Sodium hydroxide (NaOH) has a lattice energy of -887 kJ / mol and a heat of hydration of -932 kJ

step 1 Right here we have the problem 102. And for long questions like this, I always like to start by

Sodium hydroxide (NaOH) has a lattice energy of -887 kJ /...

Sodium hydroxide $(\mathrm{NaOH})$ has a lattice energy of $-887 \mathrm{kJ} / \mathrm{mol}$ and a heat of hydration of $-932 \mathrm{kJ} / \mathrm{mol} .$ How much solution could be heated to boiling by the heat evolved by the dissolution of 25.0 $\mathrm{g}$ of NaOH? (For the solution, assume a heat capacity of $4.0 \mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C},$ an initial temperature of $25.0^{\circ} \mathrm{C},$ a boiling point of $100.0^{\circ} \mathrm{C}$ , and a density of 1.05 $\mathrm{g} / \mathrm{mL}$ )

Sodium hydroxide $(\mathrm{NaOH})$ has a lattice energy of $-887 \mathrm{kJ} / \mathrm{mol}$
and a heat of hydration of $-932 \mathrm{kJ} / \mathrm{mol} .$ How much solution could be heated to boiling by the heat evolved by the dissolution of 25.0 $\mathrm{g}$ of NaOH? (For the solution, assume a heat capacity of $4.0 \mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C},$ an initial temperature of $25.0^{\circ} \mathrm{C},$ a boiling point of $100.0^{\circ} \mathrm{C}$ , and a density of 1.05 $\mathrm{g} / \mathrm{mL}$ )

Key Concepts

Heat Capacity

Heat capacity is the amount of energy needed to raise the temperature of a given mass of a substance by 1 degree Celsius. It is a key concept in thermodynamics, particularly in calculating how much a system's temperature will change when a specific energy is added or removed.

Enthalpy Change of Solution

The enthalpy change of solution is the net energy change that occurs when a solute dissolves in a solvent. It is determined by the balance between lattice energy (which must be overcome) and the heat of hydration (energy released), and it indicates whether the dissolution process is overall exothermic or endothermic.

Density

Density is defined as mass per unit volume, and it is essential for converting between mass and volume. In solution chemistry, understanding density is important for determining the volume of a solution from its mass, which in turn is crucial for various practical applications such as heating calculations.

Lattice Energy

Lattice energy is the energy released when oppositely charged ions in the gas phase come together to form a solid ionic compound. It represents the strength of the ionic bonding in a crystal lattice and is an important concept in understanding the energetics of ionic compounds.

Heat of Hydration

Heat of hydration is the energy released when gaseous ions are surrounded by water molecules during dissolution. This process stabilizes the ions in solution and can significantly contribute to the overall energy change during the formation of a solution.

Transcript

00:01 Right here we have the problem 102.

00:03 And for long questions like this, i always like to start by writing down the data that we know and then start solving the question.

00:13 So first we know the lattice energy for nalh equal to negative 887 kilojoules per mole.

00:24 And we know the heat up hydration for nalh is equal to negative 932.

00:34 32 kilojoules per mole.

00:40 And we know the mass of naaoh is equal to 25 gram.

00:49 Density of the solution is equal to 1 .05 gram per milliliter.

00:57 And the heat capacity is equal to 4 joules per gram per celsius degree.

01:10 And the initial temperature is equal to 20 degrees.

01:14 25 celsius degree and the boiling point is equal to 100 celsius degree.

01:25 So delta t equal to 100 minus 25, that's 75 degree.

01:32 All right, so the equation we know that delta h of the solution is equal to delta h of the solute plus the heat of hydration and delta h of solute is equal to negative energy of lattice.

02:06 So we have delta h solution equal to negative delta h lattice plus the heat of hydration.

02:26 So now we substitute numbers that is equal to negative, negative, 887 kilojouze per mole, plus negative 932 kilojoules per mole, and we get the delta h of the solution equal to negative 45 kilojoules per mole.

02:54 So that is the delta h of the solution...

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