Solving Chemistry Problems: Oxygen Mass Calculation

Hey guys! Let's dive into a cool chemistry problem. We're going to figure out how much oxygen is produced when potassium permanganate (KMnO₄) breaks down. This is a classic stoichiometry problem, and I'll walk you through it step by step. So, grab your notebooks, and let's get started. We need to find the mass of oxygen (O₂) formed when 12.25 grams of potassium permanganate (KMnO₄) decomposes. The balanced chemical equation for the reaction is: 2KMnO₄ → K₂MnO₄ + MnO₂ + O₂. To solve this problem, we'll use a few key concepts: molar mass, moles, and the mole ratio from the balanced equation. Don't worry if these terms sound a bit scary. I'll explain everything in simple terms. We'll break down the process into easy-to-follow steps, so you can understand the problem, even if you're new to chemistry. It's all about understanding the relationships between the amounts of reactants and products involved in a chemical reaction. And the best part is, you can apply these steps to many other chemistry problems! Keep reading, and you'll be able to solve similar problems on your own in no time. Chemistry is like a puzzle, and we're about to put the pieces together to find the mass of oxygen produced. Let’s get our calculators ready, and let's get solving this interesting problem. We will use the balanced chemical equation to find the relationship between the potassium permanganate and the oxygen. Let’s get started.

Step 1: Calculate the Molar Mass of KMnO₄

First, we need to know the molar mass of potassium permanganate (KMnO₄). The molar mass is the mass of one mole of a substance. To calculate it, we'll use the atomic masses from the periodic table: potassium (K) = 39.10 g/mol, manganese (Mn) = 54.94 g/mol, and oxygen (O) = 16.00 g/mol. Since KMnO₄ has one potassium atom, one manganese atom, and four oxygen atoms, we'll calculate the molar mass as follows: (1 × 39.10 g/mol) + (1 × 54.94 g/mol) + (4 × 16.00 g/mol) = 39.10 g/mol + 54.94 g/mol + 64.00 g/mol = 158.04 g/mol. So, the molar mass of KMnO₄ is 158.04 g/mol. This means that one mole of KMnO₄ weighs 158.04 grams. This will be an important number to help us move forward. We will need this molar mass to convert grams of KMnO₄ into moles, which we'll use in the next step. Understanding molar mass is crucial in solving any stoichiometry problem, because it gives you the conversion factor to change mass to moles, and moles to mass, and relates all the different chemical substances involved in a reaction. It is a fundamental concept in chemistry. Alright! Let’s proceed to step two, which will help us calculate the number of moles.

Step 2: Convert Grams of KMnO₄ to Moles

Now, let's convert the given mass of KMnO₄ (12.25 g) to moles. We'll use the molar mass we calculated in Step 1. The formula to convert grams to moles is: moles = mass (in grams) / molar mass. So, moles of KMnO₄ = 12.25 g / 158.04 g/mol = 0.0775 mol. This means that 12.25 grams of KMnO₄ is equivalent to 0.0775 moles. Understanding the conversion from grams to moles is essential because it allows us to use the balanced chemical equation to relate the amount of reactants to the amount of products. The balanced equation is written in terms of moles. Now that we know the number of moles of KMnO₄, we can use the balanced equation to determine how many moles of oxygen are produced. Let’s go to the next step and finish the problem to find our final answer. Just hang on, the problem is almost done. By the end of this step, we’ll see how much oxygen is produced. Let's do this!

Step 3: Determine the Moles of O₂ Produced Using the Mole Ratio

Next, we'll use the balanced chemical equation to find the mole ratio between KMnO₄ and O₂. The balanced equation is: 2KMnO₄ → K₂MnO₄ + MnO₂ + O₂. The equation shows that 2 moles of KMnO₄ produce 1 mole of O₂. So, the mole ratio is 2:1 (KMnO₄:O₂). To find the moles of O₂ produced, we'll use the following calculation: moles of O₂ = (moles of KMnO₄) × (mole ratio). Moles of O₂ = 0.0775 mol KMnO₄ × (1 mol O₂ / 2 mol KMnO₄) = 0.03875 mol O₂. This means that 0.0775 moles of KMnO₄ produce 0.03875 moles of O₂. The mole ratio is a crucial concept in stoichiometry. It tells you the proportion in which reactants combine and products are formed. It is derived directly from the coefficients in the balanced chemical equation. By using the mole ratio, we are able to convert the number of moles of one substance in the reaction to the number of moles of another substance in the reaction. In this case, we used it to convert from the reactant, potassium permanganate, to the product, oxygen. Only one more step to go and we’ll be done with the problem! We're almost at the end!

Step 4: Calculate the Mass of O₂

Finally, we'll calculate the mass of oxygen (O₂) produced. To do this, we need the molar mass of O₂. Oxygen exists as a diatomic molecule (O₂), so its molar mass is: 2 × 16.00 g/mol = 32.00 g/mol. Now, we can calculate the mass of O₂ using the following formula: mass (in grams) = moles × molar mass. So, mass of O₂ = 0.03875 mol × 32.00 g/mol = 1.24 g. Therefore, the mass of oxygen produced from the decomposition of 12.25 g of KMnO₄ is 1.24 grams. Hooray! We've successfully calculated the mass of oxygen produced in the reaction. We have determined the molar mass of the reactants, converted the mass of KMnO₄ to moles, used the mole ratio to find the moles of O₂, and finally, calculated the mass of O₂. This approach can be applied to many other similar stoichiometry problems. Remember to always start by balancing the chemical equation, calculating molar masses, and using mole ratios to convert between reactants and products. The balanced chemical equation is key to understanding the relationship between the quantities of reactants and products involved in a chemical reaction. By mastering these concepts, you'll be well on your way to conquering stoichiometry problems! Great job, guys! That was fun. You did an excellent job. I hope this detailed explanation helped you understand how to solve this type of problem. If you practice, you’ll get better at it! Don't hesitate to ask if you have any questions. Happy studying! And always remember, practice makes perfect.

I hope this helps! Good luck!