The standard enthalpy of formation of H2 O(l) at 298 K is -285.8 kJ / mol . Calculate the chang

The standard enthalpy of formation of H2 O(l) at 298 K is...

The standard enthalpy of formation of $\mathrm{H}_{2} \mathrm{O}(l)$ at $298 \mathrm{~K}$ is $-285.8$ $\mathrm{kJ} / \mathrm{mol} .$ Calculate the change in internal energy for the following process at $298 \mathrm{~K}$ and 1 atm: $$ \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \quad \Delta E^{\circ}=? $$ (Hint: Using the ideal gas equation, derive an expression for work in terms of $n, R$, and $T$.)

The standard enthalpy of formation of $\mathrm{H}_{2} \mathrm{O}(l)$ at $298 \mathrm{~K}$ is $-285.8$ $\mathrm{kJ} / \mathrm{mol} .$ Calculate the change in internal energy for the following process at $298 \mathrm{~K}$ and 1 atm:
$$
\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \quad \Delta E^{\circ}=?
$$
(Hint: Using the ideal gas equation, derive an expression for work in terms of $n, R$, and $T$.)

Key Concepts

Standard Enthalpy of Formation

This concept refers to the change in enthalpy when one mole of a compound is formed from its elements in their standard states at a specified temperature and pressure. It serves as a reference point in thermochemistry for calculating the enthalpy changes of various reactions.

Relationship Between Enthalpy and Internal Energy

Enthalpy (H) and internal energy (E) are related by the equation H = E + PV. For processes at constant pressure, the change in enthalpy is the sum of the change in internal energy and the work done by or against the system by expansion or compression. This relationship is crucial in converting between these quantities during chemical reactions.

Pressure-Volume Work

Pressure-volume work arises when a system expands or contracts under constant external pressure. In ideal gases, the work done can be expressed as w = -P?V, and using the ideal gas law, this work can be related to the change in the number of moles of gas and temperature (w = -?nRT), which plays a significant role in connecting ?H and ?E.

Ideal Gas Law

The ideal gas law (PV = nRT) links pressure, volume, temperature, and the number of moles of a gas. It is used to describe the behavior of gases under various conditions and is particularly important when analyzing thermodynamic processes that involve gaseous reactants or products, allowing the calculation of work associated with volume changes.

Transcript

00:01 So in this problem, we're asked to find delta e of this particular reaction.

00:07 So up on the board, i have the print information.

00:09 We have the reaction of water being broken down into hydrogen gas and oxygen gas.

00:16 They give us an enthalpy of the formation of water, which is a 285 .8.

00:21 Now, i went ahead and corrected the sign because they give us the formation of water is negative 285 .8.

00:28 So when water is a product formed by joining hydrogen and oxygen together, we get negative 285 .8.

00:38 However, we're doing a reverse reaction here.

00:40 So we need to keep that in mind.

00:41 We need to watch that sign.

00:43 So delta h, and these are standard state conditions, one atmosphere, 25 degrees celsius, we'll go and use delta h as positive 285.

00:53 Now, the main equation we'll use is delta h equals delta e plus p delta v.

01:00 We're just using the definition of delta h.

01:03 Here we can figure out this information mathematically.

01:09 We already have this, and then we'll ultimately solve for that value.

01:14 Now, how do we solve for p delta v? i'll give you a little bit of background on that.

01:19 P delta v is pressure times.

01:24 The final volume minus initial volume.

01:28 The final volume is gaseous.

01:30 Initial volume is liquid.

01:32 Now, the liquid water is so minimal compared to the gaseous volume that we essentially neglect it.

01:39 So what we're looking at is pressure times the volume of that gas.

01:44 Now, unfortunately, we don't have that information.

01:47 As far as the volume goes, we know it's at one atmosphere.

01:50 So we need to use the fact that this, using ideal gas law, pv equals nrt.

01:57 Well, we have enough information.

02:00 We know temperature is 298 degrees kelvin.

02:02 We have the r gas constant, and we know we have one and a half moles worth of gas from the first equation...

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