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| [[File:Carbonate system of seawater.svg|thumb|Example Bjerrum plot: Change in carbonate system of seawater from [[ocean acidification]].]]
| | I've seen worse, fallen from worse, but there is a nice ride-around if you don't want to start the ride off with wounded bike or body parts. For more serious cyclists, next to bicycles themselves, proper shoes are the most important piece of equipment. You will find two main forms of mountain and road bike stems. If you don’t need the overly aggressive styling of the Scapel 5 then you will find the Rush 6 a welcome alternative. That attitude completely misses what is important about Papago Park. <br><br> |
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| A '''Bjerrum plot''' is a graph of the [[concentration]]s of the different species of a [[Acid#Polyprotic acids|polyprotic acid]] in a [[solution]], as functions of the solution's [[pH]],<ref name=Andersen>{{Cite journal |last=Andersen|first=C. B.|coauthors= |year=2002 |title=Understanding carbonate equilibria by measuring alkalinity in experimental and natural systems |url= |archiveurl= |archivedate= | journal=Journal of Geoscience Education |volume=50 |issue=4 |pages=389–403 |doi= |pmid= |bibcode=}}</ref> when the solution is at [[Chemical equilibrium|equilibrium]]. Due to the many [[orders of magnitude]] spanned by the concentrations, they are commonly plotted on a [[logarithmic scale]]. Sometimes the ratios of the concentrations are plotted rather than the actual concentrations. Occasionally H<sup>+</sup> and OH<sup>−</sup> are also plotted.
| | Cross Country and all mountain style riders will lean towards a folding bead tire because they are much lighter and that is a crucial factor in those 2 styles of riding. You can install an electric motor on your regular bike in about an hour or hire a bike mechanic to do it. Here are the answers and meanings to each of the things you encountered in this dream walk. He or she doesn't have to get into an accident just to understand how important it is to be fully protected before riding a motorbike. He is known for his expertise on the subject and on other Business and Finance related articles. <br><br>If you liked this posting and you would like to acquire a lot more info about [http://flappybirdgameonline.net/profile/65306/lajohns Choosing the right ride for you mountain bike sizing.] kindly check out our own web page. If you are looking for the best safety mountain bike accessories then the first thing you need to look into is a helmet. It is just much easier to be a participant in a team and enter the race as a whole unit. Guided by the dolphin trainer, they will perform a series of tricks such as clapping, synchronized jumping, etc. Being humiliated by my buddies was not fun, but there were enough good things about skiing that I wanted to come back for more, just not with my buddies. The bike shop personnel should be able to advise you on how to choose the right frame size. <br><br>With knowledge on the strengths and weakness of the MTB model, they are a great source of help. In between, the biker can perform whatever new trick he or she has learnt up and this trick is known as the gap jump. But older children may have more adventurous tastes, and want for toys that are - well, still miniatures, but are flashier, more expensive, and more functional. Mountain bikes are equipped with knobby tires, large number of gears and handle bars that are wider; they also include shocks and a much stronger suspension. But that wasn't the bad part 'cause, see, those two almost invisible grey hairs were only a distraction from the real culprit. <br><br>No matter what type of bike, no matter how old it is, no matter how much money you'd like to spend. Try finding the best bike for yourself at local shops, where you can take a test ride before you finally decide. It makes sense to promote your top performers, but just make sure it. If this happens shorten the length of the sides of the rectangle otherwise go back to level 3. Some riders advocate the additional technical the trail the greater a hardtail mountain bikeis sought after. |
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| Normally the carbonate system is plotted, where the polyprotic acid is [[carbonic acid]] (a [[diprotic acid]]), and the different species are [[carbonic acid]], [[carbon dioxide]], [[bicarbonate]], and [[carbonate]]. In acidic conditions, the dominant form is {{CO2}}; in [[Base (chemistry)|basic]] (alkalinic) conditions, the dominant form is CO<sub>3</sub><sup>2−</sup>; and in between, the dominant form is HCO<sub>3</sub><sup>−</sup>. At every pH, the concentration of carbonic acid is assumed to be [[negligible]] compared to the concentration of CO<sub>2</sub>, and so is often omitted from Bjerrum plots. These plots are typically used in ocean chemistry to track the response of an ocean to changes in both pH and of inputs in carbonate and {{chem|CO|2}}.<ref name="wolfgladrow2007">{{cite journal | author=D.A. Wolf-Gladrow| title=Total alkalinity: the explicit conservative expression and its application to biogeochemical processes| journal=Marine Chemistry| year=2007| volume=106| issue=1| url=http://www.soest.hawaii.edu/oceanography/faculty/zeebe_files/Publications/WolfGladrowMarChem07.pdf}}</ref>
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| The Bjerrum plots for other polyprotic acids, including [[Silicic acid|silicic]], [[Boric acid|boric]], [[Sulfuric acid|sulphuric]] and [[Phosphoric acid|phosphoric]] acids, can also be constructed.<ref name=Andersen />
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| ==Bjerrum plot equations for carbonate system==
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| If [[carbon dioxide]], [[carbonic acid]], [[hydron (chemistry)|hydrogen ions]], [[bicarbonate]] and [[carbonate]] are all dissolved in [[water]], and at [[chemical equilibrium]], their equilibrium [[concentration]]s are often assumed to be given by: | |
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| : <math> [\textrm{CO}_2]_{eq} = \frac{[\textrm{H}^+]_{eq}^2}{[\textrm{H}^+]_{eq}^2 + K_1[\textrm{H}^+]_{eq} + K_1K_2} \times \textrm{DIC}, </math>
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| : <math> [\textrm{HCO}_3^-]_{eq} = \frac{K_1[\textrm{H}^+]_{eq}}{[\textrm{H}^+]_{eq}^2 + K_1[\textrm{H}^+]_{eq} + K_1K_2} \times \textrm{DIC}, </math>
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| : <math> [\textrm{CO}_3^{2-}]_{eq} = \frac{K_1K_2}{[\textrm{H}^+]_{eq}^2 + K_1[\textrm{H}^+]_{eq} + K_1K_2} \times \textrm{DIC}, </math>
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| where the subscript 'eq' denotes that these are equilibrium concentrations, ''K<sub>1</sub>'' is the [[equilibrium constant]] for the reaction {{chem|CO|2}} + {{chem|H|2|O}} {{eqm}} H<sup>+</sup> + HCO<sub>3</sub><sup>−</sup> (ie. the first [[acid dissociation constant]] for carbonic acid), ''K<sub>2</sub>'' is the [[equilibrium constant]] for the reaction HCO<sub>3</sub><sup>−</sup> {{eqm}} H<sup>+</sup> + CO<sub>3</sub><sup>2−</sup> (ie. the second [[acid dissociation constant]] for carbonic acid), and DIC is the (unchanging) total [[concentration]] of [[Total inorganic carbon|dissolved inorganic carbon]] in the system, i.e. [{{CO2}}] + [HCO<sub>3</sub><sup>−</sup>] + [CO<sub>3</sub><sup>2−</sup>]. ''K<sub>1</sub>'', ''K<sub>2</sub>'' and DIC each have units of a [[concentration]], eg. [[Mole (unit)|mol]]/[[litre]].
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| A Bjerrum plot is obtained by using these three equations to plot these three species against pH = –{{nowrap|log<sub>10</sub>[H<sup>+</sup>]<sub>eq</sub>}}, for given ''K<sub>1</sub>'', ''K<sub>2</sub>'' and DIC. The fractions in these equations give the three species' relative proportions, and so if DIC is unknown, or the actual concentrations are unimportant, these proportions may be plotted instead.
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| These three equations show that the curves for {{CO2}} and HCO<sub>3</sub><sup>−</sup> intersect at [H<sup>+</sup>]<sub>eq</sub> = ''K<sub>1</sub>'', and the curves for HCO<sub>3</sub><sup>−</sup> and CO<sub>3</sub><sup>2−</sup> intersect at [H<sup>+</sup>]<sub>eq</sub> = ''K<sub>2</sub>''. Therefore, the values of ''K<sub>1</sub>'' and ''K<sub>2</sub>'' that were used to create a given Bjerrum plot can easily be found from that plot, by reading off the concentrations at these points of intersection.
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| ==Chemical and mathematical derivation of Bjerrum plot equations for carbonate system==
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| Suppose that the reactions between [[carbon dioxide]], [[hydron (chemistry)|hydrogen ions]], [[bicarbonate]] and [[carbonate]] [[ions]], all dissolved in [[water]], are as follows:
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| : {{chem|CO|2}} + {{chem|H|2|O}} {{eqm}} H<sup>+</sup> + HCO<sub>3</sub><sup>−</sup> {{space}} {{space}} {{space}} {{space}} {{space}} {{space}} {{space}} (1)
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| : {{space}} {{space}} {{space}} HCO<sub>3</sub><sup>−</sup> {{eqm}} H<sup>+</sup> + CO<sub>3</sub><sup>2−</sup>. {{space}} {{space}} {{space}} {{space}} {{space}} {{space}} {{space}} (2)
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| (Note that reaction (1) is actually the combination of two [[elementary reaction]]s: {{chem|CO|2}} + {{chem|H|2|O}} {{eqm}} {{chem|H|2|CO|3}} {{eqm}} H<sup>+</sup> + HCO<sub>3</sub><sup>−</sup>.)
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| Assuming the [[mass action law]] applies to these two reactions, that water is [[Abundance (chemistry)|abundant]], and that the different chemical species are always well-mixed, their [[rate equation]]s are:
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| : <math>\frac{\textrm{d}[\textrm{CO}_2]}{\textrm{d}t}= -k_1[\textrm{CO}_2] + k_{-1}[\textrm{H}^+][\textrm{HCO}_3^-], </math>
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| : <math>\frac{\textrm{d}[\textrm{H}^+]}{\textrm{d}t}= k_1[\textrm{CO}_2] - k_{-1}[\textrm{H}^+][\textrm{HCO}_3^-] + k_2[\textrm{HCO}_3^-] - k_{-2}[\textrm{H}^+][\textrm{CO}_3^{2-}], </math>
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| : <math>\frac{\textrm{d}[\textrm{HCO}_3^-]}{\textrm{d}t}= k_1[\textrm{CO}_2] - k_{-1}[\textrm{H}^+][\textrm{HCO}_3^-] - k_2[\textrm{HCO}_3^-] + k_{-2}[\textrm{H}^+][\textrm{CO}_3^{2-}], </math>
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| : <math>\frac{\textrm{d}[\textrm{CO}_3^{2-}]}{\textrm{d}t}= k_2[\textrm{HCO}_3^-] - k_{-2}[\textrm{H}^+][\textrm{CO}_3^{2-}], </math>
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| where [{{space}}] denotes [[concentration]], ''t'' is time, and ''k<sub>1</sub>'' and ''k<sub>-1</sub>'' are appropriate [[Proportionality (mathematics)|proportionality]] constants for reaction (1), called respectively the forwards and reverse [[Reaction rate constant|rate constants]] for this reaction. (Similarly ''k<sub>2</sub>'' and ''k<sub>-2</sub>'' for reaction (2).)
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| {{space}}
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| '''At any [[Chemical equilibrium|equilibrium]]''', the concentrations are unchanging, hence the left hand sides of these equations are zero. Then, from the first of these four equations, the ratio of reaction (1)'s rate constants equals the ratio of its equilibrium concentrations, and this ratio, called ''K<sub>1</sub>'', is called the [[equilibrium constant]] for reaction (1), i.e.
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| : <math> K_1 = \frac{k_1}{k_{-1}} = \frac{[\textrm{H}^+]_{eq}[\textrm{HCO}_3^-]_{eq}}{[\textrm{CO}_2]_{eq}}, </math> {{space}} {{space}} {{space}} {{space}} (3) {{space}} {{space}} {{space}} {{space}}
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| where the subscript 'eq' denotes that these are equilibrium concentrations.
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| Similarly, from the fourth equation for the [[equilibrium constant]] ''K<sub>2</sub>'' for reaction (2),
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| : <math> K_2 = \frac{k_2}{k_{-2}} = \frac{[\textrm{H}^+]_{eq}[\textrm{CO}_3^{2-}]_{eq}}{[\textrm{HCO}_3^-]_{eq}}. </math> {{space}} {{space}} {{space}} {{space}} {{space}} (4)
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| Rearranging (3) gives
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| : <math> [\textrm{HCO}_3^-]_{eq} = \frac{K_1[\textrm{CO}_2]_{eq}}{[\textrm{H}^+]_{eq}}, </math> {{space}} {{space}} {{space}} {{space}} (5)
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| and rearranging (4), then substituting in (5), gives
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| : <math> [\textrm{CO}_3^{2-}]_{eq} = \frac{K_2[\textrm{HCO}_3^-]_{eq}}{[\textrm{H}^+]_{eq}}
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| = \frac{K_1K_2[\textrm{CO}_2]_{eq}}{[\textrm{H}^+]_{eq}^2}. </math> {{space}} {{space}} {{space}} {{space}} (6)
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| {{space}}
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| The total [[concentration]] of [[Total inorganic carbon|dissolved inorganic carbon]] in the system is given by
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| : <math> \textrm{DIC} = [\textrm{CO}_2] + [\textrm{HCO}_3^-] + [\textrm{CO}_3^{2-}] </math>
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| : {{space}} {{space}} {{space}} {{space}} {{space}} <math> = [\textrm{CO}_2]_{eq} \left(1 + \frac{K_1}{[\textrm{H}^+]_{eq}} + \frac{K_1K_2}{[\textrm{H}^+]_{eq}^2}\right) </math> {{space}} {{space}} {{space}} {{space}} {{space}} {{space}} {{space}} {{space}} substituting in (5) and (6)
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| : {{space}} {{space}} {{space}} {{space}} {{space}} <math> =
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| [\textrm{CO}_2]_{eq} \left(\frac{[\textrm{H}^+]_{eq}^2 + K_1[\textrm{H}^+]_{eq}+K_1K_2}{[\textrm{H}^+]_{eq}^2}\right). </math>
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| {{space}}
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| This gives the equation for [{{chem|CO|2}}]. The equations for [HCO<sub>3</sub><sup>−</sup>] and [CO<sub>3</sub><sup>2−</sup>] are obtained by substituting this into (5) and (6).
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| == See also ==
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| * [[Fresh water]]
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| * [[Seawater]]
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| * [[Thermohaline circulation]]
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| == References ==
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| {{reflist}}
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| [[Category:Chemical oceanography]]
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| [[Category:Aquatic ecology]]
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| [[Category:Oceanography]]
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| [[Category:Thermodynamics]]
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I've seen worse, fallen from worse, but there is a nice ride-around if you don't want to start the ride off with wounded bike or body parts. For more serious cyclists, next to bicycles themselves, proper shoes are the most important piece of equipment. You will find two main forms of mountain and road bike stems. If you don’t need the overly aggressive styling of the Scapel 5 then you will find the Rush 6 a welcome alternative. That attitude completely misses what is important about Papago Park.
Cross Country and all mountain style riders will lean towards a folding bead tire because they are much lighter and that is a crucial factor in those 2 styles of riding. You can install an electric motor on your regular bike in about an hour or hire a bike mechanic to do it. Here are the answers and meanings to each of the things you encountered in this dream walk. He or she doesn't have to get into an accident just to understand how important it is to be fully protected before riding a motorbike. He is known for his expertise on the subject and on other Business and Finance related articles.
If you liked this posting and you would like to acquire a lot more info about Choosing the right ride for you mountain bike sizing. kindly check out our own web page. If you are looking for the best safety mountain bike accessories then the first thing you need to look into is a helmet. It is just much easier to be a participant in a team and enter the race as a whole unit. Guided by the dolphin trainer, they will perform a series of tricks such as clapping, synchronized jumping, etc. Being humiliated by my buddies was not fun, but there were enough good things about skiing that I wanted to come back for more, just not with my buddies. The bike shop personnel should be able to advise you on how to choose the right frame size.
With knowledge on the strengths and weakness of the MTB model, they are a great source of help. In between, the biker can perform whatever new trick he or she has learnt up and this trick is known as the gap jump. But older children may have more adventurous tastes, and want for toys that are - well, still miniatures, but are flashier, more expensive, and more functional. Mountain bikes are equipped with knobby tires, large number of gears and handle bars that are wider; they also include shocks and a much stronger suspension. But that wasn't the bad part 'cause, see, those two almost invisible grey hairs were only a distraction from the real culprit.
No matter what type of bike, no matter how old it is, no matter how much money you'd like to spend. Try finding the best bike for yourself at local shops, where you can take a test ride before you finally decide. It makes sense to promote your top performers, but just make sure it. If this happens shorten the length of the sides of the rectangle otherwise go back to level 3. Some riders advocate the additional technical the trail the greater a hardtail mountain bikeis sought after.