Consider the following reaction: 2 CH 3 OH(g) → 2 CH 4 (g) + O 2 (g) ΔH = +252.8 kJ (c) For a given sample of CH 3 OH, the enthalpy change during the reaction is 82.1 kJ. How many grams of methane gas are produced?

All right. Hi, everyone. So this question says that charcoal is primarily carbon, determine the mass of carbon dioxide produced by burning enough carbon in the form of charcoal to produce 5.00 multiplied by 10 to the second kilojoules of heat. Now, here we have the chemical equation for the combustion of carbon and four different answer choices labeled A through D proposing different values for the mass of carbon dioxide in grams. Now, in this case, next to the chemical equation, we're given Delta H standard for this combustion reaction which equals negative 393.5 kg joules. Now because Delta H is negative recall, this means that heat has been produced as a result of this reaction, right? Is an exothermic process. Now, because we are given the amount of heat produced during this process, we can use this information to calculate the mass of carbon dioxide by treating it as a conversion factor. Notice how in the chemical equation provided one mole of carbon dioxide is produced on the on the product side. Of course, this means that for every one mole of carbon dioxide produced 393.5 kilojoules of heat are released. So we're going to use this correlation to find the mass of carbon dioxide. But before we do that recall also that the molar mass of carbon dioxide is equal to 44.01 g per mole. So lets go ahead and get started. No, in this case, we're going to start with the information that we were given, which was the amount of heat that we are intending to produce. Right. So my first value that I'm writing down is 5.00 multiplied by 10 to the second kilojoules. So this is the amount of heat that is needed. This is the amount of heat that we are intending to produce. So we're going to use delta H in this case to convert the heat needed into moles of carbon dioxide, which we can then convert into the mass of carbon dioxide. Now, to do that, we're going to treat this correlation as a conversion factor. So I'm going to treat it as a fraction with a numerator and a denominator. Now recall that the aim should always be to cancel out your starting unit. So if my starting units are kilojoules, then kilojoules should be in the denominator of my conversion factor. And the reason for this is to ensure that kilo jewels cancel out which they do. So by doing this, our answer is going to be expressed in moles of carbon dioxide. So now we can go from moles of carbon dioxide to grams of carbon dioxide. And we do that using the molar mass. So to do that, I need one more conversion factor in which moles of carbon dioxide should go in the denominator to make sure that those units cancel out, which means that the mass, the molar mass of carbon dioxide should go in the numerator. So after doing this, after setting up my second conversion factor, we can see that our answer is going to be expressed in grams of carbon dioxide, which is what we're looking for in this case. So to evaluate this expression, I'm going to go ahead and multiply together my numerators and divide by my denominators in my conversion factors. So after doing so and rounding to three significant figures, my final answer comes out to 55.9 g of carbon dioxide and this corresponds to option B in the multiple choice. So there you have it. And with that being said, thank you so very much for watching. And I hope you found this helpful.

Ch.5 - Thermochemistry

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Brown 14th Edition

Ch.5 - Thermochemistry

Problem 44c

Chapter 5, Problem 44c

Consider the following reaction: 2 CH₃OH(g) → 2 CH₄(g) + O₂(g) ΔH = +252.8 kJ (c) For a given sample of CH₃OH, the enthalpy change during the reaction is 82.1 kJ. How many grams of methane gas are produced?

Verified step by step guidance

Identify the stoichiometry of the reaction: 2 moles of CH3OH produce 2 moles of CH4 and 1 mole of O2. The enthalpy change (ΔH) for this reaction is +252.8 kJ for 2 moles of CH3OH.

Determine the enthalpy change per mole of CH3OH by dividing the given ΔH by 2, since the reaction involves 2 moles of CH3OH. This will give you the enthalpy change for 1 mole of CH3OH.

Calculate the number of moles of CH3OH that correspond to the given enthalpy change of 82.1 kJ. Use the formula: \( \text{moles of CH3OH} = \frac{\text{given enthalpy change}}{\text{enthalpy change per mole of CH3OH}} \).

Since the stoichiometry of the reaction shows that 2 moles of CH3OH produce 2 moles of CH4, the moles of CH4 produced will be equal to the moles of CH3OH reacted.

Convert the moles of CH4 to grams using the molar mass of CH4 (16.04 g/mol). Use the formula: \( \text{mass of CH4} = \text{moles of CH4} \times \text{molar mass of CH4} \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the balanced equation. It allows us to determine the relationships between the amounts of substances involved. In this case, the stoichiometric coefficients indicate that 2 moles of CH3OH produce 2 moles of CH4, establishing a 1:1 ratio for their quantities.

Enthalpy Change (ΔH)

Enthalpy change (ΔH) represents the heat absorbed or released during a chemical reaction at constant pressure. A positive ΔH indicates an endothermic reaction, meaning energy is absorbed. In this reaction, the given ΔH of +252.8 kJ signifies that 2 moles of CH3OH absorb this amount of energy to produce the products.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is essential for converting between moles and grams. For methane (CH4), the molar mass is approximately 16.04 g/mol, which will be used to calculate the mass of methane produced based on the moles derived from the enthalpy change.