Nitromethane, CH3 NO2, can be used as a fuel. When the...

Nitromethane, $\mathrm{CH}_{3} \mathrm{NO}_{2}$, can be used as a fuel. When the liquid is burned, the (unbalanced) reaction is mainly $$ \mathrm{CH}_{3} \mathrm{NO}_{2}(l)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{N}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g) $$ a. The standard enthalpy change of reaction $\left(\Delta H_{\mathrm{rxn}}^{\circ}\right)$ for the balanced reaction (with lowest whole-number coefficients) is $-1288.5 \mathrm{~kJ} .$ Calculate the $\Delta H_{\mathrm{f}}^{\circ}$ for nitromethane. b. A $15.0$ - $\mathrm{L}$ flask containing a sample of nitromethane is filled with $\mathrm{O}_{2}$ and the flask is heated to $100 .^{\circ} \mathrm{C}$. At this temperature, and after the reaction is complete, the total pressure of all the gases inside the flask is 950 . torr. If the mole fraction of nitrogen ( $\chi_{\text {nitrogen }}$ ) is $0.134$ after the reaction is complete, what mass of nitrogen was produced?

Nitromethane, $\mathrm{CH}_{3} \mathrm{NO}_{2}$, can be used as a fuel. When the liquid is burned, the (unbalanced) reaction is mainly
$$
\mathrm{CH}_{3} \mathrm{NO}_{2}(l)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{N}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)
$$
a. The standard enthalpy change of reaction $\left(\Delta H_{\mathrm{rxn}}^{\circ}\right)$ for the balanced reaction (with lowest whole-number coefficients) is $-1288.5 \mathrm{~kJ} .$ Calculate the $\Delta H_{\mathrm{f}}^{\circ}$ for nitromethane.
b. A $15.0$ - $\mathrm{L}$ flask containing a sample of nitromethane is filled with $\mathrm{O}_{2}$ and the flask is heated to $100 .^{\circ} \mathrm{C}$. At this temperature, and after the reaction is complete, the total pressure of all the gases inside the flask is 950 . torr. If the mole fraction of nitrogen ( $\chi_{\text {nitrogen }}$ ) is $0.134$ after the reaction is complete, what mass of nitrogen was produced?

Key Concepts

Stoichiometry

Stoichiometry involves the quantitative relationships between reactants and products in a chemical reaction. It enables the calculation of amounts of substances consumed or produced, based on the balanced chemical equation and measured reaction conditions.

Ideal Gas Law

The Ideal Gas Law (PV = nRT) relates the pressure, volume, temperature, and number of moles of a gas. It is a key tool in gas-phase calculations, allowing the determination of quantities such as moles and masses from measured pressures and volumes.

Mole Fraction

Mole fraction is the ratio of the number of moles of a particular component to the total number of moles in a mixture. In gas mixtures, it is directly related to partial pressure and is used to analyze the composition of the mixture after a reaction.

Balanced Chemical Equations

Balanced equations are essential to represent the correct stoichiometric relationships among reactants and products in a chemical reaction. They ensure that mass and energy are conserved and provide the basis for quantitative calculations in reaction processes.

Standard Enthalpy of Formation

This concept represents the enthalpy change when one mole of a compound is formed from its constituent elements in their standard states. It is a fundamental reference point in thermochemistry and is used to calculate reaction enthalpies by applying Hess’s Law.

Hess’s Law

Hess’s Law states that the overall enthalpy change for a reaction is independent of the pathway taken, allowing the calculation of unknown reaction enthalpies using known standard enthalpies of formation. This principle is vital for determining the energy changes in chemical reactions.

Transcript

00:01 Okay, in this problem, we're asked to find the heat of formation of nitromethane.

00:05 And then we're also tasked with trying to figure out how many grams of nitrogen is produced in a particular scenario.

00:12 So we'll go ahead and do the first question.

00:15 We're given the overall heat for the reaction, and we do need to balance the equation first.

00:21 So i went ahead and balanced the equation.

00:24 We have four molecules of the nitro methane in the presence of three oxygen molecules.

00:30 We'll get four carbon dioxide, two nitrogen gas molecules, and six gaseous water molecules.

00:37 Everything is gas except for the liquid.

00:40 I went ahead and marked that as liquid.

00:43 Everything else is gas to save room.

00:46 So as we proceed, we basically, we need to go with the fact that, let me go back to the right screen here.

00:56 We need to use that delta we need to use that delta delta h the overall heat of formation or you know enthalpy of a reaction here hold on that's the reaction here reaction is figured out by summing all the heats of formation of the products and subtracting out the heats of formation of all of the reactants so we've done this quite a few times in this particular unit and and we'll go ahead and do the math there and then solve for the missing.

01:40 We're trying to figure out the heat of formation of strictly the nitromethane gas.

01:44 So we'll go ahead and go through the math there.

01:47 On the product side, we have just the carbon dioxide and water that we're concerned about.

01:52 So for products, we have four times negative 393 .5.

02:05 And there's a six water molecules.

02:07 That's in the gaseous state.

02:09 Keep that in mind.

02:14 So we have negative 1574 and negative 1450 .8.

02:24 Now when we add those together, we get 30, 24 .8 with a negative sign.

02:32 So we'll go ahead and put that on our product side.

02:35 So delta h, which is negative 128 .8 .5, they gave that as the delta h for the overall heat of the reaction given the lowest whole number coefficients.

02:50 We have that already.

02:51 And we're going to say, okay, well, it's product minus reactants.

02:56 So we have negative 3024 .8.

03:00 Notice i left off the nitrogen.

03:02 We're not concerned with the standalone elements.

03:06 Those have the delta h of zero.

03:08 So combined with the water and carbon dioxide, we have the negative 3024 .8.

03:14 And we're going to go ahead and subtract.

03:15 Well, we have four times mystery number x.

03:18 We don't know that heated formation.

03:20 We'll find that real quick...