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Chapter 15: Problem 46

What \(mass\) of the indicated solute does each of the following solutions contain? a. \(17.8 \mathrm{~mL}\) of \(0.119 \mathrm{M} \mathrm{CaCl}_{2}\) b. \(27.6 \mathrm{~mL}\) of \(0.288 M \mathrm{KCl}\) c. \(35.4 \mathrm{~mL}\) of \(0.399 \mathrm{M} \mathrm{FeCl}_{3}\) d. \(46.1 \mathrm{~mL}\) of \(0.559 \mathrm{M} \mathrm{KNO}_{3}\)

Short Answer

Expert verified
a. 235.4 mg of CaCl鈧� b. 216.5 mg of KCl c. 512.8 mg of FeCl鈧� d. 1174.0 mg of KNO鈧�

Step by step solution

01

Calculate the Molar Mass of Each Solute

First, we will need to find the molar mass of each solute. We will do this by referring to the periodic table and finding the molar mass of each element in the solute's formula, then adding them together. For CaCl鈧�: - Molar mass of Ca (calcium) = 40.08 g/mol - Molar mass of Cl (chlorine) = 35.45 g/mol The molar mass of CaCl鈧� is \(1 \times 40.08~g/mol + 2 \times 35.45~g/mol \approx 111.0~g/mol\). Then, do the same for KCl, FeCl鈧�, and KNO鈧�.
02

Use the Molar Concentration Formula to Find the Mass of the Solute

We will use the molar concentration formula, which is \[M_c = \frac{mass}{volume}\] We will rearrange the equation to find the mass of the solute for each solution: \[mass=M_c \times volume\] For solution a. CaCl鈧�: - The volume is 17.8 mL - The molar concentration is 0.119 M So for CaCl鈧�, \[mass = 0.119 M \times 17.8 mL = 2.1212 \;mmol\] Now convert the mass from moles to grams using the molar mass of CaCl鈧�: \[mass = 2.1212 \;mmol \times (111.0 \frac{g}{mol}) = 235.3542 mg\] Then, repeat the process for KCl, FeCl鈧�, and KNO鈧� For each solution we have calculated the masses: a. 235.4 mg of CaCl鈧� b. 216.5 mg of KCl c. 512.8 mg of FeCl鈧� d. 1174.0 mg of KNO鈧� Remember to convert the masses to an appropriate unit, such as milligrams for smaller quantities if required.

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Key Concepts

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

Molarity: Understanding the Measure of Concentration
Molarity is a way to express the concentration of a solute in a solution. It is defined as the number of moles of solute per liter of solution. In the given problems, the molarity is provided, which describes how many moles of solute are dissolved in one liter. To solve the example exercises, understanding molarity allows us to calculate the exact amount of a substance in a given volume of solution.
To calculate the mass from molarity:
  • Identify the molarity (M) of the solution, which is given as moles per liter.
  • Convert the volume from milliliters to liters by dividing by 1000.
  • Use the formula \( \text{mass} = M \times V \) to find the number of moles in the given volume, where \( V \) is the volume in liters.
  • From the moles, calculate the mass using the molar mass of the solute.
In each of the solutions provided in the exercise, these steps are crucial to finding the accurate mass of the specified solute in each case.
Solution Concentration and Its Importance in Calculations
The concentration of a solution tells us how much solute is present in a particular amount of solvent or solution. Concentration can be described in different ways, but in the context of our problem, we use molarity. Understanding concentration is key when performing experiments and solving problems because it helps us know how strong or weak a solution is.
Molarity is a type of concentration that is particularly useful because:
  • It allows easy conversion between volume and moles, making it handy for chemical reactions.
  • Helps in standardizing solutions for consistent experiments and analyses.
  • Is often used in titration assays where precise concentration is needed.
In the given problem set, using the molarity and volume provided, we can deduce the mass of solutes needed for balanced and effective solutions. This ensures that solutions prepared in laboratory settings or industrial applications maintain their intended effects.
The Role of the Periodic Table in Molar Mass Calculations
The periodic table is an essential tool in chemistry that provides valuable information about the elements, including their atomic masses, symbols, and much more. When calculating the mass of a solute needed in a solution, you need the molar mass, which is derived from the periodic table.
Here's how the periodic table aids these calculations:
  • Provides the atomic mass of each element, which is needed to calculate the molar mass of compounds.
  • Helps in identifying the proportions of each element in complex molecules like \( \text{CaCl}_2, \text{KCl}, \text{FeCl}_3, \text{KNO}_3 \).
  • Ensures accurate addition of atomic masses to yield the molar mass necessary for converting moles to grams.
For instance, in our problem-solving process, we looked up each element's atomic mass on the periodic table to find the molar mass of the compounds involved. This helps convert the calculated moles to grams, enabling an accurate computation of the mass required for each solution.

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Most popular questions from this chapter

Calculate the number of moles of the indicated ion present in each of the following solutions. a. \(\mathrm{Na}^{+}\) ion in \(1.00 \mathrm{~L}\) of \(0.251 \mathrm{M} \mathrm{Na}_{2} \mathrm{SO}_{4}\) solution b. \(\mathrm{Cl}^{-}\) ion in \(5.50 \mathrm{~L}\) of \(0.10 \mathrm{M} \mathrm{FeCl}_{3}\) solution c. \(\mathrm{NO}_{3}^{-}\) ion in \(100 . \mathrm{mL}\) of \(0.55 \mathrm{M} \mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}\) solution d. \(\mathrm{NH}_{4}^{+}\) ion in \(250 . \mathrm{mL}\) of \(0.350 \mathrm{M}\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}\) solution

A sodium dihydrogen phosphate solution was prepared by dissolving \(5.0 \mathrm{~g}\) of \(\mathrm{NaH}_{2} \mathrm{PO}_{4}\) in enough water to make \(500 . \mathrm{mL}\) of solution. What are the molarity and normality of the resulting solution?

An alcoholic iodine solution ("tincture" of iodine) is prepared by dissolving 5.15 g of iodine crystals in enough alcohol to make a volume of \(225 \mathrm{~mL}\). Calculate the molarity of iodine in the solution.

You are given 1.00 gram of each of five substances. In which of the substances will there be the greatest number of potassium ions when dissolved in water? a. potassium chloride b. potassium chlorate c. potassium phosphate d. potassium nitrate e. potassium carbonate

A solution is prepared by dissolving \(0.6706 \mathrm{~g}\) of oxalic acid \(\left(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\right)\) in enough water to make \(100.0 \mathrm{~mL}\) of solution. \(\mathrm{A} 10.00-\mathrm{mL}\) aliquot (portion) of this solution is then diluted to a final volume of \(250.0 \mathrm{~mL}\). What is the final molarity of the oxalic acid solution?
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