/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 24 The solubility of \(\mathrm{MnSO... [FREE SOLUTION] | 91影视

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Chapter 13: Problem 24

The solubility of \(\mathrm{MnSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O}\) in water at \(20^{\circ} \mathrm{C}\) is \(70 \mathrm{~g}\) per \(100 \mathrm{~mL}\) of water. (a) Is a \(1.22 \mathrm{M}\) solution of \(\mathrm{MnSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O}\) in water at \(20^{\circ} \mathrm{C}\) saturated, supersaturated, or unsaturated? (b) Given a solution of \(\mathrm{MnSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O}\) of unknown concentration, what experiment could you perform to determine whether the new solution is saturated, supersaturated, or unsaturated?

Short Answer

Expert verified
(a) The 1.22 M solution of 惭苍厂翱4路贬2翱 in water at 20掳C is unsaturated, as its concentration is lower than the saturation solubility (4.14 M). (b) Heat the solution, add 惭苍厂翱4路贬2翱 until saturation is reached, and then cool the solution back to 20掳C. Observe if any precipitate forms. This allows determining if the initial solution was saturated, supersaturated, or unsaturated.

Step by step solution

01

Calculate the solubility of 惭苍厂翱4路贬2翱 at 20掳C in molarity

Given that 70g of 惭苍厂翱4路贬2翱 can dissolve in 100mL of water, we need to find the molarity of the saturated solution. First, find the molar mass of 惭苍厂翱4路贬2翱: Mn: 54.94 g/mol S: 32.07 g/mol O: 16.00 g/mol H2O: 18.02 g/mol Molar mass of 惭苍厂翱4路贬2翱: \(54.94 + 32.07 + 4(16.00) + 18.02 = 169.01\) g/mol Now, convert 70g of 惭苍厂翱4路贬2翱 to moles: \(n=\frac{mass}{molar\ mass} = \frac{70\ g}{169.01\ g/mol} = 0.414\) mol Then, convert 100mL of water to liters: \(V = 100\,\text{mL} \times \frac{1\,\text{L}}{1000\,\text{mL}} = 0.1\,\text{L}\) Finally, determine the saturation solubility in molarity: \(Saturation\ Molarity (M) = \frac{n}{V} = \frac{0.414\,\text{mol}}{0.1\,\text{L}} = 4.14\,M\)
02

Determine the state of the given 惭苍厂翱4路贬2翱 solution

Now that we have the saturation molarity, which indicates the maximum amount of 惭苍厂翱4路贬2翱 that can dissolve in water at a specific temperature, we can compare it with the given concentration in the problem, 1.22 M 惭苍厂翱4路贬2翱. Given \(Saturation\ Molarity = 4.14\,M\) Since the given solution has a lower molarity than the saturation solubility, it means it: \(1.22\,M < 4.14\,M\) So, the solution is unsaturated. (a) The 1.22 M solution of 惭苍厂翱4路贬2翱 in water at 20掳C is unsaturated.
03

Suggest an experiment to identify the state of a 惭苍厂翱4路贬2翱 solution of unknown concentration

(b) To determine whether a solution of 惭苍厂翱4路贬2翱 of unknown concentration is saturated, supersaturated, or unsaturated, you can perform the following experiment. 1. Heat the solution to slightly increase its temperature. 2. Slowly add small amounts of 惭苍厂翱4路贬2翱 to the heated solution while stirring. 3. If the added 惭苍厂翱4路贬2翱 completely dissolves, it means the initial solution was unsaturated. 4. Continue adding 惭苍厂翱4路贬2翱 until no more of the added substance dissolves, which indicates that the solution has reached saturation. 5. Remove the heating source, and allow the solution to cool back to 20掳C. 6. If any precipitate forms while cooling the solution, it means that the initial solution was supersaturated. This way, by observing the solution during heating and cooling, we can identify if it was initially saturated, supersaturated, or unsaturated.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Molarity
Molarity is an essential concept in chemistry, especially when dealing with solutions. It is defined as the number of moles of a solute per liter of solution. Molarity is commonly represented by the symbol M and is important for quantitatively describing the concentration of a solution.
Understanding molarity is crucial because it allows chemists to predict how chemical reactions will occur in solution. In the exercise, a 1.22 M solution refers to a scenario where there are 1.22 moles of dsolved 惭苍厂翱4路贬2翱 in every liter of the solution.
  • It's important for conducting experiments and calculations.
  • It helps in predicting the outcomes of chemical reactions.
  • It provides a measure of the concentration of solutes in a solution.
In essence, knowing the molarity of a solution allows you to understand how many particles of the solute are available to react or interact with other substances in chemical processes.
Saturation
Saturation is a state where a solution contains the maximum amount of dissolved solute at a given temperature. The solution cannot dissolve any more solute without changing the temperature or pressure.
When a solution is at its saturation point, adding more solute will result in the excess not dissolving; instead, it will remain as solid particles. The solubility of 惭苍厂翱4路贬2翱 at 20掳C in water is 4.14 M, which means that solution can't dissolve more 惭苍厂翱4路贬2翱 beyond this concentration without changing External conditions.
  • Saturated solutions contain as much solute as can be dissolved.
  • The presence of undissolved solute typically indicates saturation.
  • Different substances have different solubility limits.
Understanding saturation is critical because it indicates the maximum amount of solute that can dissolve under specific conditions, guiding predictive outcomes in experimental procedures.
Supersaturation
Supersaturation is a fascinating and unique state in solution chemistry where a solution contains more dissolved solute than is possible at equilibrium under normal circumstances. This happens when a solution is saturated at a higher temperature and then allowed to cool without precipitating the excess solute.
When a supersaturated solution is disturbed, such as by adding a small seed crystal or shaking the container, the excess solute can rapidly precipitate out, returning the solution to a saturated state.
  • Supersaturated solutions are unstable and are temporary.
  • They can be prepared by controlling the temperature.
  • Use in crystallization processes and other industrial applications.
Understanding supersaturation is crucial as it plays a vital role in processes like crystallization, and it's often used in creating crystals in industries for materials such as sugar and pharmaceuticals.
惭苍厂翱4路贬2翱
惭苍厂翱4路贬2翱, or Manganese(II) sulfate monohydrate, is a chemical compound that consists of manganese, sulfur, oxygen, and water. It's often used in various industrial applications, including as a nutrient in animal feed or as a supplement in fertilizers.
When dissolved in water, 惭苍厂翱4路贬2翱 can help in various experiments and processes, and understanding its solubility plays a crucial role in different areas of chemical research and industry. At 20掳C, it has a solubility that allows 70 g to dissolve in 100 mL of water, making it quite soluble under these conditions.
  • 惭苍厂翱4路贬2翱 is a compound that consists of manganese, sulfate, and water.
  • It's used in industries like agriculture and manufacturing.
  • Understanding its solubility is important for its use in various applications.
Thus, comprehending the chemical nature and properties of 惭苍厂翱4路贬2翱 can provide deeper insight into how it behaves in different environments and conditions, which is valuable for its effective use.

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Most popular questions from this chapter

At ordinary body temperature \(\left(37^{\circ} \mathrm{C}\right)\), the solubility of \(\mathrm{N}_{2}\) in water at ordinary atmospheric pressure ( \(1.0 \mathrm{~atm})\) is \(0.015 \mathrm{~g} / \mathrm{L}\). Air is approximately \(78 \mathrm{~mol} \% \mathrm{~N}_{2}\). (a) Calculate the number of moles of \(\mathrm{N}_{2}\) dissolved per liter of blood, assuming blood is a simple aqueous solution. (b) At a depth of \(100 \mathrm{ft}\) in water, the external pressure is \(4.0 \mathrm{~atm}\). What is the solubility of \(\mathrm{N}_{2}\) from air in blood at this pressure? (c) If a scuba diver suddenly surfaces from this depth, how many milliliters of \(\mathrm{N}_{2}\) gas, in the form of tiny bubbles, are released into the bloodstream from each liter of blood?

An "emulsifying agent" is a compound that helps stabilize a hydrophobic colloid in a hydrophilic solvent (or a hydrophilic colloid in a hydrophobic solvent). Which of the following choices is the best emulsifying agent? (a) \(\mathrm{CH}_{3} \mathrm{COOH}\), (b) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{COOH}\), (c) \(\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{11} \mathrm{COOH}\), (d) \(\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{11} \mathrm{COONa}\).

(a) A sample of hydrogen gas is generated in a closed container by reacting \(2.050 \mathrm{~g}\) of zinc metal with \(15.0 \mathrm{~mL}\) of \(1.00 \mathrm{M}\) sulfuric acid. Write the balanced equation for the reaction, and calculate the number of moles of hydrogen formed, assuming that the reaction is complete. (b) The volume over the solution in the container is \(122 \mathrm{~mL}\). Calculate the partial pressure of the hydrogen gas in this volume at \(25^{\circ} \mathrm{C}\), ignoring any solubility of the gas in the solution. (c) The Henry's law constant for hydrogen in water at \(25^{\circ} \mathrm{C}\) is \(7.8 \times 10^{-4} \mathrm{~mol} / \mathrm{L}\)-atm. Estimate the number of moles of hydrogen gas that remain dissolved in the solution. What fraction of the gas molecules in the system is dissolved in the solution? Was it reasonable to ignore any dissolved hydrogen in part (b)? [13.111] The following table presents the solubilities of several gases in water at \(25^{\circ} \mathrm{C}\) under a total pressure of gas and water vapor of \(1 \mathrm{~atm}\). (a) What volume of \(\mathrm{CH}_{4}(\mathrm{~g})\) under standard conditions of temperature and pressure is contained in \(4.0 \mathrm{~L}\) of a saturated solution at \(25^{\circ} \mathrm{C}\) ? (b) Explain the variation in solubility among the hydrocarbons listed (the first three compounds), based on their molecular structures and intermolecular forces. (c) Compare the solubilities of \(\mathrm{O}_{2}, \mathrm{~N}_{2}\), and \(\mathrm{NO}\), and account for the variations based on molecular structures and intermolecular forces. (d) Account for the much larger values observed for \(\mathrm{H}_{2} \mathrm{~S}\) and \(\mathrm{SO}_{2}\) as compared with the other gases listed. (e) Find several pairs of substances with the same or nearly the same molecular masses (for example, \(\mathrm{C}_{2} \mathrm{H}_{4}\) and \(\mathrm{N}_{2}\) ), and use intermolecular interactions to explain the differences in their solubilities.

A car owner who knows no chemistry has to put antifreeze in his car's radiator. The instructions recommend a mixture of \(30 \%\) ethylene glycol and \(70 \%\) water. Thinking he will improve his protection he uses pure ethylene glycol, which is a liquid at room temperature. He is saddened to find that the solution does not provide as much protection as he hoped. The pure ethylene glycol freezes solid in his radiator on a very cold day, while his neighbor, who did use the \(30 / 70\) mixture, has no problem. Suggest an explanation.

(a) Would you expect stearic acid, \(\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{16} \mathrm{COOH}_{\text {, to be }}\) more soluble in water or in carbon tetrachloride? Explain. (b) Which would you expect to be more soluble in water, cyclohexane or dioxane? Explain.
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