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The ionic lattice in which compound requires the most energy to break: \(\mathrm{KCl}, \mathrm{Mg}(\mathrm{OH})_{2}\), or \(\mathrm{NaNO}_{3}\) ? Explain your answer.

Short Answer

Expert verified
The ionic lattice in the compound Mg(OH)₂ requires the most energy to break, as it has the strongest electrostatic forces between its ions, with a charge magnitude of 4, in comparison to KCl and NaNO₃ which both have a charge magnitude of 1.

Step by step solution

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1. Identify the Ionic Charges of the Compounds

First, we have to identify the individual ionic charges of the ions in each compound. The ionic charges will determine the electrostatic force between the ions which influences the energy required to dissociate them. KCl: Potassium (K) has a +1 charge, and Chloride (Cl) has a -1 charge. Mg(OH)₂: Magnesium (Mg) has a +2 charge, and Hydroxide (OH) has a -1 charge. NaNO₃: Sodium (Na) has a +1 charge, and Nitrate (NO₃) has a -1 charge.
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2. Analyze the Electrostatic Forces Between Ions

The strength of the electrostatic forces between ions is directly proportional to the product of their charges and inversely proportional to the square of the distance between them (Coulomb's Law). In general, higher charges lead to stronger electrostatic forces and thus more energy required to break the ionic lattice. For these compounds: KCl: (+1) × (-1) = -1 (magnitude 1) Mg(OH)₂: (+2) × (-1) × 2 = -4 (magnitude 4) NaNO₃: (+1) × (-1) = -1 (magnitude 1)
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3. Determine the Compound with the Strongest Electrostatic Forces

From the previous step, we can determine that the compound with the strongest electrostatic forces is Mg(OH)â‚‚, with a charge magnitude of 4, which is the highest among all the given compounds.
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4. Conclusion

Therefore, the ionic lattice in the compound Mg(OH)₂ requires the most energy to break, as it has the strongest electrostatic forces between its ions in comparison to KCl and NaNO₃.

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Key Concepts

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

Ionic Charges
Understanding ionic charges is crucial when studying the behavior of ionic compounds. Essentially, an ionic charge is the electrical charge that an atom acquires when it loses or gains electrons to form an ion. In a neutral atom, the number of protons (positive charge) is equal to the number of electrons (negative charge). When an atom loses electrons, it becomes a positively charged ion, known as a cation. Conversely, when an atom gains electrons, it becomes a negatively charged ion, or an anion.

For example, in the compound potassium chloride (KCl), potassium (K) loses one electron and becomes a cation with a +1 charge, while chlorine (Cl) gains an electron to become an anion with a -1 charge. The understanding of these charges is vital as they influence how strongly the ions will attract each other within an ionic lattice.
Electrostatic Forces
The electrostatic force is a fundamental interaction between electrically charged particles. In ionic compounds, the electrostatic force is the attraction between cations and anions. This force is incredibly strong and is the primary factor holding the ionic lattice together. The strength of the electrostatic force directly influences the lattice energy of the compound – the energy required to separate the ions of an ionic compound into gaseous ions.

Higher ionic charges result in stronger electrostatic forces. For instance, magnesium hydroxide (Mg(OH)₂) exhibits a stronger electrostatic attraction compared to potassium chloride (KCl) because magnesium has a +2 charge, as opposed to the +1 charge of potassium, resulting in a greater force holding the ionic lattice together.
Coulomb's Law
Coulomb's Law is critical in quantifying the electrostatic force between two charged particles. This law states that the electrostatic force (\( F \)) between two point charges is directly proportional to the product of the charges (\( q_1 \text{ and } q_2 \)) and inversely proportional to the square of the distance (\( r \)) between them. Expressed mathematically, it is given by:\[\begin{equation}F = k \cdot \frac{{\left|q_1 \cdot q_2\right|}}{{r^2}}\text{, where } k \text{ is the Coulomb's constant.}\text{\end{equation}\]}Applying Coulomb's Law to ionic lattices, the force of attraction within a lattice with higher ionic charges will be greater, making the lattice more energetically stable and requiring more energy to break apart. This concept clearly explains why Mg(OH)₂, with a total charge magnitude of 4 from the magnesium ion, requires more energy to break compared to KCl or NaNO₃.
Ionic Compounds
Ionic compounds are chemical compounds consisting of ions held together by electrostatic forces termed as ionic bonding. The formation of ionic compounds typically involves a metal donating one or more electrons to a nonmetal, producing a positive metal ion (cation) and a negative nonmetal ion (anion). The resulting compound is usually a crystalline solid with a high melting point, due to the strong electrostatic forces of attraction within their lattice structure.

Take sodium nitrate (NaNO₃) as an example. It consists of sodium ions (Na⁻) and nitrate ions (NO₃⁻), each with a charge magnitude of 1. Although it is an ionic compound like KCl or Mg(OH)₂, the lattice energy required to break it apart is different due to the distinct charge interactions within its lattice as explained by Coulomb's Law and the concept of electrostatic forces.

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Most popular questions from this chapter

Our task is to measure the volume of blood in a live hippopotamus. One way to do this would be to drain its blood into a suitable container and measure its volume. Aside from the obviously disastrous effect this method would have on the hippo, it would not be very accurate since some blood would still remain behind in the tissues. Instead, we will inject the hippo with \(2.00 \mathrm{~mL}\) of a \(2.00 \mathrm{M}\) dye solution which the hippo will not appreciably metabolize or excrete in one hour, and then measure the dye concentration in the bloodstream after 30 minutes (which should be sufficient time for the dye to thoroughly mix in the bloodstream). After 30 minutes, the concentration of the dye in a \(78.0 \mathrm{~mL}\) blood sample was found to be \(0.0000125 \mathrm{M}\). What is the volume of blood in the hippo?

Your assistant tells you she measured out \(2.50\) moles of \(\mathrm{NaCl}\) and then added enough water to get \(500.0 \mathrm{~mL}\) of solution to prepare a \(5.00 \mathrm{M}\) solution of \(\mathrm{NaCl}\). (a) What was the mass of the \(\mathrm{NaCl}\) in grams? (b) Did she successfully prepare a \(2.5 \mathrm{M}\) solution? Prove your answer.

Define molarity.

A student plans to divide the molarity of his solution by its volume to determine the number of moles of solvent in it. He is making two mistakes here. Identify the mistakes and correct both of them.

How would you prepare \(250.0 \mathrm{~mL}\) of a \(0.350 \mathrm{M}\) \(\mathrm{NaOH}\) solution from a \(6.00 \mathrm{M} \mathrm{NaOH}\) stock solution?

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