Dependence of Solubility on pH - Video Tutorials & Practice Problems
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Davies Equation
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Davies Equation
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So in the past we learned that our activity coefficient which is represented by gamma and ionic strength which is represented by mu of a solution could be closely and accurately related by using the extended double Debbie huckle equation here, we'd say that the log of the activity coefficient equals negative 0.51 times the charge of the ion squared times the square root of your ionic strength divided by one plus alpha here represents the size parameter of the ion, usually in units of nanometers times the square root of your ionic strength divided by 305. Now, when the size parameter of the ion, which is alpha is unknown, we're gonna use instead the Davies equation now here because of the lack of a size parameter, this formula is most useful for mono valent ions. So ions with a charge of one plus or minus. So examples would be sodium or chloride ion. Now you could also use larger charges but it tends to be greater deviation um from credible value but you can still use larger charged ions as well. So here the equation is reformatted into log of activity coefficient equals negative 0.51 Z squared times the square root of your ionic strength divided by one plus your square root of ionic strength minus 10.3 times your ionic strength here we have our ionic strength values, they're increasing as we go down here, we have our charges plus or minus one plus or minus two plus or minus three and our activity coefficients notice that as your ionic strength is increasing, your activity coefficients are decreasing. Now we're going to say here from the Davis equations, all ions with the same magnitude in charge. So if two ions, one is plus one and the other one is minus one or plus two and minus two, they will have the same activity coefficient, which is what we're seeing here. Okay, so plus or minus, it really doesn't matter. And again that's because of the lack of an alpha value. We can group things together and make our list overall smaller. Traditionally when we're using the extended W huckle equation we segregate ions based on their charge as well as the value of their charge. Now that we've seen this attempt to do the practice question that's left here on the bottom of the page um Where were asked to determine what the activity coefficient is of calcium ion. When we have 0.25 Mueller of calcium phosphate here, we don't have the active, we don't have the size parameters so we're not gonna be able to use our typical extended W huckle equation. So try this question out if you get stuck. Don't worry, come back and see how I answer the same question
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Davies Equation
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So here it says calculate the activity coefficient of calcium ion in 0.25 moller of calcium phosphate. We're gonna have to utilize the Davies equation at some point. But first we need to understand what are ionic strength will be. We're gonna say here ionic strength equals half concentration. One times charge one squared plus concentration two times charge two squared. We're gonna say that this breaks up into three calcium ions plus two phosphate ions. Because there's three calcium ions, it's three times 30.25 molar. Which is gonna give me .075 moller and there's two phosphates. So that's two times .025 moller. Give Me .050 Moller. We're gonna say our ionic strength equals half. So the concentration of calcium ions times the charge squared of calcium plus the charge the concentration of phosphate ions times a charge squared. When we do all that we get an ionic strength of .375 molar. Now with that ionic strength we can plug it into each one of these ionic strengths here We use the charge of calcium ion to find log of our activity coefficient. So log of activity coefficient equals negative .51 plus two squared Times Square root of .375, Divided by one plus .375 Square root of that -3 times .375. So that's gonna equal negative 2.04 Times .612372 Divided by 1.612372 -1125. Then we're gonna say log of our activity coefficient equals negative .545-83. We don't want the log of our activity coefficient. We just want the activity coefficient. So activity coefficient equals 10 to the negative .545283. Which is gonna give me .28 as my activity coefficient. So here, utilizing the equation, we're able to find the activity coefficient of calcium ion Here, these values are just estimates there will be deviations from it if we venture away from mono valent ions. So here are charges plus two. So it's not a valid, it's di valid because it charges to with a charge. So this is how we get this activity coefficient of 0.28. Remember we rely on the Davies equation. If we don't know what the size parameter for the ion is. If we do know the size parameter then we rely on things such as interpolation or the extended huh? Debbie Hucles equation to help us find the activity coefficient for a specified ion. So remember the two equations that extended Debbie Hucles equation. Because when we know what the size parameter is, we can use interpretation as well to help us determine what the activity coefficient is. When size parameters are not known, rely more on the Davies equation
Ionic Salts & Solubility
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Ionic Salts & Solubility
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So remember when we talked about acids and bases reacting with one another, they helped to create water and assault that salt represents an ionic compound that's composed of a positive ion which is our cat ion and a negative ion which is our an ion. Remember based on the identities of these ions we can make either an acidic basic or neutral solution. Now we're going to see through the creation of these ions. How does ph play a factor on their cell viability? So if we take a look at cat ions which are positive ions, remember they're grouped as transition metals, main group metals as well as positive means remember for transition metals they have to be plus two or higher in charge to be acidic. If they're less than plus two then they are neutral. Here we have manganese, five iodide And we have five iodide. Remember we're only concerned with the positive ion for now since its transition metal with a charge of plus two or higher it is acidic. The main group metals they have to be plus three or higher in charge to be acidic. If they're less than plus three then they would be neutral. Here we have aluminum fluoride, aluminum and group +38. So it's plus three and then we have our three fluoride ions because aluminum is plus three it is high enough that it is acidic. Finally remember positive amines are automatically acidic here we have methyl ammonium ion as our positive ion and we have quarried i on this would be acidic. Now how does this tie into some liability and ph well we're gonna say remember cat ions make either an acidic or basic or acidic or neutral solution, we're gonna say here, if we increase if we're increasing the sai ability, that's a direct result of increasing your ph So if you make the solution more basic, it makes your acidic salt more soluble. That's because if we think about it, let's say we have here, Aluminum three plus that is acidic ion. An acidic ion would help to form acidic ions in solution. If I increase the ph that means I'm adding O H minus O H minus here is going to eat up this H plus ion and decrease its amount. If we decrease that amount according to the chandeliers principle, our reaction to shift to the right in order to replenish the ion that we just lost. So that's how the identity of our ionic salt can be affected by the presence of our ph. Now that we've seen. Can ions click onto the next video to look at and ions
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Ionic Salts & Solubility
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now for an ions we're gonna say here for an an eye and we're gonna add H plus ion to it. If you add an H plus ion to an an ion and you create a weak acid then your negative ion is basic. Here we have sodium nitrite nitrite ion is our negative ion. We add an H Plus to it to give us nitrous acid. Nitrous acid is a weak acid because it's a weak acid. That means that the negative ion is basic. If we add an H plus ion to the an ion and you create a strong acid though that means your negative ion is neutral. Here are negative ion in potassium chloride. Is the chloride ion add an H plus two. It gives us hcl. Now each sales a strong acid. And remember if you're strong as an asset that means you're conjugate base is incredibly weak. So weak that we just say that you're neutral. Now how does this tie in a solid ability? And ph again remember and ions are basically neutral here to increase the survivability of a basic ion. We want the solution to be acidic. So we want decreasing the ph because remember what's happening here is uh an eye on that is basic would react with water. And because it's basic that means water work as would act as an acid and donating H plus to the basic ion here we would get this plus O. H minus if you decrease the ph of a solution that means that you're making it more acidic by adding H. Plus that H Plus would actually counteract or neutralize this O. H minus or losing product. And according to the on the shuttlers principle to replenish that ion we'd have to move in the forward direction to make more. This means that more of this ion would have to break up in order to form that product and thereby increase the susceptibility of that particular ion. So remember for acidic salts we want to make the solution more basic to make it more soluble for basic salts. You want to make the solution more acidic to increase reliability. And remember for an esoteric species we have our acidic Amfa Terek species and our basic Amfa Terek species, they themselves also follow the same type of guidelines. Since they're acidic. You would want to increase the ph to make it more basic in order to increase their suitability. And these guys which are basic, you'd want to decrease the ph to make it more acidic and thereby increase their suitability.
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Ionic Salts & Solubility Calculations 1
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So here it states that barium carbonate is the slightly soluble ionic salt that results from the reaction between barium hydroxide and carbonic acid, identify the effect of increasing acidity on the solid ability of the given compound. Well here we have barium carbonate and it breaks up into barium ion and your carbonate ion here, barium is a main group metal. Remember main group metals have to be plus three or higher in order to be acidic because it's less than plus three or higher, it is neutral carbonate ion itself is a negative ion here. It's going to be a basic ionic salt. That's because if hydrogen carbonate or bicarbonate is basic in terms of an esoteric species, this which has even one less hydrogen would also be basic because it's basic, it would react with water. It would act as the base water would act as the acid donating an H. Plus to it. We would create Hc 03 minus plus O H minus. If we're increasing the acidity, that means we're adding H plus. Which does what it's going to neutralize this hydroxide ion because it's going to neutralize that hydroxide ion, it's going to decrease in amount. And according to settlers principle, we have to shift to the right in order to replenish it, thereby making this compound overall more soluble because it's gonna break up to form more of these products. Now in this question we're increasing the acidity of the compound technically this is basic and O H minus is basic but O H minus is a stronger base and therefore react even quicker and more so with any H. Plus that's added to my solution. So that's what we're focusing on the effect of O. H. Minus in terms of increasing acidity. So just remember if your basic ionic salt, your salt ability will increase as the ph decreases and the solution overall becomes more acidic. Now that you've seen this attempt to do the example question left on the bottom.
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Ionic Salts & Solubility Calculations 1
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So here it states which salts will be more soluble in an acidic solution than in pure water. So if you're in an acidic solution, remember that you'll be affected by that if you are a basic ion, basic ions become more soluble in acidic solution. And remember your basic ions are your negative ions. So here this is B R minus S. 0. 4 2 S. 0. 3 2 oh H minus and C L 04 minus first of all, bromide ion. When you add an H plus two it gives you Hbr which is a strong acid. So that means this negative ion is neutral. So that's out per chloride ion. Same thing, add an H plus to it. You create per cleric acid which is a strong acid. So the negative ion is neutral. If we look at the other options O H minus is if we add H plus to it we create water which is an esoteric, therefore weak. So and also you can say O H minus is a basic ion. So of course it's going to be affected by an acidic solution. So this would be one answer here, you add an H plus to it. You're going to create a church S. 03 minus which is a basic Amfa Terek ion. Since basic it will be affected and then here add an H plus to this this hydrogen sulfate or by sulfate is actually an acidic Amfa Terek ion. So it will not be affected in the same way. So because it's an acidic Amfa Terek ion it won't become more soluble, it'll become less soluble in acidic solution. So out of the choice is given only option C and D. Are the correct choice.
