Question

Rank the following ionic compounds in order of increasing coulombic attraction between their ions: \(\mathrm{KBr}, \mathrm{SrBr}_{2},\) and \(\mathrm{CsBr}.\)

Short answer

Question: Rank the ionic compounds KBr, SrBr2, and CsBr in the order of increasing Coulombic attraction between their ions. Answer: CsBr < KBr < SrBr2

Step-by-step solution

Find the charges of the ions

In each ionic compound, determine the charges of the cations and anions. For KBr, K has a charge of +1 and Br has a charge of -1. For SrBr2, Sr has a charge of +2 and Br has a charge of -1. For CsBr, Cs has a charge of +1 and Br has a charge of -1.

Find the ionic radii

Determine the ionic radii of each ion involved. The ionic radii can be found in a periodic table or a reference book. Based on the ionic radii, we have K=1.51 Å, Br=1.96 Å, Sr=1.18 Å, Cs=1.81 Å.

Calculate the distance between ions in each compound

Add the ionic radii of the cations and anions in each compound to find the distance between the ions. For KBr, d(KBr) = 1.51 Å + 1.96 Å = 3.47 Å. For SrBr2, d(SrBr) = 1.18 Å + 1.96 Å = 3.14 Å. For CsBr, d(CsBr) = 1.81 Å + 1.96 Å = 3.77 Å.

Calculate the Coulombic attraction for each compound

Using the Coulombic attraction formula \(F=k * \frac{q_{1} * q_{2}}{d^{2}}\), calculate the attraction between the ions in each compound. In our case, we will compare the relative values of \(\frac{q_{1} * q_{2}}{d^{2}}\) for each compound. For KBr: \(\frac{(+1)(-1)}{(3.47)^{2}} = \frac{-1}{12.04}\) For SrBr2: \(\frac{(+2)(-1)}{(3.14)^{2}} =\frac{-2}{9.86}\) For CsBr: \(\frac{(+1)(-1)}{(3.77)^{2}} = \frac{-1}{14.21}\)

Rank the compounds in order of increasing Coulombic attraction

Compare the relative values of \(\frac{q_{1} * q_{2}}{d^{2}}\) for each compound: For KBr: \(\frac{-1}{12.04}\) For SrBr2: \(\frac{-2}{9.86}\) For CsBr: \(\frac{-1}{14.21}\) The compound with the lowest value has the weakest Coulombic attraction, and the compound with the highest value has the strongest attraction. In terms of increasing Coulombic attraction, the order is CsBr < KBr < SrBr2.

Key concepts

Ionic Compounds

Ionic compounds are formed when atoms transfer electrons to achieve stable electron configurations. These compounds consist of positively charged ions called cations and negatively charged ions called anions. The electrostatic force between these ions holds them together. This force is known as ionic or Coulombic attraction. Ionic compounds are typically solid at room temperature and have high melting and boiling points. This is due to the strong attraction between the ions, which requires significant energy to break. Familiar examples include sodium chloride (table salt) and potassium bromide (KBr).

• Formed from metals and non-metals.
• Characterized by high melting points.
• Conduct electricity when dissolved in water.

Ionic Charges

Ionic charges are critical in determining the strength of the attraction in ionic compounds. Each element can lose or gain electrons to form ions with positive or negative charges. For example, potassium (K) loses one electron to form a +1 cation, while bromine (Br) gains one electron to form a -1 anion. The magnitude of these charges plays a key role in the attraction force, with greater charges leading to stronger attraction. This is why strontium bromide (\(\text{SrBr}_2\) ) exhibits a stronger attraction than potassium bromide (KBr), as the strontium ion has a +2 charge.

• Cations are typically metals.
• Anions are typically non-metals.
• Charge magnitude influences attraction strength.

Ionic Radii

Ionic radii refer to the size of an ion and can influence how closely ions pack together in a compound. The size is affected by both the number of electrons and the effective nuclear charge. Larger ionic radii result in larger spaces between ions in a compound, which can decrease the Coulombic attraction. The radii can be found on the periodic table and are crucial for calculating the distance between ions. For example, the ionic radii of K and Br are 1.51 Å and 1.96 Å respectively, determining the spacing and overall structure of KBr.

• Ionic radii vary across the periodic table.
• Larger ions result in weaker attractions.
• Important for determining ionic distances.

Periodic Table

The periodic table is an essential tool in understanding the behavior of elements, their ionic charges, and their radii. Elements are arranged based on atomic number and chemical properties. Groups and periods help predict whether an element will form an ion and what its charge might be. For example, elements in Group 1 like potassium will likely form +1 ions, while Group 17 elements like bromine will form -1 ions. The periodic trends also help estimate ionic radii, which decrease across a period and increase down a group.

• Provides information on ionic charges.
• Helps predict ion formation.
• Shows trends in ionic radii.

Coulomb's Law

Coulomb's Law describes the force between two charged particles, crucial for understanding ionic attraction. Mathematically, it is expressed as \(F = k \cdot \frac{q_1 \cdot q_2}{d^2}\) , where \(F\) is the force of attraction, \(k\) is Coulomb's constant, \(q_1\) and \(q_2\) are the charges of the ions, and \(d\) is the distance between them. This law shows that larger charges and smaller distances result in a stronger force of attraction. Applying Coulomb's Law helps in ranking compounds like KBr, SrBr2, and CsBr by their attraction strength, crucial for understanding material properties and behaviors.

• Explains ionic strength.
• Driven by ion charge and distance.
• Applicable to various compounds.