_{M}*e.g*., Na

*A*) is the only substance penetrating the velocity constant will increase with increase of external pH value: if molecules of H

*A*and the ions of a salt Na

*A*. penetrate together the velocity constant may increase or decrease while the internal pH value rises.

The initial rate

See PDF for Equation

(*i.e*., the rate when *M _{i}* = 0 and

*A*= 0) falls off with increase of external pH value if H

_{i}*A*alone is present and penetrates as molecules or as ions (or in both forms). But if a salt (

*e.g*., Na

*A*) penetrates the initial rate may in some cases decrease and then increase as the external pH value increases.

At equilibrium the value of *M _{i}* equals that of

*M*(no matter whether molecules alone penetrate, or ions alone, or both together). If the total external concentration (

_{o}*S*=

_{o}*M*+

_{o}*A*) be kept constant a decrease in the external pH value will increase the value of

_{o}*M*and make a corresponding increase in the rate of entrance and in the value at equilibrium no matter whether molecules alone penetrate, or ions alone, or both together.

_{o}What is here said of weak acids holds with suitable modifications for weak bases and for amphoteric electrolytes and may also be applied to strong electrolytes.

## Footnotes

- Accepted: 31 May 1929