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Chapter 4: Problem 109

An aqueous solution contains \(4.50 \mathrm{~g}\) of calcium chloride, \(\mathrm{CaCl}_{2}\), per liter. What is the molarity of \(\mathrm{CaCl}_{2}\) ? When calcium chloride dissolves in water, the calcium ions, \(\mathrm{Ca}^{2+}\), and chloride ions, \(\mathrm{Cl}^{-}\), in the crystal go into the solution. What is the molarity of each ion in the solution?

Short Answer

Expert verified
The molarity of \(\mathrm{CaCl}_2\) is \(0.0405\, \mathrm{mol/L}\), \(\mathrm{Ca}^{2+}\) is \(0.0405\, \mathrm{mol/L}\), and \(\mathrm{Cl}^{-}\) is \(0.0810\, \mathrm{mol/L}\).

Step by step solution

01

Calculate Molar Mass of CaCl鈧�

First, determine the molar mass of \(\mathrm{CaCl}_2\). The atomic mass of \(\mathrm{Ca}\) is approximately \(40.08\,\mathrm{g/mol}\), and the atomic mass of \(\mathrm{Cl}\) is approximately \(35.45\,\mathrm{g/mol}\). Since there are two chloride ions in \(\mathrm{CaCl}_2\), the molar mass is calculated as: \[ \text{Molar Mass of } \mathrm{CaCl}_2 = 40.08 + 2\times 35.45 = 110.98 \, \mathrm{g/mol} \]
02

Calculate Moles of CaCl鈧�

Using the molar mass, calculate the moles of \(\mathrm{CaCl}_2\) in the solution. You have \(4.50 \, \mathrm{g}\) in 1 liter, so the moles are given by: \[ \text{Moles of } \mathrm{CaCl}_2 = \frac{4.50 \, \mathrm{g}}{110.98 \, \mathrm{g/mol}} \approx 0.0405 \, \mathrm{mol} \]
03

Calculate Molarity of CaCl鈧�

Molarity is defined as moles of solute per liter of solution. Since the solution is 1 liter, the molarity of \(\mathrm{CaCl}_2\) is: \[ \text{Molarity of } \mathrm{CaCl}_2 = 0.0405 \, \mathrm{mol/L} \]
04

Determine Molarity of Ca虏鈦� and Cl鈦� Ions

When \(\mathrm{CaCl}_2\) dissolves, it disassociates into one \(\mathrm{Ca}^{2+}\) ion and two \(\mathrm{Cl}^{-}\) ions. Therefore, the molarity of \(\mathrm{Ca}^{2+}\) ions is the same as \(\mathrm{CaCl}_2\), which is \(0.0405 \, \mathrm{mol/L}\). The molarity of \(\mathrm{Cl}^-\) ions is twice that of \(\mathrm{CaCl}_2\), as each formula unit of \(\mathrm{CaCl}_2\) provides two chloride ions: \[ \text{Molarity of } \mathrm{Cl}^- = 2 \times 0.0405 \, \mathrm{mol/L} = 0.0810 \, \mathrm{mol/L} \]

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Key Concepts

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

Aqueous Solution
An aqueous solution is a mixture where water acts as the solvent. This means water is the component in the largest amount, and other substances dissolve in it. Aqueous solutions are common in many fields like chemistry and biology due to water's excellent solvent properties. - Water can dissolve many substances because it is polar, having a positive and a negative side. - This property allows it to interact and stabilize charged particles, also known as ions, from substances dissolved in it. For example, when you dissolve table salt, \( ext{NaCl}\), in water, the sodium and chloride ions separate, creating an aqueous solution.
Calcium Chloride
Calcium chloride, often represented as \( ext{CaCl}_2\), is a common salt used in various applications such as de-icing roads and in pool maintenance. It consists of one calcium ion and two chloride ions. - When calcium chloride is placed in water, it dissociates, or separates, into individual ions. - This compound is very soluble in water, which makes it ideal for creating concentrated aqueous solutions. Calcium chloride solution's ability to absorb moisture also makes it useful in drying operations.
Calcium Ions
Calcium ions have the chemical symbol \( ext{Ca}^{2+}\). These ions play crucial roles in various biological processes, such as muscle function and bone formation. - In an aqueous solution, calcium ions are completely surrounded by water molecules. - This allows them to move freely, which is critical for their biological activities.In the context of calcium chloride solutions, for every mole of \( ext{CaCl}_2\) that dissolves, one mole of calcium ions is released. This dissociation is straightforward, making calcium ions easily available in the solution.
Chloride Ions
Chloride ions, denoted as \( ext{Cl}^{-}\), are anions, meaning they have a negative charge. These ions are essential in maintaining the electrical neutrality in biological cells and are found abundantly in the human body.- Like calcium ions, chloride ions are well stabilized in aqueous solutions by water molecules.- For each mole of calcium chloride that dissolves, two moles of chloride ions enter the solution.This increase in chloride ion concentration is essential in chemical applications and determines the solution's overall ionic strength.

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Most popular questions from this chapter

Magnesium metal reacts with hydrobromic acid to produce hydrogen gas and a solution of magnesium bromide. Write the molecular equation for this reaction. Then write the corresponding net ionic equation.

A \(1.345-\mathrm{g}\) sample of a compound of barium and oxygen was dissolved in hydrochloric acid to give a solution of barium ion, which was then precipitated with an excess of potassium chromate to give \(2.012 \mathrm{~g}\) of barium chromate, \(\mathrm{BaCrO}_{4}\). What is the formula of the compound?

An antacid tablet has calcium carbonate as the active ingredient; other ingredients include a starch binder. You dissolve the tablet in hydrochloric acid and filter off insoluble material. You add potassium oxalate to the filtrate (containing calcium ion) to precipitate calcium oxalate. If a tablet weighing \(0.680 \mathrm{~g}\) gave \(0.629 \mathrm{~g}\) of calcium oxalate, what is the mass percentage of active ingredient in the tablet?

Iron forms a sulfide with the approximate formula \(\mathrm{Fe}_{7} \mathrm{~S}_{8}\). Assume that the oxidation state of sulfur is \(-2\) and that iron atoms exist in both \(+2\) and \(+3\) oxidation states. What is the ratio of Fe(II) atoms to Fe(III) atoms in this compound?

A \(71.2-g\) sample of oxalic acid, \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\), was dissolved in \(1.00 \mathrm{~L}\) of solution. How would you prepare \(1.00 \mathrm{~L}\) of \(0.150 \mathrm{M}\) \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\) from this solution?
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