Chapter 1: Problem 52
Which of the following mixtures contain less number of ions?
(1)
Short Answer
Expert verified
Mixture 2 contains the least number of ions.
Step by step solution
01
- List the components for each mixture
Identify the components of each mixture and their concentrations.(1) Mixture 1: 2 M K2SO4 and 3 M Na2CO3(2) Mixture 2: 2 M NaCl and 2 M KCl(3) Mixture 3: 2 M MnSO4 and 2 M K2SO4(4) Mixture 4: 2 M K2SO4 and 2 M (NH4)2SO4
02
- Dissociate each compound into ions
Write the dissociation equation for each compound in water:(1) K2SO4 → 2K⁺ + SO4²⁻Na2CO3 → 2Na⁺ + CO3²⁻(2) NaCl → Na⁺ + Cl⁻KCl → K⁺ + Cl⁻(3) MnSO4 → Mn²⁺ + SO4²⁻K2SO4 → 2K⁺ + SO4²⁻(4) K2SO4 → 2K⁺ + SO4²⁻(NH4)2SO4 → 2NH4⁺ + SO4²⁻
03
- Calculate the total number of ions for each mixture
Calculate the number of ions produced by each compound in the mixture and sum them up:(1) K2SO4: 2 M produces 3 ions (2K⁺ and 1 SO4²⁻), 6 ions total.Na2CO3: 3 M produces 3 ions (2Na⁺ and 1 CO3²⁻), 9 ions total.Total for Mixture 1: 15 ions(2) NaCl: 2 M produces 2 ions (Na⁺ and Cl⁻), 4 ions total.KCl: 2 M produces 2 ions (K⁺ and Cl⁻), 4 ions total.Total for Mixture 2: 8 ions(3) MnSO4: 2 M produces 2 ions (Mn²⁺ and SO4²⁻), 4 ions total.K2SO4: 2 M produces 3 ions (2K⁺ and 1 SO4²⁻), 6 ions total.Total for Mixture 3: 10 ions(4) K2SO4: 2 M produces 3 ions (2K⁺ and 1 SO4²⁻), 6 ions total.(NH4)2SO4: 2 M produces 3 ions (2NH4⁺ and SO4²⁻), 6 ions total.Total for Mixture 4: 12 ions
04
- Compare the total number of ions for each mixture
Compare the total number of ions calculated for each mixture:Mixture 1: 15 ionsMixture 2: 8 ionsMixture 3: 10 ionsMixture 4: 12 ionsMixture 2 contains the least number of ions (8 ions).
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Ionic Compounds
Ionic compounds are a type of chemical compound composed of cations (positively charged ions) and anions (negatively charged ions). These ions are held together by ionic bonds, which are strong electrostatic forces of attraction between oppositely charged ions. When ionic compounds dissolve in water, they dissociate into their constituent ions. For example, when sodium chloride (NaCl) dissolves, it dissociates into sodium ions (Na⁺) and chloride ions (Cl⁻).
Sodium chloride is a simple ionic compound, but there are many others with more complex structures.
Sodium chloride is a simple ionic compound, but there are many others with more complex structures.
- Common ionic compounds include salts, such as potassium sulfate (K₂SO₄) and ammonium sulfate ((NH₄)₂SO₄).
- The structure of ionic compounds usually forms a crystalline lattice which minimizes the potential energy of the system.
Dissociation Equations
Dissociation equations describe the process in which an ionic compound separates into its constituent ions when it dissolves in water. This is a physical change, not a chemical change, because the compound itself is not altered; rather, its ions are simply dispersed in solution. For example, the dissociation of sodium chloride can be written as:
Each dissociation equation shows what ions are produced from one formula unit of the ionic compound in water.
Each dissociation equation shows what ions are produced from one formula unit of the ionic compound in water.
- For potassium sulfate (K₂SO₄):
- For ammonium sulfate ((NH₄)₂SO₄):
Molarity
Molarity (M) is a way to express the concentration of a solution. It is defined as the number of moles of solute (the substance being dissolved) per liter of solution. The formula for molarity is:
For example, a 2 M solution of potassium sulfate (K₂SO₄) means there are 2 moles of K₂SO₄ dissolved in 1 liter of solution. Molarity is important because it helps quantify the concentration of ions in a solution after dissociation. When calculating how many ions are in a solution, you need to know the molarity of the original solution.
In a problem that involves comparing ion concentrations, knowing the molarity of each component helps determine which mixture has more or fewer ions. For instance, if you have 2 M K₂SO₄ and 3 M Na₂CO₃, the molarity tells you how many ions form when each dissolves.
For example, a 2 M solution of potassium sulfate (K₂SO₄) means there are 2 moles of K₂SO₄ dissolved in 1 liter of solution. Molarity is important because it helps quantify the concentration of ions in a solution after dissociation. When calculating how many ions are in a solution, you need to know the molarity of the original solution.
In a problem that involves comparing ion concentrations, knowing the molarity of each component helps determine which mixture has more or fewer ions. For instance, if you have 2 M K₂SO₄ and 3 M Na₂CO₃, the molarity tells you how many ions form when each dissolves.
- 2 M K₂SO₄ produces 2 K⁺ and 1 SO₄²⁻, hence producing 6 ions for the 2 moles total.
- 3 M Na₂CO₃ produces 2 Na⁺ and 1 CO₃²⁻ for each formula unit, leading to a total of 9 ions from 3 moles.
Ion Counting
Ion counting involves determining the total number of ions present in a solution. This process is essential in understanding chemical reactions and solution properties. To count ions, follow these steps:
First, write the dissociation equation for each compound in the solution. Then, use the molarity to determine how many moles of each ion are produced. Finally, sum up the ions.
Here's an example:
First, write the dissociation equation for each compound in the solution. Then, use the molarity to determine how many moles of each ion are produced. Finally, sum up the ions.
Here's an example:
- For 2 M K₂SO₄:
Each mole of K₂SO₄ produces 3 ions (2 K⁺ and 1 SO₄²⁻). So, 2 M K₂SO₄ gives 6 ions total. - For 3 M Na₂CO₃:
Each mole of Na₂CO₃ produces 3 ions, giving us 9 ions total.