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Chapter 8: Problem 25

For which of the following compounds is it possible to make a \(1.0 M\) solution at \(0^{\circ} \mathrm{C} ?\) a. \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O},\) solubility \(=23.1 \mathrm{g} / 100 \mathrm{mL}\) b. \(A g N O_{3},\) solubility \(=122\) g/ 100 mL c. \(\mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O},\) solubility \(=113 \mathrm{g} / 100 \mathrm{mL}\) d. \(\mathrm{Ca}(\mathrm{OH})_{2}\), solubility \(=0.185 \mathrm{g} / 100 \mathrm{mL}\)

Short Answer

Expert verified
a. CuSO4路5H2O b. AgNO3 c. Fe(NO3)2路6H2O d. Ca(OH)2

Step by step solution

01

Calculate the molar mass of each compound

To calculate the molar mass of each compound, first, determine the atomic mass of each element in the compound and then sum them up. For simplicity, we will not show the full calculation for each compound. Using a periodic table, this is done as follows: a. CuSO4路5H2O: Molar mass \(\approx 249.7 \mathrm{g/mol}\). b. AgNO3: Molar mass \(\approx 169.9 \mathrm{g/mol}\). c. Fe(NO3)2路6H2O: Molar mass \(\approx 179.9 \mathrm{g/mol}\). d. Ca(OH)2: Molar mass \(\approx 74.1 \mathrm{g/mol}\).
02

Calculate the maximum concentration of each compound at \(0^{\circ}\mathrm{C}\)"

To do this, divide the solubility by the molar mass and then convert the result from moles per 100 mL of solution to moles per 1 L (moles/L or M): a. CuSO4路5H2O: \(\text{Maximum Concentration} = \dfrac{23.1 \mathrm{g}}{249.7 \mathrm{g/mol}} \cdot \dfrac{1000 \mathrm{mL}}{100 \mathrm{mL}} = \dfrac{23.1}{249.7} * 10 \approx 0.93 \text{ M}\). b. AgNO3: \(\text{Maximum Concentration} = \dfrac{122 \mathrm{g}}{169.9 \mathrm{g/mol}} \cdot \dfrac{1000 \mathrm{mL}}{100 \mathrm{mL}} = \dfrac{122}{169.9} * 10 \approx 7.18 \text{ M}\). c. Fe(NO3)2路6H2O: \(\text{Maximum Concentration} = \dfrac{113 \mathrm{g}}{179.9 \mathrm{g/mol}} \cdot \dfrac{1000 \mathrm{mL}}{100 \mathrm{mL}} = \dfrac{113}{179.9} * 10 \approx 6.28 \text{ M}\). d. Ca(OH)2: \(\text{Maximum Concentration} = \dfrac{0.185 \mathrm{g}}{74.1 \mathrm{g/mol}} \cdot \dfrac{1000 \mathrm{mL}}{100 \mathrm{mL}} = \dfrac{0.185}{74.1} * 10 \approx 0.025 \text{ M}\).
03

Compare the maximum concentration to the desired 1.0 M concentration

We now compare the maximum concentration of each compound (calculated in Step 2) to the desired concentration of \(1.0\,\text{M}\). If the maximum concentration is equal to or greater than 1.0, it is possible to make a \(1.0\) M solution at \(0^{\circ}\mathrm{C}\). Otherwise, it is not possible. a. CuSO4路5H2O: Maximum concentration: \(0.93 \text{ M}\). Not possible. b. AgNO3: Maximum concentration: \(7.18 \text{ M}\). Possible. c. Fe(NO3)2路6H2O: Maximum concentration: \(6.28 \text{ M}\). Possible. d. Ca(OH)2: Maximum concentration: \(0.025 \text{ M}\). Not possible. In conclusion, it is possible to make a \(1.0\,\text{M}\) solution at \(0^{\circ}\mathrm{C}\) for the compounds b (AgNO3) and c (Fe(NO3)2路6H2O).

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Key Concepts

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

Molar Mass Calculation
Understanding how to calculate the molar mass of a compound is crucial in determining how much of a compound is needed to achieve a certain concentration. Each element has a specific atomic mass, which can be found on the periodic table. To determine the molar mass of a compound, you sum up the atomic masses of all elements in that compound, taking into account the number of atoms of each element in its chemical formula.
  • For example, in the compound CuSO鈧劼�5H鈧侽, we need the atomic masses of Cu, S, O, and H. Calculate it as: Cu (63.55 g/mol) + S (32.07 g/mol) + O鈧� (4 x 16.00 g/mol) + 5H鈧侽 (5 x (2 x 1.01 + 16.00) g/mol).
  • Once calculated, the molar mass of CuSO鈧劼�5H鈧侽 is approximately 249.7 g/mol.
This calculated molar mass is essential for converting the amount of solubility from grams to moles, which is the next step in concentration calculations.
Maximum Concentration Calculation
Once the molar mass of a compound is known, we can determine the maximum concentration of that compound in a given volume of solvent at a specific temperature. This involves using the solubility of the compound, usually given in grams per 100 mL, and converting it to moles per liter (Molarity, M).
  • First, the solubility in grams is divided by the molar mass to convert to moles.
  • Then, convert the volume from 100 mL to 1 liter by multiplying the result by 10 (since 1000 mL = 1 L).
For example, if AgNO鈧� has a solubility of 122 g/100 mL, its molar mass is 169.9 g/mol. The calculation for maximum concentration is: \(\frac{122}{169.9} \times 10\), which results in roughly 7.18 M.
Chemical Solutions
In chemistry, a solution is a homogenous mixture where solutes are dissolved in a solvent, like water. Understanding solutions goes beyond knowing that they are mixtures; it involves comprehending the behavior of solutes and solvents at a molecular level.
  • Concentration is key, quantified as Molarity (M), defined as moles of solute per liter of solution.
  • Compounds dissolve at certain rates depending on properties like temperature and pressure.
  • Not all compounds have the same solubility, which influences how solutions are prepared and utilized in various applications.
Solutions are foundational in chemical reactions, with their properties significantly affecting reaction rates and outcomes.
Solubility at Specific Temperatures
Solubility is the maximum amount of solute that can dissolve in a solvent at a given temperature and pressure. The solubility often depends heavily on temperature; a compound may be much more soluble in a warm solution than in a cold one.
  • It's measured as grams of solute per 100 mL of solvent, simplified further into molarity when needed.
  • Understanding solubility can indicate which solution concentrations are feasible at certain temperatures, such as in the exercise where measurements are at \(0^{\circ}C\).
At \(0^{\circ}C\), some compounds dissolve sufficiently to create concentrated solutions, while others may not reach desired concentrations without temperature adjustments.

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Most popular questions from this chapter

For each of the following acid-base reactions, identify the acid and the base and then write the net ionic equation: a. \(\mathrm{H}_{2} \mathrm{SO}_{4}(a q)+\mathrm{Ca}(\mathrm{OH})_{2}(s) \rightarrow \mathrm{CaSO}_{4}(a q)+2 \mathrm{H}_{2} \mathrm{O}(\ell)\) b. \(\mathrm{PbCO}_{3}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \rightarrow \mathrm{PbSO}_{4}(s)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(\ell)\) c. \(\mathrm{Ca}(\mathrm{OH})_{2}(s)+2 \mathrm{CH}_{3} \mathrm{COOH}(a q) \rightarrow\) \(\mathrm{Ca}\left(\mathrm{CH}_{3} \mathrm{COO}\right)_{2}(a q)+2 \mathrm{H}_{2} \mathrm{O}(\ell)\)

Silver tarnish is the result of silver metal reacting with sulfur compounds, such as \(\mathrm{H}_{2} \mathrm{S},\) and \(\mathrm{O}_{2}\) in the air. The tarnish on silverware \(\left(\mathrm{Ag}_{2} \mathrm{S}\right)\) can be removed by soaking the silverware in a slightly basic solution of \(\mathrm{NaHCO}_{3}\) (baking soda) in a basin lined with aluminum foil. a. Write a balanced chemical equation for the tarnish formation reaction. b. Write a balanced net ionic equation for the tarnish removal process in which Ag_S S reacts with A1 metal, forming \(\mathrm{Al}(\mathrm{OH})_{3}(s), \mathrm{Ag}\) metal, and \(\mathrm{HS}^{-}\) ions.

Show, with appropriate net ionic reactions, how \(\mathrm{Cr}^{3+}\) and \(\mathrm{Cd}^{2+}\) can be removed from wastewater by treatment with solutions of sodium hydroxide.

The concentration of manganese in one brand of soluble plant fertilizer is \(0.05 \%\) by mass. If a \(20 \mathrm{g}\) sample of the fertilizer is dissolved in 2.0 L of solution, what is the molarity of dissolved Mn in the solution?

The solubility of \(\mathrm{CaCl}_{2}\) in water at \(25^{\circ} \mathrm{C}\) is \(81.1 \mathrm{g} / 100 \mathrm{mL}\) at \(0^{\circ} \mathrm{C}\) its solubility decreases to \(59.5 \mathrm{g} / 100 \mathrm{mL} .\) Answer the following questions about an aqueous solution of \(26.4 \mathrm{g}\) of \(\mathrm{CaCl}_{2}\) in a volume of \(37.5 \mathrm{mL}\) a. At \(25^{\circ} \mathrm{C},\) is this a saturated solution? b. If the solution is cooled to \(0^{\circ} \mathrm{C},\) do you expect a precipitate to form? c. If the solution is slowly cooled to \(0^{\circ} \mathrm{C}\) and no precipitate forms, then what kind of solution is it?
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