Problem 1 - Biomass As A Sustainable Energy Source For The Future

Question

Dry woody biomass can be represented with the molecular formula \(\mathrm{CH}_{1.4} \mathrm{O}_{0.6}\). A sample of this biomass is torrefied to give a product gas with the following composition (on a mass basis): \(\mathrm{H}_{2} \mathrm{O}, 51 \%\); acetic acid \(\left(\mathrm{CH}_{3} \mathrm{COOH}\right), 20 \%\); \(\mathrm{CO}_{2}, 26 \%\); and \(\mathrm{CO}, 3 \%\).

Step-by-Step Solution

Answer

Answer: In the product gas, there are 1.03 moles of Carbon (C), 6.32 moles of Hydrogen (H), and 5.03 moles of Oxygen (O).

Step 1: Convert mass percentages to mass values

In this step, we assume a basis of 100g of dry woody biomass and convert the given mass percentages of products to mass values. This will allow us to work with absolute values and make it easier to understand the transformation. 1. \(\mathrm{H}_{2} \mathrm{O}\): 51% of 100g = 51g 2. Acetic acid (\(\mathrm{CH}_{3}\mathrm{COOH}\)): 20% of 100g = 20g 3. \(\mathrm{CO}_{2}\): 26% of 100g = 26g 4. \(\mathrm{CO}\): 3% of 100g = 3g

Step 2: Calculate the moles of each component

Here we will use the molecular weights of each component to calculate the moles of each in the product gas mixture: 1. Moles of \(\mathrm{H}_{2} \mathrm{O}\): \(\frac{51g}{18 g/mol} = 2.83\) mol 2. Moles of Acetic acid (\(\mathrm{CH}_{3}\mathrm{COOH}\)): \(\frac{20g}{60 g/mol} = 0.33\) mol 3. Moles of \(\mathrm{CO}_{2}\): \(\frac{26g}{44 g/mol} = 0.59\) mol 4. Moles of \(\mathrm{CO}\): \(\frac{3g}{28 g/mol} = 0.11\) mol

Step 3: Calculate the moles of elements in initial biomass

In this step, we will calculate the moles of each element (C, H, and O) in the initial biomass. We will use the molecular formula \(\mathrm{CH}_{1.4} \mathrm{O}_{0.6}\). Assume one mole of initial biomass, we have: 1. Moles of C: 1 mol 2. Moles of H: 1.4 mol 3. Moles of O: 0.6 mol

Step 4: Calculate the moles of elements in the product gas

In this step, we will use the moles of each component calculated in Step 2 and the molecular formulas of each to determine the moles of elements in the product gas mixture: 1. Moles of C: (0.33 mol from \(\mathrm{CH}_{3}\mathrm{COOH}\)) + (0.59 mol from \(\mathrm{CO}_{2}\)) + (0.11 mol from \(\mathrm{CO}\)) = 1.03 mol 2. Moles of H: (5.66 mol from \(\mathrm{H}_{2} \mathrm{O}\)) + (2 x 0.33 mol from \(\mathrm{CH}_{3}\mathrm{COOH}\)) = 6.32 mol 3. Moles of O: (2.83 mol from \(\mathrm{H}_{2} \mathrm{O}\)) + (2 x 0.33 mol from \(\mathrm{CH}_{3}\mathrm{COOH}\)) + (2 x 0.59 mol from \(\mathrm{CO}_{2}\)) + (0.11 mol from \(\mathrm{CO}\)) = 5.03 mol Now we have converted the given mass percentages into the moles of each element in the product gas. This could be used as a starting point for further analysis and understanding of the torrefaction process and reactions involved.

Key Concepts

Molecular Formula

Understanding the molecular formula is crucial when analyzing substances, as it provides information about the types of atoms and their quantities in a molecule. In the case of biomass torrefaction, knowing the molecular formula of dry woody biomass, which is \textbf{CH}\(_{1.4}\)\textbf{O}\(_{0.6}\), enables us to determine the relative amounts of carbon (C), hydrogen (H), and oxygen (O) before the process begins. Here, each molecule of biomass contains one carbon atom, 1.4 hydrogen atoms, and 0.6 oxygen atoms.

During torrefaction, this biomass is heated in the absence of oxygen, causing it to decompose into various gases. The molecular formulas of these product gases, such as \textbf{H}\(_2\)\textbf{O}, acetic acid (\textbf{CH}\(_3\)\textbf{COOH}), \textbf{CO}\(_2\), and \textbf{CO}, reveal the nature of the chemical transformation. A firm grasp on molecular formulas serves as a baseline for analyzing chemical reactions and understanding the changes undergone by the biomass.

Mass-to-Mole Conversion

In chemistry, the mole is a fundamental unit that quantifies matter at the molecular level. When we apply the process of mass-to-mole conversion to torrefaction, we're translating the mass of gases released to the number of moles. This step is vital because chemical reactions and stoichiometry are discussed in terms of moles rather than mass.

To convert mass to moles, we use the molecular weight of the substance. The calculation involves dividing the given mass of a substance by its molecular weight, expressed in grams per mole (\textbf{g/mol}). For example, if we have 51 grams of water (\textbf{H}\(_2\)\textbf{O}), with a molecular weight of 18 \textbf{g/mol}, we get \textbf{2.83 moles} of water. This conversion is a fundamental skill in chemistry, helping to link the tangible (mass) with the theoretical (molecular count).

Chemical Reaction Analysis

Chemical reaction analysis is an examination of the conversion of reactants to products during a chemical process. In biomass torrefaction, this involves tracking the transformation of solid biomass into various gases. The analysis not only considers the molecular formulas and mass-to-mole conversions but also the stoichiometry of the reaction – the relationships between the amounts of reactants used and products formed.

In our case, we start with dry woody biomass identified by the formula \textbf{CH}\(_{1.4}\)\textbf{O}\(_{0.6}\) and end with a mix of \textbf{H}\(_2\)\textbf{O}, \textbf{CH}\(_3\)\textbf{COOH}, \textbf{CO}\(_2\), and \textbf{CO}. By quantifying the moles of each product, we can infer the efficiency of the process and which elements are most prevalent in the end products. This insight is not only critical for optimizing torrefaction but also for understanding the impact on energy yield and potential emissions from the biomass.

Elements in Biomass

Biomass consists of organic materials, derived mainly from plants. The key elements present are carbon (C), hydrogen (H), and oxygen (O), typically found in the cellulose and lignin that compose the structural framework of plant cells. In the case of dry woody biomass used for torrefaction, the molecular formula \textbf{CH}\(_{1.4}\)\textbf{O}\(_{0.6}\) highlights the ratio of these elements.

Knowing the elemental composition is essential when considering energy content and the potential products of thermal processes like torrefaction or combustion. The elements carbon and hydrogen primarily contribute to the combustion process, while oxygen is crucial in reactions involving oxidation. Understanding the elemental makeup of biomass not only helps us predict the possible outcomes and efficiencies of processes like torrefaction but also to estimate the environmental footprint and sustainability of using biomass as a renewable energy source.