Question

Carbon dioxide dissolves in water to form carbonic acid, which is primarily dissolved CO2. Dissolved CO2 satisfies the equilibrium equation CO2(g) CO2(aq) K=0.032 The acid dissociation constants listed in most standard reference texts for carbonic acid actually apply to dissolved CO2. For a CO2 partial pressure of 1.9x10-4 bar in the atmosphere, what is the pH of water in equilibrium with the atmosphere? (For carbonic acid Ka1 = 4.46x10-7 and Ka2 = 4.69x 10-11).

Answer 1

Step-by-step explanation:

The reaction equation will be as follows.

`CO_(2)(aq) + H_(2)O \rightleftharpoons H^(+)(aq) + HCO^(-)_(3)(aq)`

Calculate the amount of
`CO_(2)` dissolved as follows.

`CO_(2)(aq) = K_{CO_(2)} * P_{CO_(2)}`

It is given that
`K_{CO_(2)}` = 0.032 M/atm and
`P_{CO_(2)}` =
`1.9 * 10^(-4)` atm.

Hence,
`[CO_(2)]` will be calculated as follows.

`[CO_(2)]` =
`K_{CO_(2)} * P_{CO_(2)}`

=
`0.032 M/atm * 1.9 * 10^(-4)atm`

=
`0.0608 * 10^(-4)`

or, =
`0.608 * 10^(-5)`

It is given that
`K_(a) = 4.46 * 10^(-7)`

As,
`K_(a) = ([H^(+)]^(2))/([CO_(2)])`

`4.46 * 10^(-7) = ([H^(+)]^(2))/(0.608 * 10^(-5))`

`[H^(+)]^(2)` =
`2.71 * 10^(-12)`

`[H^(+)]` =
`1.64 * 10^(-6)`

Since, we know that pH =
`-log [H^(+)]`

So, pH =
`-log (1.64 * 10^(-6))`

= 5.7

Therefore, we can conclude that pH of water in equilibrium with the atmosphere is 5.7.