Answer  Hint: Potassium nitrate also known as saltpetre has a chemical formula $KN{O_3}$. It is a white solid that is soluble in water and is formed when sodium nitrate and potassium chloride solution undergo fractional distillation. It is widely used in gunpowder and in chemistry labs for preparation of nitric acid. Complete answer: At room temperature, the structure of potassium nitrate is an orthorhombic crystal which converts to a trigonal system when the temperature rises to ${129^ \circ }C$. Ionic compounds are more soluble in water as compared to covalent compounds and potassium nitrate i.e., $KN{O_3}$ is an ionic salt of potassium ion \[({K^ + })\] and nitrate ions \[(N{O_3}^ - )\] and when dissolved in water, the positive side of the water dipole is attracted by \[N{O_3}^ - \] ions whereas the negative side of the dipole of water is attracted by \[{K^ + }\] ions. Hence it is soluble in water.Potassium nitrate is not highly soluble in water but as the temperature increases, its solubility in water also increases. It has a tendency to absorb $0.03\% $ of water in $80\% $ relative humidity over $50$ days, hence it is not very hygroscopic i.e., it has a very less tendency to hold water molecules in its surroundings. The variation of solubility of potassium nitrate with temperature is shown as per following graph:
Note: Potassium nitrate has many uses like it is widely used as gunpowder in the explosives like grenades, bombs, etc. It is also used in the production and manufacturing of cigarettes. It is also used in the food industry as a preservative for meat and other food products. So, you know that potassium nitrate, #"KNO"3#, has a solubility of #"155 g"# per #"100 g"# of water at #75^@"C"# and of #"38.0 g"# at #25^@"C"#. What that means is that at #75^@"C"#, you can dissolve as much as #"155 g"# of solid potassium nitrate in water without the solution becoming saturated. Once you hit that #"155 g"# mark, the solution becomes saturated, which means that the solution can't dissolve any more solid. Now, the same thing can be said for the solution at #25^@"C"#. At this temperature, dissolving less than #"38.0 g"# of potassium nitrate per #"100 g"# of water will result in an unsaturated solution. At the #"38.0 g"# mark, the solution will become saturated. Now, take a look at how the solubility graph for potassium nitrate looks like So, you are starting with #"100 g"# of saturated solution at #75^@"C"#. Mind you, you have #"100 g"# of solution that contains as much dissolved potassium nitrate as possible. This solution will contain
Now, potassium nitrate's solubility is given per #"100 g"# of water. Calculate how much water you have in this initial solution
Next, determine how much potassium nitrate can be dissolved in #"39.22 g"# of water at #26^@"C"# in order to make a saturated solution, i.e. have the maximum amount of dissolved potassium nitrate possible
This means that when the initial solution is cooled from #75^@"C"# to #25^@"C"#, the amount of water that it contained will only hold #"14.9 g"# of dissolved potassium nitrate. The rest will crystallize out of solution
The answer is rounded to three sig figs. From Sciencemadness Wiki
Potassium nitrate, also known as saltpeter or saltpetre or Indian saltpeter, is an important chemical compound in both industry and chemistry. Known for centuries for its role in early pyrotechnics, the nitrate ion makes KNO3 a widely used oxidizer with a variety of uses inside and outside pyrotechnics. PropertiesChemicalPotassium nitrate is a good source of both potassium and nitrate ions. When heated to to temperatures between 550 and 790 °C, under an oxygen atmosphere, it loses oxygen and converts into potassium nitrite: 2 KNO3 → 2 KNO2 + O2Molten potassium nitrate will react with carbon dioxide and water vapors to form potassium carbonate and hydroxide.[1] Potassium nitrate will react with hydrochloric acid to release nitric acid, that will give off nitrogen dioxide fumes: 2 KNO3 + 2 HCl + H2O → 2 KCl + HNO3 + NO2 + H2OBy adding an excess of HCl, this reaction can be used to generate "poor man's aqua regia". A substantial amount of energetic materials are based on the nitrate ion, and it is arguably the most important ion when it comes to explosives, such as black powder. 10 KNO3 + 3 S + 8 C → 2 K2CO3 + 3 K2SO4 + 6 CO2 + 5 N2A less known reaction is the synthesis of potassium cyanide, by reacting a mixture of potassium nitrate and charcoal in a cast iron bowl, in an inert atmosphere to prevent combustion or oxidation to potassium cyanate: 2 KNO3 + 7 C → KCN + KOCN + 5 CO[2]If you attempt to try this reaction, AVOID ADDING ACID TO THE RESULTED SLAG AS IT WILL GIVE OFF HYDROGEN CYANIDE GAS WHICH CAN BE DEADLY (see the Sciencemadness thread below). Presence of iron may also lead to formation of Prussian blue. A mixture of sucrose (most sugars work) and potassium nitrate known as rock candy can be ignited, producing pink flames and large amounts of white smoke, useful for improvised smoke bombs. The solid end product of this reaction is potassium carbonate, plus some of the leftover reactants. KNO3 + C12H22O11 → K2CO3 + CO2 + N2The ignition also releases copious amounts of caramelized sugar particles, giving the smoke a sweet fragrance. PhysicalPotassium nitrate is white solid with a melting point of 334 °C. Its solubility curve makes recrystallization easy, being only somewhat soluble in freezing water (13.3 g/100 ml at 0 °C), but very soluble in boiling water (246 g/100 ml at 100 °C). It is not hygroscopic, absorbing about 0.03% water in 80% relative humidity over a period of 50 days. Potassium nitrate is soluble in anhydrous basic solvents, like ammonia and hydrazine, as well as glycerol, but only slightly soluble in ethanol and methanol. Pure KNO3 is odorless and has a slight bitter taste. AvailabilityIn many American hardware stores, potassium nitrate is sold in a reasonably pure form as a stump remover, which can be purified by recrystallization from water. Care must be taken if it is being bought this way, as some stump removers mostly consist of other agents, such as sodium metabisulfite, which can be a rude awakening to one treating it as potassium nitrate. Potassium nitrate is much more commonly encountered as fertilizer, either pure or mixed with traces of other substances. If it's present as prills, recrystallization might be required as the granules are difficult to grind properly in a mortar. Some types of prills tend to be covered with an anti-caking agent, such as calcium stearate, and filtration before recrystallization is required for purification. It's easy to determine if the saltpeter source has anticaking agent, as when the solution gets more concentrated solution, it will darken. Potassium nitrate fertilizers can be identified after the NPK number 13-0-46. Potassium nitrate occurs naturally as the mineral niter (or nitre). PreparationPotassium nitrate can be prepared by neutralizing KOH with nitric acid or adding ammonium nitrate to it. KOH + HNO3 → KNO3 + H2O KOH + NH4NO3 → KNO3 + NH3 + H2OIt can also be made by a double displacement reaction between ammonium nitrate and potassium sulfate or potassium chloride, and then recrystallizing the KNO3 out at low temperatures. This reaction can also be done using potassium sulfate and sodium nitrate, but instead of crystallizing potassium nitrate, sodium sulfate is crystallized out along with some of the potassium nitrate at low temperatures, leaving most of the desired product in solution. A reaction between a small amount of ice or water, potassium hydroxide, and ammonium nitrate easily proceeds to completion very exothermically, driving ammonia gas out of the mixture and producing potassium nitrate as an end product. This can also be done with potassium carbonate, but the carbonate route requires heating the two in solution. Another method is a double displacement from barium nitrate with potassium carbonate or potassium sulfate. The resulting barium carbonate or sulfate can be filtered off, leaving potassium nitrate in solution. The nitrate ion itself is very difficult to make from other OTC chemicals, and despite the increasing difficulty in obtaining this salt, buying it in pure or impure from is the only real viable option. An old method of making saltpeter involves separating nitrates from manure, and adding potash. The resulting solution is recrystallized repeatedly until fairly pure saltpeter is obtained. This method requires large amounts of manure, but can be done fairly easy if one has a farm or a big garden. ProjectsHandlingSafetyPotassium nitrate is virtually non-toxic, and is even approved for use in food as a preservative (E252). Soldiers of the early modern era even used the saltpeter-based black powder as a table salt substitute to sprinkle on their rations. While generally quite stable, it is an oxidizing agent, so mixtures with reducing agents like sucrose, red phosphorus, sulfur, magnesium or aluminium should not be ground or pressed together, and the risk of spontaneous ignition is ever present. Sulfur is especially dangerous, as acidic traces can greatly increase the sensitivity of energetic mixtures. As it is not hygroscopic, like its sodium cousin, it poses a greater fire hazard.[3] StoragePotassium nitrate should be stored in closed bottles, away from any flammable materials as well as organic and acidic vapors. It is not hygroscopic, so there's no need to seal it. DisposalPotassium nitrate is a good fertilizer, and unless it's contaminated with heavy metals or other toxicants, it can be disposed pretty much anywhere. Gallery
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What is the solubility of potassium nitrate in water?
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