The Carbon Cycle and the Climate

Chemical Equilibrium Definition: “When the reactants and products are in a constant ratio. The forward reaction and the reverse reactions occur at the same rate when a system is in equilibrium.” (Chemicool)

One way to look at equilibrium is using the analogy of singles versus couples at a dance. Everyone comes to the dance unaccompanied but soon couples begin to form and get to know each other a bit and after a dance or two some will break up to reform singles. Equilibrium would be the state when the numbers of singles forming couples was equal to the number of couples breaking up to reform singles. This is also known as a dynamic equilibrium because if you look at the individual entities, the people in this analogy, they are constantly changing between being single or part of a couple, however if you look at the whole, the ratio of singles and couples, remains the same. This system is considered "dynamic" because change is occurring and at "equilibrium" because the overall effect is unchanged. Le Chatelier’s principle states that “when a stress is applied to a chemical system at equilibrium, the equilibrium concentrations will shift in a direction that reduces the effect of the stress.” This principle is a guide to show what will happen in a reaction once equilibrium has been established if a stress is placed on that reaction such as the addition or removal of reactants, products, temperature or pressure. (chemguide)

I think of the application of Le Chatelier’s Principle on equilibrium a bit like regaining the balance on a seesaw.

\[\text{A} + \text{B} \rightleftharpoons \text{C} + \text{D}\nonumber\]

When you add something on one side then in order to get back to equilibrium the reaction must shift to correct for the stress. For example if I dump in additional reactant A, in order to get back to equilibrium the reaction must shift to the right.

So what does shift to the right mean? More A present would result in more collisions between A and B creating more products and using up reactants. Eventually equilibrium would be established again.

Now be careful here, equilibrium does not mean equal mass or volume on both sides of the reaction. Sometimes equilibrium is established that favors the reactants and sometime it favors the products depending on the reactivity or stability of the substances involved.

An equilibrium expression and equilibrium constant are used to describe and calculate the relative concentrations to be found for each component of the reaction once equilibrium has been reached. The general reaction is written as:

\[a\text{A} + b\text{B} \rightleftharpoons c\text{C} + d\text{D}\nonumber\]

The equilibrium expression would be the equation:

\[\text{K}_{eq} = \dfrac{[\text{C}]^c[\text{D}]^d}{[\text{A}]^a[\text{B}]^b}\nonumber\]

where [C] represents the concentration or molarity of C when the reaction has reached equilibrium. And the superscript ^c is the coeffiecient from the balanced equation.

It should be noted that the Keq value is a constant for a particular reaction at a given temperature. If the temperature under which the reaction is carried out changes then the Keq value will also change, however at a constant temperature the Keq value will remain constant despite changes in the concentration of reactants used or the pressure the system is under. (chemguide)

Remember Le Chatelier’s principle from above? One important thing to remember here is that although it has been shown that a reaction will shift to balance out a stress this does not affect the value of Keq unless that change involves temperature. Any other change such as adding or removing reactants or products is balanced out by the shift and mathematically results in Keq remaining constant.

The Carbon Cycle, Le Chatelier’s principle, and The Climate.

One example of equilibrium found in environmental science is the contribution of the carbon cycle as a buffer to minimize the impacts of CO₂(g) on global temperatures.

Atmospheric CO₂(g) is in equilibrium with dissolved CO₂(aq). Atmospheric CO₂(g) leaves the atmosphere to become dissolved CO₂(aq) through direct contact with the water’s surface (lake, ocean or precipitation) and biological processes such as photosynthesis and digestion of organic carbon. Dissolved CO₂(aq) is released into the atmosphere by processes such as volcanic eruptions, respiration, decay and combustion of stored carbon such as firewood and fossil fuels.

So how does this balancing act work? Let’s look at some possible scenarios involving geology but rest assured that there are many other examples out there:

1. What will the results be if CO₂(g) concentration increases in the atmosphere because of an increased rate of outgassing?
Following Le Chatelier’s principle this will result in more CO₂(g) dissolving into water forming carbonic acid H₂C'O_3(g).
In the mean time and at the new equilibrium more CO₂(g) in the atmosphere causes an increase in air temperature due to additional absorption of UV radiation.

\[\ce{CO2 + H2O <-> H2CO3}\nonumber\]

Rising temperature and more dissolved CO₂(aq) (in the form of carbonic acid) lead to increased weathering of crustal rocks as a result of faster reaction rates (temperature effect) and greater acidity.

This form of chemical weathering reacts mineral material with carbonic acid forming calcium ions and bicarbonate ions \(\text{HCO}_3^-\). CO₂(g) has been removed from the air (albeit temporarily) and so air temperatures will decrease.

2. What will be the effect on the \(\ce{CO2 (g) -> CO2 (aq)}\) relationship if global temperatures cool “as a result of some astronomical forcing or tectonic/ocean circulation effect for example, the lower temperatures will result in lower rates of chemical weathering”?
First decreased weathering means less CO₂(g) being absorbed from the atmosphere by weathering reactions, leaving more CO₂(g) in the atmosphere.

What will happen to temperature in the atmosphere as a result?

You got it, they will increase as CO₂(g) is a greenhouse gas and converts wave energy to heat energy. (The Carbon Cycle)

3. And finally what if more rocks become available for weathering “as a result of mountain uplift” for example? More rocks exposed means an increased rate of weathering which will consume higher quantities of CO₂(g) in the form of carbonic acid. This creates a higher difference or gradient between dissolved aqueous CO₂(aq) and atmospheric CO₂(g). In order to reestablish equilibrium CO₂(g) will dissolve at a higher rate lowering the atmospheric CO₂(g) and resulting in a decrease of global temperatures.

“But the decreased temperatures will slow reaction rates, thereby using less CO₂(g), thus allowing temperatures to moderate”. (The Carbon Cycle)

(The Carbon Cycle) References: “Definition of equilibrium.” Chemicool Periodic Table. 6/16/2011 http://www.chemicool.com/definition/equilibrium.html. Clark, Jim. "An Introduction to Chemical Equilibria." Chemguide. UK, July 2010. Web. 16 Jun 2011. <http://www.chemguide.co.uk/physical/equilibria/introduction.html#top>. "The Carbon Cycle and Earth's Climate." Columbia University, n.d. Web. 16 Jun 2011. <http://www.columbia.edu/~vjd1/carbon.htm>.

From ChemPRIME: 13.0: Prelude to Equilibria

Contributors and Attributions

• Ed Vitz (Kutztown University), John W. Moore (UW-Madison), Justin Shorb (Hope College), Xavier Prat-Resina (University of Minnesota Rochester), Tim Wendorff, and Adam Hahn.