Titanium Carbonate & Gold Phosphate: A Chemical Reaction Breakdown

by TheNnagam 67 views

Hey guys! Let's dive into a fascinating chemistry problem. We're going to break down the reaction between titanium(IV) carbonate and gold(III) dihydrogen phosphate. This involves figuring out the reaction equation, the molarity of gold(III) dihydrogen phosphate, and the number of product particles. It might sound complex, but don't worry, we'll go through it step by step. So, grab your lab coats (metaphorically, of course!), and let's get started. We'll be using some key concepts like stoichiometry, molarity, and balanced chemical equations. This is a classic example of how to apply these principles to solve a real-world (or at least, a textbook-world) chemical problem. Remember, the goal is not just to get the answer, but to understand why the answer is what it is. Understanding the 'why' will help you with similar problems in the future. Ready? Let's go!

Step-by-Step Guide: Unraveling the Chemical Reaction

Alright, let's break this down into manageable chunks. The first thing we need to do is understand the reactants. We have titanium(IV) carbonate and gold(III) dihydrogen phosphate. Knowing the formulas is key! Titanium(IV) carbonate is Ti(CO₃)₂, and gold(III) dihydrogen phosphate is Au(H₂PO₄)₃. These formulas tell us the elements involved and their ratios within each molecule. The roman numeral indicates the charge of the titanium and gold ions. Titanium has a +4 charge (hence the IV), and gold has a +3 charge (hence the III). Now, we have to write the balanced chemical equation. This shows the exact amounts of reactants needed and products formed. This is where stoichiometry comes into play, making sure the number of atoms of each element is the same on both sides of the equation. This is a crucial step because it gives us the mole ratios which we need to calculate molarity and the amount of product formed. It is very important for understanding reaction. Then, we are going to find out the molarity of gold(III) dihydrogen phosphate and number of the particle products, all while maintaining the accuracy and precision in our calculation and understanding. Remember that the balanced equation is the roadmap of the reaction.

Writing the Balanced Chemical Equation

Okay, here's where the magic happens! We're starting with: Ti(CO₃)₂ + Au(H₂PO₄)₃ → Products. Notice that on the product side we’ll have a titanium and gold compound, and carbonate will react with dihydrogen phosphate. But which compounds will be formed? Well, the positive ions swap places to form new compounds. Titanium will pair with phosphate, and gold will pair with carbonate. Thus, our first, unbalanced equation is Ti(CO₃)₂ + Au(H₂PO₄)₃ → Ti₃(PO₄)₄ + Au₂(CO₃)₃. Next, we need to balance the equation by adjusting the coefficients in front of each compound so that the number of each type of atom is the same on both sides. This is essential for following the law of conservation of mass. After balancing, the balanced equation becomes: 3 Ti(CO₃)₂ + 2 Au(H₂PO₄)₃ → Ti₃(PO₄)₄ + 3 Au₂(CO₃)₃. This means that for every 3 molecules of titanium(IV) carbonate that react, 2 molecules of gold(III) dihydrogen phosphate react. Now we have the recipe for our reaction. This is the cornerstone of our calculations, as it tells us the ratio in which the reactants combine and the products form.

Calculating Molarity of Gold(III) Dihydrogen Phosphate

Now, let's get into the nitty-gritty calculations. We're given that the volume of titanium(IV) carbonate is 50,000 mL (which is the same as 50 L), and its molarity is 0.3 M. Remember, molarity (M) is defined as moles of solute per liter of solution. Let's find out how many moles of titanium(IV) carbonate we have: Moles of Ti(CO₃)₂ = Molarity × Volume = 0.3 mol/L × 50 L = 15 moles. Using the balanced equation, we know that 3 moles of Ti(CO₃)₂ react with 2 moles of Au(H₂PO₄)₃. So, to find the moles of Au(H₂PO₄)₃ that react, we can use the mole ratio from the balanced equation: Moles of Au(H₂PO₄)₃ = (Moles of Ti(CO₃)₂ / 3) × 2 = (15 moles / 3) × 2 = 10 moles. Now, to find the molarity of Au(H₂PO₄)₃, we need the volume. Unfortunately, we aren't given the volume of the gold(III) dihydrogen phosphate solution. However, we can calculate its molarity if we assume that the reaction takes place in a solution with a combined volume of 50 L (the volume of the titanium(IV) carbonate solution, assuming negligible volume change upon mixing). If the volume were different, the molarity would also change. The Molarity of Au(H₂PO₄)₃ = Moles / Volume = 10 moles / 50 L = 0.2 M. So, the molarity of gold(III) dihydrogen phosphate is 0.2 M (assuming the volumes are additive). Keep in mind this assumes ideal conditions.

Determining the Number of Product Particles

Finally, let's figure out the number of product particles. From the balanced equation, we can see that one mole of titanium(IV) phosphate (Ti₃(PO₄)₄) and three moles of gold(III) carbonate (Au₂(CO₃)₃) are formed. We know the moles of each product is based on the limiting reactant. In this case, since we have calculated based on the starting amount of titanium(IV) carbonate, it is the limiting reactant. Let's start with Ti₃(PO₄)₄: We have 15 moles of Ti(CO₃)₂ which produced (15/3) = 5 moles of Ti₃(PO₄)₄ (because the ratio is 3:1). Now, we calculate the number of molecules of Ti₃(PO₄)₄. We'll use Avogadro's number (6.022 × 10²³) as a conversion factor (this is the number of particles in a mole). Number of Ti₃(PO₄)₄ molecules = Moles × Avogadro's number = 5 moles × 6.022 × 10²³ molecules/mole = 3.011 × 10²⁴ molecules. Next, let's calculate the amount of Au₂(CO₃)₃. Since 3 moles of Au₂(CO₃)₃ are formed for every 3 moles of Ti(CO₃)₂, the gold carbonate formed is (15/3) × 3 = 15 moles. Number of Au₂(CO₃)₃ molecules = Moles × Avogadro's number = 15 moles × 6.022 × 10²³ molecules/mole = 9.033 × 10²⁴ molecules. The total number of product particles is the sum of these molecules, so 3.011 × 10²⁴ + 9.033 × 10²⁴ = 1.2044 × 10²⁵. So, there are a whopping 1.2044 × 10²⁵ particles in the products. Pretty awesome, right?

Conclusion: Wrapping It All Up

Alright, guys, we've successfully navigated this chemistry challenge! We determined the balanced equation for the reaction, calculated the molarity of gold(III) dihydrogen phosphate, and figured out the total number of product particles formed. Remember the key takeaways: balancing chemical equations, understanding mole ratios, and using molarity. This problem showcases the importance of stoichiometry in chemical reactions. Keep practicing, and you'll become a pro at these calculations in no time. Chemistry can be fun if you break it down like this. Keep experimenting and exploring the fascinating world of chemistry. That's all for today, folks! Hope you learned something cool, and happy experimenting. Remember, the more you practice, the easier it gets! Have a great day and keep learning!