Wednesday, March 18, 2020

Ksp Chemistry Complete Guide to the Solubility Constant

Ksp Chemistry Complete Guide to the Solubility Constant SAT / ACT Prep Online Guides and Tips Are you learning chemistry but don’t quite understand the solubility product constant or want to learn more about it? Not sure how to calculate molar solubility from $K_s_p$? The solubility constant, or $K_s_p$, is an important part of chemistry, particularly when you’re working with solubility equations or analyzing the solubility of different solutes. When you have a solid grasp of $K_s_p$, those questions become much easier to answer! In this $K_s_p$ chemistry guide, we’ll explain the $K_s_p$ chemistry definition, how to solve for it (with examples), which factors affect it, and why it’s important. At the bottom of this guide, we also have a table with the $K_s_p$ values for a long list of substances to make it easy for you to find solubility constant values. What Is $K_s_p$? $K_s_p$ is known as the solubility constant or solubility product. It’s the equilibrium constant used for equations when a solid substance is dissolving in a liquid/aqueous solution. As a reminder, a solute (what is being dissolved) is considered soluble if more than 1 gram of it can be completely dissolved in 100 ml of water. $K_s_p$ is used for solutes that are only slightly soluble and don’t completely dissolve in solution. (A solute is insoluble if nothing or nearly nothing of it dissolves in solution.) $K_s_p$ represents how much of the solute will dissolve in solution. The value of $K_s_p$ varies depending on the solute. The more soluble a substance is, the higher its $K_s_p$ chemistry value. And what are the $K_s_p$ units? Actually, it doesn’t have a unit! The $K_s_p$ value does not have any units because the molar concentrations of the reactants and products are different for each equation. This would mean the $K_s_p$ unit would be different for every problem and would be difficult to solve, so in order to make it simpler, chemists generally drop $K_s_p$ units altogether. How nice of them! How Do You Calculate $K_s_p$? In this section, we explain how to write out $K_s_p$ chemistry expressions and how to solve for the value of $K_s_p$. For most chemistry classes, you’ll rarely need to solve for the value of $K_s_p$; most of the time you’ll be writing out the expressions or using $K_s_p$ values to solve for solubility (which we explain how to do in the â€Å"Why Is $K_s_p$ Important† section). Writing $K_s_p$ Expressions Below is the solubility product equation which is followed by four $K_s_p$ chemistry problems so you can see how to write out $K_s_p$ expressions. For the reaction $A_aB_b$(s) â‡Å' $aA^b^{+}$(aq) + $bB^a^{-}$ (aq) The solubility expression is $K_s_p$= $[A^b^{+}]^a$ $[B^a^{-}]^b$ The first equation is known as a dissociation equation, and the second is the balanced $K_s_p$ expression. For these equations: A and B represent different ions and solids. In these equations, they are also referred to as "products". a and b represent coefficients used to balance the equation (aq) and (s) indicate which state the product is in (aqueous or solid, respectively) Brackets stand for molar concentration. So [AgCl] represents the molar concentration of AgCl. In order to write $K_s_p$ expressions correctly, you need to have a good knowledge of chemical names, polyatomic ions, and the charges associated with each ion. Also, the key thing to be aware of with these equations is that each concentration (represented by square brackets) is raised to the power of its coefficient in the balanced $K_s_p$ expression. Let’s look at a few examples. Example 1 $PbBr_2$(s) â‡Å' $Pb^2^{+}$ (aq) + $2Br^{ ¯}$ (aq) $K_s_p$= $[Pb^2^{+}]$ $[Br ¯]^2$ In this problem, don’t forget to square the Br in the $K_s_p$ equation. You do this because of the coefficient â€Å"2† in the dissociation equation. Example 2 CuS(s) â‡Å' $Cu^{+}$ (aq) + S ¯(aq) $K_s_p$= [$Cu^{+}$] [S ¯] Example 3 $Ag_2CrO_4$ (s) â‡Å' 2$Ag^{+}$ (aq) + $CrO_4^2^{-}$ (aq) $K_s_p$= $[Ag^{+}]^2$ [$CrO_4^2$] Example 4 $Cu_3$ $(PO_4)^2$ (s) â‡Å' $3Cu^2^{+}$ (aq) + $2PO_4^3^{ ¯}$ (aq) $K_s_p$ = $[Cu^2^{+}]^3$ [$PO_4^3^ ¯$]$^2$ Solving for $K_s_p$ With Solubility In order to calculate a value for $K_s_p$, you need to have molar solubility values or be able to find them. Question: Determine the $K_s_p$ of AgBr (silver bromide), given that its molar solubility is 5.71 x $10^{ ¯}^7$ moles per liter. First, we need to write out the two equations. AgBr(s) â‡Å' $Ag^{+}$ (aq) + $Br^{ ¯}$ (aq) $K_s_p$ = [$Ag^{+}$] [$Br^{ ¯}$] Now, since in this problem we're solving for an actual value of $K_s_p$, we plug in the solubility values we were given: $K_s_p$ = (5.71 x $10^{ ¯}^7$) (5.71 x $10^{ ¯}^7$) = 3.26 x $10^{ ¯}^13$ The value of $K_s_p$ is 3.26 x $10^{ ¯}^13$ What Factors Affect $K_s_p$? In this section, we discuss the main factors that affect the value of the solubility constant. Temperature Most solutes become more soluble in a liquid as the temperature is increased. If you’d like proof, see how well instant coffee mixes in a cup of cold water compared to a cup of hot water. Temperature affects the solubility of both solids and gases but hasn’t been found to have a defined impact on the solubility of liquids. Pressure Pressure can also affect solubility, but only for gases that are in liquids. Henry's law states that the solubility of a gas is directly proportional to the partial pressure of the gas. Henry’s law is written as p=kc, where p is the partial pressure of the gas above the liquid k is Henry’s law constant c is the concentration of gas in the liquid Henry’s law shows that, as partial pressure decreases, the concentration of gas in the liquid also decreases, which in turn decreases solubility. So less pressure results in less solubility, and more pressure results in more solubility. You can see Henry’s law in action if you open up a can of soda. When the can is closed, the gas is under more pressure, and there are lots of bubbles because a lot of the gas is dissolved. When you open the can, the pressure decreases, and, if you leave the soda sitting out long enough, the bubbles will eventually disappear because solubility has decreased and they are no longer dissolved in the liquid (they’ve bubbled out of the drink). Molecular Size Generally, solutes with smaller molecules are more soluble than ones with molecules particles. It’s easier for the solvent to surround smaller molecules, so those molecules can be dissolved faster than larger molecules. Why Is $K_s_p$ Important? Why does the solubility constant matter? Below are three key times you’ll need to use $K_s_p$ chemistry. To Find the Solubility of Solutes Wondering how to calculate molar solubility from $K_s_p$? Knowing the value of $K_s_p$ allows you to find the solubility of different solutes. Here’s an example: The $K_s_p$ value of $Ag_2SO_4$ ,silver sulfate, is 1.4Ãâ€"$10^{–}^5$. Determine the molar solubility. First, we need to write out the dissociation equation: $K_s_p$=$ [Ag^{+}]^2$ $[SO_4^2]$ Next, we plug in the $K_s_p$ value to create an algebraic expression. 1.4Ãâ€"$10^{–}^5$= $(2x)^2$ $(x)$ 1.4Ãâ€"$10^{–}^5$= $4x^3$ $x$=[$SO_4^2$]=1.5x$10^{-}^2$ M $2x$= [$Ag^{+}$]=3.0x$10^{-}^2$ M To Predict If a Precipitate Will Form in Reactions When we know the $K_s_p$ value of a solute, we can figure out if a precipitate will occur if a solution of its ions is mixed. Below are the two rules that determine the formation of a precipitate. Ionic product $K_s_p$ then precipitation will occur Ionic product $K_s_p$ then precipitation will not occur To Understand the Common Ion Effect $K_s_p$ also is an important part of the common ion effect. The common ion effect states that when two solutions that share a common ion are mixed, the solute with the smaller $K_s_p$ value will precipitate first. For example, say BiOCl and CuCl are added to a solution. Both contain $Cl^{-}$ ions. BiOCl’s $K_s_p$ value is 1.8Ãâ€"$10^{–}^31$ and CuCl’s $K_s_p$ value is 1.2Ãâ€"$10^{–}^6$. BiOCl has the smaller $K_s_p$ value, so it will precipitate before CuCl. Solubility Product Constant Table Below is a chart showing the $K_s_p$ values for many common substances. The $K_s_p$ values are for when the substances are around 25 degrees Celsius, which is standard. Because the $K_s_p$ values are so small, there may be minor differences in their values depending on which source you use. The data in this chart comes from the University of Rhode Island’s Department of Chemistry. Substance Formula $K_s_p$ Value Aluminum hydroxide $Al(OH)_3$ 1.3Ãâ€"$10^{–}^33$ Aluminum phosphate $AlPO_4$ 6.3Ãâ€"$10^{–}^19$ Barium carbonate $BaCO_3$ 5.1Ãâ€"$10^{–}^9$ Barium chromate $BaCrO_4$ 1.2Ãâ€"$10^{–}^10$ Barium fluoride $BaF_2$ 1.0Ãâ€"$10^{–}^6$ Barium hydroxide $Ba(OH)_2$ 5Ãâ€"$10^{–}^3$ Barium sulfate $BaSO_4$ 1.1Ãâ€"$10^{–}^10$ Barium sulfite $BaSO_3$ 8Ãâ€"$10^{–}^7$ Barium thiosulfate $BaS_2O_3$ 1.6Ãâ€"$10^{–}^6$ Bismuthyl chloride $BiOCl$ 1.8Ãâ€"$10^{–}^31$ Bismuthyl hydroxide $BiOOH$ 4Ãâ€"$10^{–}^10$ Cadmium carbonate $CdCO_3$ 5.2Ãâ€"$10^{–}^12$ Cadmium hydroxide $Cd(OH)_2$ 2.5Ãâ€"$10^{–}^14$ Cadmium oxalate $CdC_2O_4$ 1.5Ãâ€"$10^{–}^8$ Cadmium sulfide $CdS$ 8Ãâ€"$10^{–}^28$ Calcium carbonate $CaCO_3$ 2.8Ãâ€"$10^{–}^9$ Calcium chromate $CaCrO_4$ 7.1Ãâ€"$10^{–}^4$ Calcium fluoride $CaF_2$ 5.3Ãâ€"$10^{–}^9$ Calcium hydrogen phosphate $CaHPO_4$ 1Ãâ€"$10^{–}^7$ Calcium hydroxide $Ca(OH)_2$ 5.5Ãâ€"$10^{–}^6$ Calcium oxalate $CaC_2O_4$ 2.7Ãâ€"$10^{–}^9$ Calcium phosphate $Ca_3(PO_4)_2$ 2.0Ãâ€"$10^{–}^29$ Calcium sulfate $CaSO_4$ 9.1Ãâ€"$10^{–}^6$ Calcium sulfite $CaSO_3$ 6.8Ãâ€"$10^{–}^8$ Chromium (II) hydroxide $Cr(OH)_2$ 2Ãâ€"$10^{–}^16$ Chromium (III) hydroxide $Cr(OH)_3$ 6.3Ãâ€"$10^{–}^31$ Cobalt (II) carbonate $CoCO_3$ 1.4Ãâ€"$10^{–}^13$ Cobalt (II) hydroxide $Co(OH)_2$ 1.6Ãâ€"$10^{–}^15$ Cobalt (III) hydroxide $Co(OH)_3$ 1.6Ãâ€"$10^{–}^44$ Cobalt (II) sulfide $CoS$ 4Ãâ€"$10^{–}^21$ Copper (I) chloride $CuCl$ 1.2Ãâ€"$10^{–}^6$ Copper (I) cyanide $CuCN$ 3.2Ãâ€"$10^{–}^20$ Copper (I) iodide $CuI$ 1.1Ãâ€"$10^{–}^12$ Copper (II) arsenate $Cu_3(AsO_4)_2$ 7.6Ãâ€"$10^{–}^36$ Copper (II) carbonate $CuCO_3$ 1.4Ãâ€"$10^{–}^10$ Copper (II) chromate $CuCrO_4$ 3.6Ãâ€"$10^{–}^6$ Copper (II) ferrocyanide $Cu[Fe(CN)_6]$ 1.3Ãâ€"$10^{–}^16$ Copper (II) hydroxide $Cu(OH)_2$ 2.2Ãâ€"$10^{–}^20$ Copper (II) sulfide $CuS$ 6Ãâ€"$10^{–}^37$ Iron (II) carbonate $FeCO_3$ 3.2Ãâ€"$10^{–}^11$ Iron (II) hydroxide $Fe(OH)_2$ 8.0$10^{–}^16$ Iron (II) sulfide $FeS$ 6Ãâ€"$10^{–}^19$ Iron (III) arsenate $FeAsO_4$ 5.7Ãâ€"$10^{–}^21$ Iron (III) ferrocyanide $Fe_4[Fe(CN)_6]_3$ 3.3Ãâ€"$10^{–}^41$ Iron (III) hydroxide $Fe(OH)_3$ 4Ãâ€"$10^{–}^38$ Iron (III) phosphate $FePO_4$ 1.3Ãâ€"$10^{–}^22$ Lead (II) arsenate $Pb_3(AsO_4)_2$ 4Ãâ€"$10^{–}^6$ Lead (II) azide $Pb(N_3)_2$ 2.5Ãâ€"$10^{–}^9$ Lead (II) bromide $PbBr_2$ 4.0Ãâ€"$10^{–}^5$ Lead (II) carbonate $PbCO_3$ 7.4Ãâ€"$10^{–}^14$ Lead (II) chloride $PbCl_2$ 1.6Ãâ€"$10^{–}^5$ Lead (II) chromate $PbCrO_4$ 2.8Ãâ€"$10^{–}^13$ Lead (II) fluoride $PbF_2$ 2.7Ãâ€"$10^{–}^8$ Lead (II) hydroxide $Pb(OH)_2$ 1.2Ãâ€"$10^{–}^15$ Lead (II) iodide $PbI_2$ 7.1Ãâ€"$10^{–}^9$ Lead (II) sulfate $PbSO_4$ 1.6Ãâ€"$10^{–}^8$ Lead (II) sulfide $PbS$ 3Ãâ€"$10^{–}^28$ Lithium carbonate $Li_2CO_3$ 2.5Ãâ€"$10^{–}^2$ Lithium fluoride $LiF$ 3.8Ãâ€"$10^{–}^3$ Lithium phosphate $Li_3PO_4$ 3.2Ãâ€"$10^{–}^9$ Magnesium ammonium phosphate $MgNH_4PO_4$ 2.5Ãâ€"$10^{–}^13$ Magnesium arsenate $Mg_3(AsO_4)_2$ 2Ãâ€"$10^{–}^20$ Magnesium carbonate $MgCO_3$ 3.5Ãâ€"$10^{–}^8$ Magnesium fluoride $MgF_2$ 3.7Ãâ€"$10^{–}^8$ Magnesium hydroxide $Mg(OH)_2$ 1.8Ãâ€"$10^{–}^11$ Magnesium oxalate $MgC_2O_4$ 8.5Ãâ€"$10^{–}^5$ Magnesium phosphate $Mg_3(PO_4)_2$ 1Ãâ€"$10^{–}^25$ Manganese (II) carbonate $MnCO_3$ 1.8Ãâ€"$10^{–}^11$ Manganese (II) hydroxide $Mn(OH)_2$ 1.9Ãâ€"$10^{–}^13$ Manganese (II) sulfide $MnS$ 3Ãâ€"$10^{–}^14$ Mercury (I) bromide $Hg_2Br_2$ 5.6Ãâ€"$10^{–}^23$ Mercury (I) chloride $Hg_2Cl_2$ 1.3Ãâ€"$10^{–}^18$ Mercury (I) iodide $Hg_2I_2$ 4.5Ãâ€"$10^{–}^29$ Mercury (II) sulfide $HgS$ 2Ãâ€"$10^{–}^53$ Nickel (II) carbonate $NiCO_3$ 6.6Ãâ€"$10^{–}^9$ Nickel (II) hydroxide $Ni(OH)_2$ 2.0Ãâ€"$10^{–}^15$ Nickel (II) sulfide $NiS$ 3Ãâ€"$10^{–}^19$ Scandium fluoride $ScF_3$ 4.2Ãâ€"$10^{–}^18$ Scandium hydroxide $Sc(OH)_3$ 8.0Ãâ€"$10^{–}^31$ Silver acetate $Ag_2CH_3O_2$ 2.0Ãâ€"$10^{–}^3$ Silver arsenate $Ag_3AsO_4$ 1.0Ãâ€"$10^{–}^22$ Silver azide $AgN_3$ 2.8Ãâ€"$10^{–}^9$ Silver bromide $AgBr$ 5.0Ãâ€"$10^{–}^13$ Silver chloride $AgCl$ 1.8Ãâ€"$10^{–}^10$ Silver chromate $Ag_2CrO_4$ 1.1Ãâ€"$10^{–}^12$ Silver cyanide $AgCN$ 1.2Ãâ€"$10^{–}^16$ Silver iodate $AgIO_3$ 3.0Ãâ€"$10^{–}^8$ Silver iodide $AgI$ 8.5Ãâ€"$10^{–}^17$ Silver nitrite $AgNO_2$ 6.0Ãâ€"$10^{–}^4$ Silver sulfate $Ag_2SO_4$ 1.4Ãâ€"$10^{–}^5$ Silver sulfide $Ag_2S$ 6Ãâ€"$10^{–}^51$ Silver sulfite $Ag_2SO_3$ 1.5Ãâ€"$10^{–}^14$ Silver thiocyanate $AgSCN$ 1.0Ãâ€"$10^{–}^12$ Strontium carbonate $SrCO_3$ 1.1Ãâ€"$10^{–}^10$ Strontium chromate $SrCrO_4$ 2.2Ãâ€"$10^{–}^5$ Strontium fluoride $SrF_2$ 2.5Ãâ€"$10^{–}^9$ Strontium sulfate $SrSO_4$ 3.2Ãâ€"$10^{–}^7$ Thallium (I) bromide $TlBr$ 3.4Ãâ€"$10^{–}^6$ Thallium (I) chloride $TlCl$ 1.7Ãâ€"$10^{–}^4$ Thallium (I) iodide $TlI$ 6.5Ãâ€"$10^{–}^8$ Thallium (III) hydroxide $Tl(OH)_3$ 6.3Ãâ€"$10^{–}^46$ Tin (II) hydroxide $Sn(OH)_2$ 1.4Ãâ€"$10^{–}^28$ Tin (II) sulfide $SnS$ 1Ãâ€"$10^{–}^26$ Zinc carbonate $ZnCO_3$ 1.4Ãâ€"$10^{–}^11$ Zinc hydroxide $Zn(OH)_2$ 1.2Ãâ€"$10^{–}^17$ Zinc oxalate $ZnC_2O_4$ 2.7Ãâ€"$10^{–}^8$ Zinc phosphate $Zn_3(PO_4)_2$ 9.0Ãâ€"$10^{–}^33$ Zinc sulfide $ZnS$ 2Ãâ€"$10^{–}^25$ Conclusion: $K_s_p$ Chemistry Guide What is $K_s_p$ in chemistry? The solubility product constant, or $K_s_p$, is an important aspect of chemistry when studying solubility of different solutes. $K_s_p$ represents how much of the solute will dissolve in solution, and the more soluble a substance is, the higher the chemistry $K_s_p$ value. To calculate the solubility product constant, you’ll first need to write out the dissociation equation and balanced $K_s_p$ expression, then plug in the molar concentrations, if you’re given them. The solubility constant can be affected by temperature, pressure, and molecular size, and it’s important for determining solubility, predicting if a precipitate will form, and understand the common ion effect.

Monday, March 2, 2020

Summary and Review of Proof, a Play from David Auburn

Summary and Review of Proof, a Play from David Auburn Proof  by David Auburn premiered on Broadway in October 2000. It received national attention, earning the Drama Desk Award, the Pulitzer Prize, and the Tony Award for Best Play. The play is intriguing with fascinating dialogue and two characters who are well-developed and an academic, mathematical theme. It does, however, have a few downfalls. Plot Overview of Proof Catherine, the twenty-something daughter of an esteemed mathematician, has just laid her father to rest. He died after suffering from a prolonged mental illness. Robert, her father, had once been a gifted, ground-breaking professor. But as he lost his sanity, he lost his ability to coherently work with numbers. The audience quickly learns: Catherine is brilliant in her own right, but she fears that she might possess the same mental illness which ultimately incapacitated her father.Her older sister wants to take her to New York where she can be cared for, in an institution if need be.Hal (a devoted student of Roberts) searches through the professors files hoping to discover something usable so that his mentors final years wont have been a complete waste. During the course of his research, Hal discovers a pad of paper filled with profound, cutting-edge calculations. He incorrectly assumes the work was Roberts. In truth, Catherine wrote the mathematic proof. No one believes her. So now she must provide proof that the proof belongs to her. (Note the double-entendre in the title.) What Works in Proof? Proof  works very well during the father-daughter scenes. Of course, there are only a couple of these since the father character, after all, is dead. When Catherine does converse with her father, these flashbacks reveal her often conflicting desires. We learn that Catherines academic goals are thwarted by her responsibilities to her ailing father. Her creative urges are offset for her propensity for lethargy. And she worries that her so-far undiscovered genius might be a tell-tale symptom of the same affliction to which her father succumbed. David Auburns writing is at its most heartfelt when father and daughter express their love (and sometimes despair) for math. There is a poetry to their theorems. In fact, even when Roberts logic has failed him, his equations exchange rationality for a unique form of poetry: Catherine (Reading from her fathers journal.)Let X equal the quantities of all quantities of X.Let X equal the cold.Its cold in December.The months of cold equal November through February. Another strong point of the play is Catherine herself. She is a strong female character: incredibly bright, but by no means prone to flaunting her intellect. She is by far the most well-rounded of the characters (in fact, with the exception of Robert, the other characters seem bland and flat by comparison). Proof  has been embraced by colleges and high school drama departments. And with a leading character like Catherine, it is easy to understand why. A Weak Central Conflict One of the major conflicts of the play is Catherines inability to convince Hal and her sister that she actually invented the proof in her fathers notebook. For a while, the audience ​is unsure as well. After all, Catherines sanity is in question. Also, she has yet to graduate from college. And, to add one more layer of suspicion, the math is written in her fathers handwriting. But Catherine has a lot of other things on her plate. Shes dealing with grief, sibling rivalry, romantic tension, and the slow sinking feeling of losing ones mind. She isnt terribly concerned about proving that the proof is hers. She is deeply annoyed that the people closest to her fail to believe her. For the most part, she doesnt spend much time trying to prove her case. In fact, she even tosses the notepad down, saying that Hal can publish it under his name. Ultimately, because she doesnt really care about the proof, we the audience dont care too much about it either, thereby diminishing the conflict. A Poorly Conceived Romantic Lead One more downside: Hal. This character is sometimes nerdy, sometimes romantic, sometimes charming. But for the most part, hes a dweeb. Hes the most skeptical about Catherines academic abilities, yet it seems that if he wanted, he could talk to her for about five minutes and discover her mathematical skills. But he never bothers until the plays resolution. Hal never states this, but it seems that his main contention against Catherines authorship of the proof boils down to sexism. Throughout the play, he seems on the verge of shouting: You couldnt have written this proof! Youre just a girl! How could you be good at math? Sadly, theres a half-hearted love story tacked on. Or maybe its a lust story. Its hard to say. During the second half of the play, Catherines sister discovers that Hal and Catherine have been sleeping together. Their sexual relationship seems very casual, but it does kick the level of betrayal up a notch when Hal continues to doubt Catherines genius.