The enthalpy of formation of magnesium oxide, MgO(s), is -601827 kJ / kmol at 25^∘ C. The meltin

The enthalpy of formation of magnesium oxide, MgO(s), is...

The enthalpy of formation of magnesium oxide, $\mathrm{MgO}(\mathrm{s}),$ is $-601827 \mathrm{kJ} / \mathrm{kmol}$ at $25^{\circ} \mathrm{C}$. The melting point of magnesium oxide is approximately $3000 \mathrm{K},$ and the increase in enthalpy between 298 and $3000 \mathrm{K}$ is $128449 \mathrm{kJ} / \mathrm{kmol}$. The enthalpy of sublimation at $3000 \mathrm{K}$ is estimated at 418000 $\mathrm{kJ} / \mathrm{kmol}$, and the specific heat of magnesium oxide vapor above $3000 \mathrm{K}$ is estimated at 37.24 $\mathrm{kJ} / \mathrm{kmol} \mathrm{K}.$

Key Concepts

Temperature Dependence of Enthalpy

Enthalpy is a state function that can vary with temperature. Adjusting enthalpy values from one temperature to another requires integration of the heat capacity over the temperature range, a concept that is crucial for accurate thermodynamic analyses across different conditions.

Enthalpy of Sublimation

The enthalpy of sublimation is the energy required for a substance to convert directly from the solid phase to the gas phase without passing through a liquid phase. It combines the energy needed to overcome the lattice energy of the solid and the energy to form the gaseous state, serving as an important parameter in thermodynamic calculations involving phase transitions.

Specific Heat Capacity

Specific heat capacity refers to the amount of energy required to increase the temperature of a unit amount of a substance by one degree. It is essential for understanding how temperature changes influence the internal energy of a substance.

Enthalpy of Formation

This is the heat change that accompanies the formation of a compound from its constituent elements in their standard states. It is a key concept in thermochemistry used to calculate the energy released or absorbed during chemical reactions and to assess the stability of compounds.

Phase Changes

Phase changes, such as melting and sublimation, involve transitions between different states of matter (solid, liquid, and gas). They require specific amounts of energy (latent heat) which are separate from the energy needed for temperature changes, and are fundamental in analyzing material behavior under varying conditions.

Transcript

00:01 And this problem, we have magnesium oxide, or we have magnesium that's combusting with oxygen to make magnesium oxide.

00:09 So it's a solid fuel.

00:12 So we're told that the enthalpyal formation of magnesium oxide, which is a solid also, is minus 602 megajoules per kilamol at 25c.

00:28 And we know that the melting point of magnesium oxide is approximately, 3 ,000 kelvin.

00:37 So we are not sure exactly when we react this, whether this is a solid or a liquid.

00:45 And let's see here.

00:46 There increased an entropy between room temperature and 3 ,000 kelvin, where it melts, is about 120, 128 megajoules per kilmole.

01:00 And then we have the entropy of sublimation.

01:02 I guess this never goes through a liquid phase, so it just sublimates to a gas.

01:06 The entropy of sublimation at 3 ,000 kelvin is estimated at 418 megajoules per kilomole.

01:15 And the specific heat of the magnesium oxide vapor above 3 ,000 kelvin is estimated to be 37 .24 kilojoules per kilomore calvin.

01:28 Okay, so we got a lot of information here about magnesium or magnesium oxide anyway.

01:33 So we are asked to determine the entropy of combustion for a kilogram of this stuff, or per kilogram.

01:47 So the entropy of combustion is just going to be the entropy of the reactants, or the products minus that of the reactants.

01:58 Well, there's no entropy of formation of these reactants.

02:02 This is base.

02:03 These are base molecules or base atom.

02:08 And so that means that the entropy of combustion per kilomole is just the entropy of formation of the magnesium oxide, which is 602 megajoules per kilomole or minus that.

02:21 But we were asked for it in kilograms, so we need to divide by the molecular mass of magnesium, which we can look up.

02:28 And so we get minus 247, minus 24 ,000, minus 24 ,000, minus 24 ,000, minus 24 ,000, minus 24, 7.

02:38 100 kilojoules per kilogram...

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