General Chemistry: Energy Conversion and Electrostatic Potential in Ionic Compounds

Chapter 5: Energy and Electrostatics in Chemistry

Energy Conversion: Calories to Joules

Understanding energy conversion is essential in chemistry, especially when dealing with nutritional values and chemical reactions. The joule (J) is the SI unit of energy, while the calorie (cal) is commonly used in food energy.

• Definition: 1 calorie is the amount of energy required to raise the temperature of 1 gram of water by 1°C.

• Conversion Factor: $1\ \text{calorie} = 4.184\ \text{Joules}$

• Application: To convert calories to joules, multiply the number of calories by 4.184.

Example: How much energy in joules is contained in a candy bar having 195 Calories?

• Note: Food Calories (with a capital 'C') are actually kilocalories (kcal).

• Calculation: $195\ \text{Cal} \times 1000\ \text{cal/Cal} \times 4.184\ \text{J/cal} = 816,000\ \text{J}$

• Expressed in scientific notation: $8.16 \times 10^5\ \text{J}$

Answer: $8.16 \times 10^5\ \text{J}$

Electrostatic Potential Energy in Ionic Compounds

The electrostatic potential energy between ions in an ionic compound is determined by Coulomb's Law. The magnitude of this energy depends on the charges of the ions and the distance between them.

• Coulomb's Law: $E = \dfrac{kQ_1Q_2}{r}$, where $E$ is the potential energy, $k$ is a constant, $Q_1$ and $Q_2$ are the charges, and $r$ is the distance between ions.

• Charge Comparison:

  • MgO: $\text{Mg}^{2+}$ and $\text{O}^{2-}$ (charges: $+2$ and $-2$)

  • NaF: $\text{Na}^{+}$ and $\text{F}^{-}$ (charges: $+1$ and $-1$)

• Relative Potential Energy:

  • MgO: $E \propto (+2) \times (-2) = -4$

  • NaF: $E \propto (+1) \times (-1) = -1$

  • Ratio: $\dfrac{|-4|}{|-1|} = 4$

Answer: The electrostatic potential energy between the ions in MgO is 4 times greater than that in NaF, assuming the same internuclear distance.

Compound	Cation Charge	Anion Charge	Product of Charges	Relative Potential Energy
MgO	+2	-2	-4	4x (compared to NaF)
NaF	+1	-1	-1	1x

Additional info: The strength of ionic bonds increases with the magnitude of the charges and decreases with increasing distance between ions. MgO has a much higher lattice energy than NaF due to the higher charges.