Determining The Chemical Formula Of A Copper Chlorine Compound

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Hey there, chemistry enthusiasts! Today, we're diving into a fascinating problem: figuring out the chemical formula of a compound. We've got a 2-gram sample that contains 0.945 grams of copper and 1.055 grams of chlorine. Our mission, should we choose to accept it (and we totally do!), is to determine the chemical formula of this compound. Buckle up, because we're about to embark on a chemical adventure!

The Quest for the Chemical Formula

So, how do we go about finding the chemical formula? The chemical formula, guys, is basically a shorthand way of telling us the types and numbers of atoms that make up a molecule of a compound. Think of it as a recipe for a molecule! To crack the code, we need to figure out the ratio of copper atoms to chlorine atoms in our compound. This involves a few key steps, but don't worry, we'll break it down nice and easy.

Step 1: Converting Grams to Moles

The first thing we need to do is convert the masses of copper and chlorine into moles. Why moles, you ask? Well, moles are the chemist's best friend! They provide a standardized way of counting atoms and molecules. Remember, the chemical formula represents the mole ratio of the elements, not the mass ratio. To convert grams to moles, we'll use the molar mass of each element, which we can find on the periodic table.

  • For Copper (Cu): The molar mass of copper is approximately 63.55 grams per mole (g/mol). So, to find the number of moles of copper, we'll divide the mass of copper (0.945 g) by its molar mass (63.55 g/mol).

    Moles of Cu = 0.945 g / 63.55 g/mol ≈ 0.01487 mol

  • For Chlorine (Cl): The molar mass of chlorine is approximately 35.45 grams per mole (g/mol). We'll do the same calculation for chlorine, dividing its mass (1.055 g) by its molar mass (35.45 g/mol).

    Moles of Cl = 1.055 g / 35.45 g/mol ≈ 0.02976 mol

Great! Now we know how many moles of each element are present in our sample. We're one step closer to unlocking the chemical formula.

Step 2: Finding the Mole Ratio

Next up, we need to determine the mole ratio of copper to chlorine. This ratio tells us how many atoms of each element combine to form the compound. To find this, we'll divide the number of moles of each element by the smallest number of moles we calculated. In this case, the smallest number of moles is that of copper (0.01487 mol).

  • Ratio for Copper: 0.01487 mol Cu / 0.01487 mol ≈ 1

  • Ratio for Chlorine: 0.02976 mol Cl / 0.01487 mol ≈ 2

So, the mole ratio of copper to chlorine is approximately 1:2. This means that for every one mole of copper, there are two moles of chlorine. This is a crucial piece of information for determining the chemical formula.

Step 3: Writing the Chemical Formula

Alright, the moment we've been waiting for! Now we can write the chemical formula based on the mole ratio we just calculated. The mole ratio of 1:2 tells us that the compound contains one copper atom for every two chlorine atoms. We simply write the symbols of the elements (Cu for copper and Cl for chlorine) with subscripts indicating the number of atoms of each element.

Therefore, the chemical formula of the compound is CuCl₂.

CuCl₂: Copper(II) Chloride

So, there you have it! The chemical formula of the compound is CuCl₂. This compound is known as copper(II) chloride. The (II) indicates that copper has a +2 oxidation state in this compound. Copper(II) chloride is a bluish-green solid that is soluble in water. It's used in various applications, such as in the production of pigments, as a catalyst, and in the refining of copper.

Key Concepts in Determining Chemical Formulas

Let's recap the key concepts involved in determining chemical formulas. Understanding these concepts will help you tackle similar problems in the future. Plus, it's just cool to know how all this stuff works!

Molar Mass and the Mole Concept

The molar mass is the mass of one mole of a substance, expressed in grams per mole (g/mol). It's a fundamental concept in chemistry and a crucial tool for converting between mass and moles. As we saw earlier, we used the molar masses of copper and chlorine to convert their masses into moles.

The mole concept itself is a cornerstone of quantitative chemistry. A mole is defined as the amount of substance that contains the same number of particles (atoms, molecules, ions, etc.) as there are atoms in 12 grams of carbon-12. This number, known as Avogadro's number, is approximately 6.022 x 10ÂČÂł. The mole allows us to relate the microscopic world of atoms and molecules to the macroscopic world of grams and kilograms. Think of it as the bridge between the tiny and the tangible!

Empirical Formula vs. Molecular Formula

It's also important to distinguish between the empirical formula and the molecular formula. The empirical formula represents the simplest whole-number ratio of atoms in a compound, while the molecular formula represents the actual number of atoms of each element in a molecule. In our example, CuCl₂ is both the empirical and molecular formula because the ratio 1:2 is already the simplest whole-number ratio. However, there are cases where the empirical and molecular formulas differ. For instance, the molecular formula of glucose is C₆H₁₂O₆, but its empirical formula is CH₂O. To determine the molecular formula, you'd need additional information, such as the molar mass of the compound.

The Importance of Stoichiometry

Our adventure in finding the chemical formula also touches upon the concept of stoichiometry. Stoichiometry is the study of the quantitative relationships between reactants and products in chemical reactions. It's all about the ratios in which substances combine and react. By understanding stoichiometry, we can predict the amount of reactants needed or products formed in a chemical reaction. In our case, we used stoichiometric principles to determine the mole ratio of copper and chlorine, which ultimately led us to the chemical formula.

Practice Makes Perfect: Try These Problems!

Now that we've tackled this problem together, it's time to put your newfound knowledge to the test! Here are a few similar problems you can try:

  1. A compound contains 2.01 g of aluminum and 17.79 g of chlorine. What is the empirical formula of the compound?
  2. A 5.325 g sample of a metal alloy contains 3.583 g of iron and 1.742 g of oxygen. What is the empirical formula of the iron oxide in the alloy?
  3. A compound contains 40.0% carbon, 6.7% hydrogen, and 53.3% oxygen by mass. What is its empirical formula?

Working through these problems will solidify your understanding of the concepts and make you a chemical formula-finding pro in no time!

Wrapping Up

So, guys, we've successfully navigated the world of chemical formulas and figured out that a 2-gram sample containing 0.945 grams of copper and 1.055 grams of chlorine has the chemical formula CuCl₂. We learned how to convert grams to moles, find the mole ratio, and write the chemical formula. We also touched upon important concepts like molar mass, the mole concept, empirical vs. molecular formulas, and stoichiometry. Chemistry is an exciting journey, and the more we explore, the more we discover! Keep experimenting, keep learning, and most importantly, keep having fun with chemistry!