Moles Of Copper And Sulfur: A Chemistry Calculation

Hey guys! Today, we're diving into a classic chemistry problem involving the reaction between copper and sulfur to form copper(I) sulfide. We'll break down how to calculate the number of moles of reactants given their mass. Let's get started!

Understanding the Balanced Equation

The balanced equation provides the foundation for all stoichiometric calculations:

$2 Cu + S \rightarrow Cu_2S$

This equation tells us that two moles of copper (Cu) react with one mole of sulfur (S) to produce one mole of copper(I) sulfide ($Cu_2S$). The coefficients in front of each chemical formula are crucial for determining the mole ratios between the reactants and products. These ratios are the key to converting between moles of different substances in the reaction. For example, if we know we have 4 moles of copper, we can determine that we need 2 moles of sulfur to react completely with it, based on the 2:1 ratio from the balanced equation.

Understanding the balanced equation is not just about reading the numbers; it's about grasping the proportional relationships between the reactants and products. This understanding allows us to predict how much product will be formed from a given amount of reactants, or how much of a reactant is needed to react completely with another. It’s like having a recipe where you know exactly how much of each ingredient you need to make a perfect dish. In chemistry, the 'dish' is the product, and the 'ingredients' are the reactants. By mastering the interpretation of balanced equations, we can accurately perform calculations and make predictions about chemical reactions.

The balanced equation also adheres to the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction. This means that the number of atoms of each element must be the same on both sides of the equation. In our case, we have 2 copper atoms and 1 sulfur atom on both the reactant and product sides, confirming that the equation is indeed balanced. Balancing chemical equations is a fundamental skill in chemistry, ensuring that our calculations and predictions are based on sound principles and that we are accounting for all the atoms involved in the reaction.

Calculating Moles of Copper (Cu)

So, the question is: How many moles are present in 40.2 g of Cu? To determine the number of moles of copper, we'll use the following formula:

$Moles = \frac{Mass}{Molar\,Mass}$

First, we need to know the molar mass of copper (Cu). You can find this information on the periodic table. The molar mass of copper is approximately 63.55 g/mol. Now we can plug the values into our formula:

$Moles\,of\,Cu = \frac{40.2\,g}{63.55\,g/mol} = 0.632\,mol$

Therefore, there are approximately 0.632 moles of copper in 40.2 g of Cu. Remember to always include the units in your calculations to ensure that you are using the correct values and that your final answer is in the correct units. In this case, we divided grams by grams per mole, which resulted in moles, as expected. This simple calculation demonstrates how we can easily convert between mass and moles using the molar mass as a conversion factor. Mastering this concept is crucial for solving a wide range of stoichiometry problems in chemistry.

The molar mass of an element or compound is a fundamental property that relates the mass of a substance to the amount of substance in moles. It is defined as the mass of one mole of a substance, expressed in grams per mole (g/mol). The molar mass is numerically equal to the atomic or molecular weight of the substance, which can be found on the periodic table or calculated from the chemical formula. For example, the atomic weight of copper (Cu) is approximately 63.55 atomic mass units (amu), so the molar mass of copper is 63.55 g/mol. This means that one mole of copper atoms has a mass of 63.55 grams. Similarly, the molecular weight of water ($H_2O$) is approximately 18.01 amu, so the molar mass of water is 18.01 g/mol.

Calculating Moles of Sulfur (S)

Next up: How many moles are present in 14.1 g of S? We'll use the same formula as before:

$Moles = \frac{Mass}{Molar\,Mass}$

We need the molar mass of sulfur (S). Looking at the periodic table, the molar mass of sulfur is approximately 32.07 g/mol. Plugging in the values:

$Moles\,of\,S = \frac{14.1\,g}{32.07\,g/mol} = 0.440\,mol$

So, there are approximately 0.440 moles of sulfur in 14.1 g of S. Again, always double-check your units to ensure the calculation is correct! This calculation reinforces the relationship between mass and moles, and how the molar mass acts as the bridge between these two quantities. Whether you're dealing with copper, sulfur, or any other substance, the same principle applies: use the molar mass to convert between mass and moles. This is a fundamental skill that will help you succeed in chemistry and related fields.

Understanding the concept of moles is crucial for performing quantitative analysis in chemistry. The mole is the SI unit for the amount of substance, and it represents a specific number of particles (atoms, molecules, ions, etc.). One mole is defined as exactly $6.02214076 × 10^{23}$ elementary entities, which is known as Avogadro's number ($N_A$). Avogadro's number provides a bridge between the microscopic world of atoms and molecules and the macroscopic world of grams and kilograms. By using the mole concept, chemists can accurately measure and control the amounts of reactants and products in chemical reactions.

Putting It All Together

Now that we've calculated the moles of both copper and sulfur, we can relate these values back to the balanced equation. We found that we have 0.632 moles of Cu and 0.440 moles of S. According to the balanced equation:

$2 Cu + S \rightarrow Cu_2S$

Two moles of copper react with one mole of sulfur. To determine if we have enough of each reactant for the reaction to go to completion, we can compare the mole ratio of Cu to S in our sample to the stoichiometric ratio from the balanced equation. In our sample, the mole ratio of Cu to S is:

$\frac{Moles\,of\,Cu}{Moles\,of\,S} = \frac{0.632}{0.440} = 1.44$

The stoichiometric ratio from the balanced equation is 2:1, or 2. Therefore, we can see that we have less copper than we would need to react with all of the sulfur. This means that copper is the limiting reactant, and sulfur is the excess reactant. The amount of product formed will be determined by the amount of copper available.

Understanding the concept of limiting reactants is essential for maximizing the yield of a chemical reaction. The limiting reactant is the reactant that is completely consumed in a reaction, and it determines the amount of product that can be formed. The excess reactant is the reactant that is present in a greater amount than necessary to react with the limiting reactant. To identify the limiting reactant, we need to compare the mole ratio of the reactants in the reaction mixture to the stoichiometric ratio from the balanced equation. The reactant that has the smallest mole ratio compared to the stoichiometric ratio is the limiting reactant. Once we have identified the limiting reactant, we can calculate the theoretical yield of the product, which is the maximum amount of product that can be formed based on the amount of limiting reactant available.

Conclusion

So, there you have it! We've successfully calculated the number of moles of copper and sulfur in given masses using the molar mass. Remember, the key to solving these types of problems is understanding the relationship between mass, moles, and molar mass. Keep practicing, and you'll become a pro in no time! Keep up the great work, guys!