Linear congruence theorem: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older edit
en>Fox Wilson
→‎System of linear congruences: all latexified now (hopefully)
Clarity: `external links'
 
Line 1: Line 1:
{{Unreferenced|date=December 2009}}
[[Wilhelm Ostwald]]’s '''dilution law''' is a relationship between the [[dissociation constant]] ''{{math|K<sub>d</sub>}}'' and the degree of dissociation ''{{math|α}}'' of a weak [[electrolyte]]. The law takes the form


<math>K_d = \cfrac{[A^+ ] [B^- ]}{[AB]} = \frac{\alpha^2}{1-\alpha} \cdot c_0 </math>


Where the square brackets denote concentration, and ''{{math|c<sub>0</sub>}}'' is the total concentration of electrolyte.
As vast as the San Diego harbor is, a simple walk<br><br>about it does not do it justice!  To partake in the<br><br>beauty that is San Diego Harbor, you need to have to take a<br><br>tour of the bay. San Diego Harbor Excursion can<br><br>aid you do that, as they are the most established<br><br>tour organization all through the bay.<br><br>As a guest, they will treat you with as 1 of them,<br><br>assisting to bring your cruise to life.  There are<br><br>a handful of parts to the tour, ensuring that you get the<br><br>most out of your time on the cruise.<br><br>Tour of the North Bay<br><br>On your tour of the North Bay, you will see the North<br><br>Island Naval Air Station, Shelter Islands, and even<br><br>the Naval Sub Base. If you look closely, you will<br><br>also be in a position see the Cabrillo National Monument as<br><br>well.<br><br>The tour of the [http://Search.Huffingtonpost.com/search?q=North+Bay&s_it=header_form_v1 North Bay] is around 12 miles in length<br><br>and lasts about an hour.  This is a fine tour for<br><br>anyone interested in the Navy as nicely. In the course of your<br><br>tour the guides will clarify every little thing to you as<br><br>you see it.  This way, you&quot;ll often know what is going<br><br>on.<br><br>Tour of the South Bay<br><br>Your tour of the South Bay consists of the Star of<br><br>India, the Naval surface fleet, Coronado Bay Bridge,<br><br>and the shipyards. This is a extremely busy and hectic<br><br>region, which makes a tour superb to see every thing<br><br>that this place has to provide.<br><br>The tour of South Bay is roughly 12 miles in length<br><br>and also lasts about an hour.  The guides will explain<br><br>issues here to you as nicely, ensuring that you know<br><br>exactly what you are seeing.<br><br>Tour of the Bay<br><br>Those of you who are hunting to see it all must go<br><br>for the [http://search.huffingtonpost.com/search?q=deluxe+tour&s_it=header_form_v1 deluxe tour] of the whole bay. You&quot;ll see<br><br>every little thing covered in the North and South Bay, along<br><br>with every thing else the bay has to provide. The tour<br><br>is about 25 miles in length and lasts around two hours.<br><br>To get started on your tour, all you need to have to do is<br><br>speak to the Harbor Excursion. The value for the tour<br><br>is very sensible, taking into consideration everything you will be<br><br>seeing.<br><br>If you take place to live in San Diego, taking the tour is<br><br>simpler than ever.  These of you who are going to or on<br><br>holiday really should give the tour a shot as effectively. For alternative viewpoints, people are able to gaze at: [http://www.cheap-lotrogold.com/with-tour-guide-training-you-can-get-paid-to-travel/ discover cyprus tours].  This way<br><br>you&quot;ll get to experience every little thing that San Diego Bay<br><br>has to offer you without having getting to stroll about. And<br><br>greatest of all - tour guides will explain the sights to<br><br>you - so you are going to never miss a second.<br><br>(word count 433)<br><br>PPPPP. Dig up further on this affiliated URL by navigating to [http://alendronatesodium.net/archives/7940 Charter Planes | Alen Dronate Sodium].<br><br>If you have any kind of inquiries pertaining to where and just how to make use of health issues ([http://www.playerforge.de/nullmisfit2212 linked resource site]), you can call us at our web site.
 
Concerning conductivity, this results in the following relation:
 
<math>K_c = \cfrac{\Lambda_c^2}{(\Lambda_0 - \Lambda_c)\Lambda_0} \cdot c </math>
 
==Derivation==
 
Consider a binary electrolyte AB which dissociates reversably into A<sup>+</sup> and B<sup>-</sup> ions. Ostwald noted that the [[law of mass action]] can be applied to such systems as dissociating electrolytes. The equilibrium state is represented by the equation:
 
<math>AB \rightleftharpoons  A^+ + B^-</math>
 
If ''{{math|α}}'' is the fraction of dissociated electrolyte, then ''{{math|αc<sub>0</sub>}}'' is the concentration of each ionic species. {{math|(1 - ''α'' )}} must, therefore be the fraction of ''undissociated'' electrolyte, and {{math|(1 - ''α'' )''c<sub>0</sub>''}} the concentration of same. The dissociation constant may therefore be given as
 
<math>K_d = \cfrac{[A^+ ] [B^- ]}{[AB]} = \cfrac{(\alpha c_0 )(\alpha c_0 )}{(1-\alpha) c_0 } = \cfrac{\alpha^2}{1-\alpha} \cdot c_0 </math>
 
 
For very weak electrolytes {{math|''α'' << 1}}, implying that {{math|(1 - ''α'' ) ≈ 1}}.
 
<math>K_d = \frac{\alpha^2}{1-\alpha} \cdot c_0 \approx \alpha^2 c_0 </math>
 
This gives the following results;
 
<math>\alpha = \sqrt{\cfrac{K_d }{c_0 }} </math>
 
Thus, degree of dissociation of a weak electrolyte is proportional to the inverse square root of the concentration, or the square root of the dilution. The concentration of any one ionic species is given by the root of the product of the dissociation constant and the concentration of the electrolyte.
 
<math>[A^+ ] = [B^- ] = \alpha c_0 = \sqrt{K_d c_0 } </math>
 
==Limitations==
 
The law holds good only for weak electrolytes and fails completely in the case of strong electrolytes. The value of 'α' is determined by conductivity measurements by applying the formula Λ/Λ∞. The value of 'α' determined at various dilutions of an electrolyte when substituted in Eq. (i) gives a constant value of K only in the case of weak electrolytes like CH3COOH, NH4OH, etc. the cause of failure of Ostwald's dilution law in the case of strong electrolytes is due to the following factors"
 
(i)  The law is based on the fact that only a portion of the electrolyte is dissociated into ions at ordinary dilution and completely at infinite dilution. Strong electrolytes are almost completely ionized at all dilutions and Λ/Λ∞ does not give accurate value of 'α'.
 
(ii) When concentration of the ions is very high, the presence of charges on the ions appreciably effects the equilibrium. Hence, law of mass action its simple form cannot be strictly applied in the case of strong electrolytes.
 
* K<sub>c</sub>: constant of dissociation
* <math>\Lambda_c</math>: [[conductivity (electrolytic)|equivalent conductivity]]
* <math>\Lambda_0</math>: boundary conductivity
* c: concentration of electrolyte.
 
==See also==
[[Autosolvolysis]]
{{DEFAULTSORT:Law Of Dilution}}
[[Category:Physical chemistry]]
[[Category:Enzyme kinetics]]

Latest revision as of 15:37, 27 February 2014


As vast as the San Diego harbor is, a simple walk

about it does not do it justice! To partake in the

beauty that is San Diego Harbor, you need to have to take a

tour of the bay. San Diego Harbor Excursion can

aid you do that, as they are the most established

tour organization all through the bay.

As a guest, they will treat you with as 1 of them,

assisting to bring your cruise to life. There are

a handful of parts to the tour, ensuring that you get the

most out of your time on the cruise.

Tour of the North Bay

On your tour of the North Bay, you will see the North

Island Naval Air Station, Shelter Islands, and even

the Naval Sub Base. If you look closely, you will

also be in a position see the Cabrillo National Monument as

well.

The tour of the North Bay is around 12 miles in length

and lasts about an hour. This is a fine tour for

anyone interested in the Navy as nicely. In the course of your

tour the guides will clarify every little thing to you as

you see it. This way, you"ll often know what is going

on.

Tour of the South Bay

Your tour of the South Bay consists of the Star of

India, the Naval surface fleet, Coronado Bay Bridge,

and the shipyards. This is a extremely busy and hectic

region, which makes a tour superb to see every thing

that this place has to provide.

The tour of South Bay is roughly 12 miles in length

and also lasts about an hour. The guides will explain

issues here to you as nicely, ensuring that you know

exactly what you are seeing.

Tour of the Bay

Those of you who are hunting to see it all must go

for the deluxe tour of the whole bay. You"ll see

every little thing covered in the North and South Bay, along

with every thing else the bay has to provide. The tour

is about 25 miles in length and lasts around two hours.

To get started on your tour, all you need to have to do is

speak to the Harbor Excursion. The value for the tour

is very sensible, taking into consideration everything you will be

seeing.

If you take place to live in San Diego, taking the tour is

simpler than ever. These of you who are going to or on

holiday really should give the tour a shot as effectively. For alternative viewpoints, people are able to gaze at: discover cyprus tours. This way

you"ll get to experience every little thing that San Diego Bay

has to offer you without having getting to stroll about. And

greatest of all - tour guides will explain the sights to

you - so you are going to never miss a second.

(word count 433)

PPPPP. Dig up further on this affiliated URL by navigating to Charter Planes | Alen Dronate Sodium.

If you have any kind of inquiries pertaining to where and just how to make use of health issues (linked resource site), you can call us at our web site.

Retrieved from "https://en.formulasearchengine.com/index.php?title=Linear_congruence_theorem&oldid=220121"