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# pH and Henry's Law

APCHEM-HEPYXF

Gaseous carbon dioxide, ${ CO }_{ 2 }(g)$, dissolves in water, producing an aqueous solution of carbonic acid, ${ H }_{ 2 }C{ O }_{ 3 }(aq)$. The reaction that occurs is actually an equilibrium between water (${ H }_{ 2 }O(l)$), dissolved carbon dioxide (${ CO }_{ 2 }(aq)$), and carbonic acid (${ H }_{ 2 }C{ O }_{ 3 }(aq)$).

$${ CO }_{ 2 }(aq)+{ H }_{ 2 }O(l)\rightleftharpoons { H }_{ 2 }C{ O }_{ 3 }(aq)$$

Carbonic acid is a very weak acid with a very small ${ K }_{ a(1) }$ value.

$${ H }_{ 2 }C{ O }_{ 3 }(aq)\rightleftharpoons { H }^{ + }(aq)+HC{ O }_{ 3 }^{ - }(aq)\quad \qquad { K }_{ a(1) }=4.3 \times { 10 }^{ -7 }$$

According to Henry's law, the concentration of a dissolved gas (${ C }_{ gas }$) is directly proportional to the partial pressure of the gas (${ P }_{ gas }$) in contact with the solution:

$${ C }_{ gas }=k{ P }_{ gas }$$

...where $k$ is called the Henry's Law constant and is specific to the particular gas-solvent system.

The figure below shows a cylinder fitted with a piston containing gaseous ${ CO }_{ 2 }$ in contact with an aqueous solution of the gas, ${ CO }_{ 2 }(aq)$.

If the pressure on the piston, indicated by the downward-pointing arrow, is increased at a constant temperature, which of the following will be the effect on the pH of the solution?

Consider both the predicted effect and the explanation given.

A

The pH will stay the same. The equilibrium constant, ${ K }_{ a(1) }=4.3 \times { 10 }^{ -7 }$, is unaffected by anything except a temperature change.

B

The pH will decrease. Increasing the pressure increases the concentration of ${ CO }_{ 2 }(aq)$, which, in turn, causes an increase in the concentration of ${ H }_{ 2 }C{ O }_{ 3 }(aq)$, shifting the equilibrium ionization of carbonic acid to the right, increasing $\left[ { H }^{ + } \right]$. Since $\left[ { H }^{ + } \right]$ increases, pH decreases.

C

The pH will stay the same. The concentration of ${ CO }_{ 2 }(aq)$ increases, but the percentage of ${ CO }_{ 2 }(aq)$ that is converted to ${ H }_{ 2 }C{ O }_{ 3 }(aq)$ remains the same, so long as temperature is constant.

D

The pH will increase. Increasing pressure favors the direction that produces fewer molecules/particles, causing ${ H }^{ + }(aq)$ and $HC{ O }_{ 3 }^{ - }(aq)$ to reunite, forming ${ H }_{ 2 }C{ O }_{ 3 }(aq)$. Since $\left[ { H }^{ + } \right]$ decreases, pH increases.