Carbon Combustion: Finding Reaction Yield

Hey there, chemistry enthusiasts! Let's dive into a classic problem: calculating the reaction yield when carbon burns. We'll break down the steps, making it super easy to understand. So, grab your lab coats (metaphorically, of course!) and let's get started. The core of this problem revolves around the combustion of carbon. When carbon (C) burns in the presence of oxygen (O2), it produces carbon dioxide (CO2) gas. The problem gives us some key data: 2.4 grams of carbon reacted, and 0.15 moles of gas were produced. Our mission is to calculate the reaction yield, often expressed as a percentage. This tells us how efficiently the reaction converted the carbon into carbon dioxide. Think of it like this: if you expected to bake a perfect dozen cookies, but only got 9, your yield would be 75%. Same concept applies here, but with carbon and CO2.

First, let's look at the balanced chemical equation, which is crucial for any stoichiometry problem: C + O2 -> CO2. This equation tells us that one mole of carbon reacts with one mole of oxygen to produce one mole of carbon dioxide. Knowing this, we can move forward with our calculations. We'll need to figure out how many moles of CO2 should have been produced if the reaction went perfectly. Then, we compare that theoretical yield to the actual yield (0.15 moles, as given in the problem) to determine the percentage yield. This process is fundamental to understanding how chemical reactions work and is super important in fields like industrial chemistry, where maximizing yield can lead to significant cost savings. We need to remember that in the real world, reactions rarely go to 100%. Various factors such as incomplete reactions, side reactions, or loss of product during the experiment all play a role in reducing the yield. The concept of yield is closely related to the concept of limiting reagents, which dictates how much product can be formed. The theoretical yield represents the maximum amount of product that can be formed based on the amount of limiting reactant, assuming that the reaction goes to completion. Therefore, in our case, the theoretical yield of CO2 is based on how much carbon we have available to react.

To begin, we need to convert the mass of carbon (2.4 g) into moles. The molar mass of carbon (C) is approximately 12 g/mol. We can use this to find the number of moles of carbon present using the formula: moles = mass / molar mass. So, moles of C = 2.4 g / 12 g/mol = 0.2 moles. According to the balanced equation, one mole of carbon produces one mole of carbon dioxide. Therefore, if we started with 0.2 moles of carbon, the theoretical yield of CO2 is also 0.2 moles. This is the amount of CO2 we should have gotten if the reaction was perfect.

Calculating the Percentage Yield

Okay, now that we've got the theoretical yield (0.2 moles) and the actual yield (0.15 moles), we can calculate the percentage yield. The formula for percentage yield is: Percentage Yield = (Actual Yield / Theoretical Yield) * 100%. Plugging in our values: Percentage Yield = (0.15 moles / 0.2 moles) * 100% = 75%. This means that the reaction produced 75% of the amount of CO2 it could have produced if it went perfectly. So, what does this tell us? The percentage yield gives us a measure of how efficiently the reaction proceeded. A yield of 100% means that all the reactants were converted to products without any loss. In real-world scenarios, however, obtaining a 100% yield is rare due to various factors that may affect the reaction, like competing side reactions, the volatility of the reactants or products (leading to losses), and incomplete reactions (where the reactants do not fully convert into products). The value of yield greatly impacts different industries. For example, in the pharmaceutical industry, a high yield is a key factor in manufacturing drugs because it can affect the costs, the efficiency of the production, and the environmental impact of the process. In the world of research, chemists are constantly striving to maximize the yield of their reactions through optimizing the reaction conditions (such as temperature, pressure, or the presence of a catalyst).

The calculation also helps us understand potential sources of error and areas for improvement in the experiment or process. If the yield is lower than expected, it could indicate issues like contamination of reactants, incorrect measurements, or inadequate reaction conditions. Improving the yield involves careful consideration of the reaction conditions and the optimization of variables such as temperature, pressure, reaction time, and the presence of catalysts. Sometimes, optimizing reaction conditions requires trial and error, a fundamental aspect of the scientific method. Experimenters often begin with a set of standard conditions and then systematically change one variable at a time while measuring the impact on the yield. This process helps them identify the best conditions to maximize the yield of the desired product. In cases where the desired product may decompose under the reaction conditions, a technique known as