The total volume of hydrogen gas needed to fill the...

The total volume of hydrogen gas needed to fill the Hindenburg was $2.0 \times 10^{8} \mathrm{L}$ at 1.0 atm and $25^{\circ} \mathrm{C}$. Given that $\Delta H_{\mathrm{f}}^{\circ}$ for $\mathrm{H}_{2} \mathrm{O}(l)$ is $-286 \mathrm{kJ} / \mathrm{mol},$ how much heat was evolved when the Hindenburg exploded, assuming all of the hydrogen reacted to form water?

Key Concepts

Ideal Gas Law

The ideal gas law (PV = nRT) is a fundamental relation in physical chemistry that connects pressure, volume, temperature, and the number of moles of a gas. It is used to calculate the amount of gas present under specific conditions, which is crucial for converting volumes (like that of a gas-filled container) into moles for subsequent energy calculations in chemical reactions.

Standard Enthalpy of Formation

The standard enthalpy of formation is the enthalpy change when one mole of a compound is formed from its elements in their standard states under standard conditions. This concept is important in thermochemistry because it provides a reference point for calculating the heat changes in reactions where compounds are formed or consumed.

Reaction Stoichiometry

Reaction stoichiometry involves the use of balanced chemical equations to relate the quantities of reactants and products involved in a chemical reaction. It allows for the conversion of amounts from one substance (measured in moles) to another, ensuring that the proportions in the chemical equation are maintained during energy calculations.

Calculation of Reaction Enthalpy

The calculation of reaction enthalpy involves determining the overall heat change associated with a chemical reaction, often by combining the standard enthalpies of formation of the reactants and products. By using the stoichiometrically determined number of moles of a reactant that participates in the reaction, one can multiply it by the enthalpy change per mole to find the total heat evolved or absorbed during the reaction.

Transcript

00:02 Hello.

00:03 In this question, we are trying to determine how much energy was released when the hindenburg exploded.

00:11 So we are given some information here in the problem.

00:15 We know that we are assuming a pressure of one atmosphere.

00:24 We have a volume given of 2 .0 times 10 to the 8th liters.

00:36 And we have a temperature of 25 degrees celsius.

00:42 I'm going to go ahead and add 273 to that right way to convert it to kelvin.

00:50 All right, so we have that information concerning the gas.

00:54 We are also given a heat of formation for liquid water.

01:03 And that is equal to negative 286 kilojoules per mole.

01:15 Again, this is for liquid water, but the problem says to assume that the hydrogen reacted to form.

01:22 Water, assuming that all of it reacted.

01:26 All right, so that gives us a way to solve this.

01:29 We have the amount of energy per mole.

01:32 So if we can determine the number of moles of hydrogen we have, we should be able to use that heat of formation to calculate the amount of energy released.

01:42 Fortunately, we do have a way to find the number of moles.

01:45 We can use the ideal gas law.

01:49 Pv equals nrt.

01:52 Because we have a pressure of volume and a temperature, r is a constant, so we have that as well.

02:00 So if we are trying to solve for n, rearranging this equation, we give us pv divided by rt.

02:08 So let's go ahead and solve for a number of moles.

02:14 So number of moles, the pressure is one atmosphere, volume 2 .0 times 10 to the 8th liters, the r value...

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