Chemical Thermodynamics: CO2 dissolves in water, find molality and pH.

In summary: I've been admonished in the past for doing it. You can always start a new thread and include a link to the old one as reference.Yeah, but the folks running PF don't like having old threads dredged up. I've been admonished in the past for doing it. You can always start a new thread and include a link to the old one as reference.In summary, the conversation discusses the reaction of carbon dioxide with water to form carbonic acid, which can then dissociate into H+ and bicarbonate ions. The molality of carbonic acid and bicarbonate ions are calculated, along with the resulting pH of the solution. The potential issue of the resulting pH being highly acidic is brought up and
  • #1
Bosley
10
0

Homework Statement


When carbon dioxide "dissolves" in water, essentially all of it reacts to form carbonic acid, H2CO3:

CO2(s) + H2O(l) <--> H2CO3(aq).

The carbonic acid can then dissociate into H+ and bicarbonate ions,
H2CO3(aq) <--> H+(aq) + HCO3-(aq).

Consider a body of otherwise pure water that is in equilibrium with the atmosphere near sea level, where the partial pressure of carbon dioxide is 3.4 x 10-5 bar (aka 340 ppm). Calculate the molality of carbonic acid and of bicarbonate ions in the water, and determine the pH of the solution. Note that even 'natural' precipitation is somewhat acidic.

Homework Equations


At 298 K and 1 bar:
[tex]\Delta G[/tex] of [tex] H_{2}CO_{3}[/tex](aq) = -623.08 kJ
[tex]\Delta G[/tex] of [tex] CO_{2}[/tex](g) = -394.36 kJ
[tex]\Delta G[/tex] of [tex] H_{2}O[/tex](l) = -237.13 kJ
[tex]\Delta G[/tex] of [tex] H^{+}[/tex](aq) = 0 kJ
[tex]\Delta G[/tex] of [tex] HCO_{3}^{–} [/tex](aq) = -586.77 kJ

The Attempt at a Solution



Molalilty of carbonic acid:
First reaction [tex]\Delta G = 8.41 kJ[/tex].
[tex] m = (P/P_o)e^{-\Delta G / RT} [/tex]
[tex] m = (3.4 x 10^(-4) bar)/(1 bar) * e^{\frac{-8.41 x 10^3 J}{(8.315 J/mol k)* 298 K}} [/tex]
[tex] m = 1.141 x 10^{-5} [/tex] mol/kg

Molality of Bicarbonate ions:
Second reaction: [tex]\Delta G = 36.31 kJ[/tex].
[tex] m_{H^{+}} m_{HCO_{3}^{–}} = e^{-\Delta G / RT} [/tex]
[tex] m_{H^{+}} m_{HCO_{3}^{–}} = \displaystylee^{\frac{-36.31 x 10^3 J}{(8.315 J/mol k)*298 K}} [/tex]
[tex] m_{H^{+}} m_{HCO_{3}^{–}} = 4.3247 x 10^{-7} [/tex]
Since one of each ion comes out of every carbonic acid molecule, we must have:
[tex]m_{H+}=m_{CO_{3}^{–}} = sqrt{(4.3247E{-7})} = 6.576E{-4} mol / kg [/tex].

Then the pH is:
[tex] pH = –log_{10}(m_{H^{+}}) = –log_{10}(6.576 x 10^{-4}) = 3.18 [/tex]

This all seems well and good, but the final answer for pH that I'm getting is hugely acidic. And the problem says that we should get something just slightly acidic, since this is like rain water. I sense that the issue might be that when I calculate the molality of the bicarbonate ions, I'm not taking into account the fact that the carbonic acid was already really dilute. But I don't know how I would take that into account. Help please?

Thanks!
 
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  • #2
divide by molality in equation below \displaystylee is my guess.
 
  • #3
marty99 said:
divide by molality in equation below \displaystylee is my guess.
Please don't necropost to these old threads. The OP hasn't been seen on PF in more than 3 years and is long gone.
 
  • #4
SteamKing said:
Please don't necropost to these old threads. The OP hasn't been seen on PF in more than 3 years and is long gone.
what's the harm. someone might google this the way i did, it's not necessarily for OP.
 
  • #5
marty99 said:
what's the harm. someone might google this the way i did, it's not necessarily for OP.
Yeah, but the folks running PF don't like having old threads dredged up.
 

1. What is chemical thermodynamics?

Chemical thermodynamics is the study of the energy and heat changes that occur during chemical reactions and processes. It involves the application of thermodynamic principles to understand and predict the behavior of chemical systems.

2. How does CO2 dissolve in water?

CO2 dissolves in water through a process called dissolution, where the CO2 molecules are attracted to the water molecules and become surrounded by them. This forms a weak bond between the CO2 and water molecules, allowing the CO2 to dissolve in the water.

3. How do you find the molality of CO2 in water?

The molality of CO2 in water can be calculated by dividing the moles of CO2 by the mass of the water in kilograms. This can be expressed as mol/kg.

4. What is the pH of a solution containing dissolved CO2 in water?

The pH of a solution containing dissolved CO2 in water depends on the concentration of CO2. When CO2 dissolves in water, it reacts with water molecules to form carbonic acid (H2CO3), decreasing the pH of the solution. The lower the pH, the more acidic the solution is.

5. How does the molality of CO2 affect the pH of a solution?

The molality of CO2 has a direct effect on the pH of a solution. As the molality of CO2 increases, so does the concentration of carbonic acid in the solution. This results in a decrease in pH, making the solution more acidic.

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