Dichlorobenzene Mass Calculation From Benzene & Chlorine
Hey guys! Let's dive into calculating the mass of dichlorobenzene that can be produced from benzene when a specific volume of chlorine is used in the reaction. This is a classic stoichiometry problem, and we'll break it down step by step to make it super easy to understand. We'll cover everything from the balanced chemical equation to the final mass calculation. So, grab your calculators, and let's get started!
Understanding the Reaction: Benzene and Chlorine
Before we jump into the calculations, let's first understand the chemical reaction involved. When benzene reacts with chlorine, it undergoes a substitution reaction where one or more hydrogen atoms on the benzene ring are replaced by chlorine atoms. In this case, we're interested in the production of dichlorobenzene, which means two chlorine atoms will substitute two hydrogen atoms.
The balanced chemical equation for the reaction is crucial for stoichiometric calculations. It tells us the exact molar ratios of the reactants and products. For the formation of dichlorobenzene, the reaction is:
C₆H₆ + 2Cl₂ → C₆H₄Cl₂ + 2HCl
This equation tells us that one mole of benzene (C₆H₆) reacts with two moles of chlorine gas (2Cl₂) to produce one mole of dichlorobenzene (C₆H₄Cl₂) and two moles of hydrogen chloride (2HCl). Knowing this stoichiometry is fundamental for calculating the mass of dichlorobenzene produced.
Why is a Balanced Equation Important?
A balanced chemical equation is the backbone of any stoichiometric calculation. It ensures that the number of atoms for each element is the same on both sides of the equation, adhering to the law of conservation of mass. Without a balanced equation, our mole ratios would be incorrect, leading to inaccurate results. Always double-check that your equation is balanced before proceeding with any calculations. It's a simple step that can save you from major headaches later on!
Step-by-Step Calculation
Now that we understand the reaction, let's walk through the calculation step-by-step. We'll start with the given information and use it to find the mass of dichlorobenzene produced.
Step 1: Convert the Volume of Chlorine to Moles
We're given that 22.4 liters of chlorine gas (Cl₂) are consumed in the reaction. To perform stoichiometric calculations, we need to convert this volume to moles. We'll use the ideal gas law for this conversion. At standard temperature and pressure (STP), one mole of any gas occupies 22.4 liters. The conditions weren't specified, so we will assume we are at STP for ease of calculation. This is something to clarify if you are doing this for a test.
So, the number of moles of Cl₂ can be calculated as follows:
Moles of Cl₂ = Volume of Cl₂ / Molar volume at STP Moles of Cl₂ = 22.4 L / 22.4 L/mol Moles of Cl₂ = 1 mol
This tells us that 1 mole of chlorine gas was used in the reaction. This is our starting point for determining how much dichlorobenzene can be formed.
Step 2: Use the Stoichiometric Ratio to Find Moles of Dichlorobenzene
Now, we'll use the balanced chemical equation to find the mole ratio between chlorine and dichlorobenzene. From the equation:
C₆H₆ + 2Cl₂ → C₆H₄Cl₂ + 2HCl
We see that 2 moles of Cl₂ produce 1 mole of C₆H₄Cl₂. This gives us the mole ratio:
Moles of C₆H₄Cl₂ / Moles of Cl₂ = 1 / 2
Using this ratio, we can find the moles of dichlorobenzene produced:
Moles of C₆H₄Cl₂ = (1 / 2) * Moles of Cl₂ Moles of C₆H₄Cl₂ = (1 / 2) * 1 mol Moles of C₆H₄Cl₂ = 0.5 mol
So, 0.5 moles of dichlorobenzene are produced from the reaction.
Step 3: Calculate the Molar Mass of Dichlorobenzene
To convert moles of dichlorobenzene to grams, we need its molar mass. Dichlorobenzene (C₆H₄Cl₂) has the following atomic masses:
- Carbon (C): 12.01 g/mol
- Hydrogen (H): 1.01 g/mol
- Chlorine (Cl): 35.45 g/mol
The molar mass of C₆H₄Cl₂ is calculated as:
Molar mass = (6 * 12.01) + (4 * 1.01) + (2 * 35.45) Molar mass = 72.06 + 4.04 + 70.90 Molar mass = 147.00 g/mol (approximately)
This means one mole of dichlorobenzene weighs approximately 147 grams.
Step 4: Convert Moles of Dichlorobenzene to Grams
Finally, we can calculate the mass of dichlorobenzene produced by multiplying the moles of dichlorobenzene by its molar mass:
Mass of C₆H₄Cl₂ = Moles of C₆H₄Cl₂ * Molar mass of C₆H₄Cl₂ Mass of C₆H₄Cl₂ = 0.5 mol * 147.00 g/mol Mass of C₆H₄Cl₂ = 73.5 g
Therefore, 73.5 grams of dichlorobenzene can be produced from the reaction when 22.4 liters of chlorine are consumed.
Common Mistakes to Avoid
When solving stoichiometry problems, it's easy to make mistakes if you're not careful. Here are a few common pitfalls to watch out for:
- Not Balancing the Chemical Equation: This is a crucial first step. An unbalanced equation will lead to incorrect mole ratios and, consequently, wrong answers. Always double-check that your equation is balanced.
- Incorrectly Converting Volumes to Moles: Make sure you use the correct conditions (STP or given temperature and pressure) when converting gas volumes to moles. Using the wrong molar volume can throw off your calculations.
- Using the Wrong Mole Ratio: The stoichiometric coefficients in the balanced equation give you the mole ratios. Make sure you're using the correct ratio for the reactants and products you're interested in.
- Incorrectly Calculating Molar Mass: Double-check your atomic masses and make sure you're adding them correctly to find the molar mass of the compound.
- Forgetting Units: Always include units in your calculations and final answer. This helps you keep track of what you're calculating and ensures your answer is meaningful.
Real-World Applications of Dichlorobenzene
Dichlorobenzene isn't just a theoretical chemical; it has several real-world applications. Understanding its uses can give you a better appreciation for why these calculations are important.
Insecticides
Dichlorobenzene is used as an insecticide to control moths, beetles, and other pests. Its properties make it effective in fumigating enclosed spaces, such as storage areas and museum collections. While its use has declined due to environmental concerns, it's still used in some specialized applications.
Chemical Intermediate
It serves as a crucial intermediate in the production of other chemicals. It's used in the synthesis of dyes, pharmaceuticals, and other organic compounds. The ability to precisely calculate the mass of dichlorobenzene produced is essential for efficient industrial processes.
Solvent
Dichlorobenzene is also used as a solvent for various materials, including resins, waxes, and greases. Its solvency properties make it useful in industrial cleaning and degreasing applications. However, its use as a solvent is also carefully regulated due to its potential environmental impact.
Practice Problems
To really nail this concept, let's try a couple of practice problems. These will help you solidify your understanding of stoichiometry and mass calculations.
Practice Problem 1
If 44.8 liters of chlorine gas react completely with benzene, what mass of dichlorobenzene is produced? Assume the reaction occurs at STP.
Solution:
- Convert the volume of chlorine to moles: 44.8 L / 22.4 L/mol = 2 mol Cl₂
- Use the mole ratio: 2 mol Cl₂ * (1 mol C₆H₄Cl₂ / 2 mol Cl₂) = 1 mol C₆H₄Cl₂
- Calculate the molar mass of dichlorobenzene: 147.00 g/mol
- Convert moles of dichlorobenzene to grams: 1 mol * 147.00 g/mol = 147 g C₆H₄Cl₂
So, 147 grams of dichlorobenzene are produced.
Practice Problem 2
What mass of benzene is required to react completely with 11.2 liters of chlorine gas to produce dichlorobenzene? Assume the reaction occurs at STP.
Solution:
- Convert the volume of chlorine to moles: 11.2 L / 22.4 L/mol = 0.5 mol Cl₂
- Use the mole ratio: 0.5 mol Cl₂ * (1 mol C₆H₆ / 2 mol Cl₂) = 0.25 mol C₆H₆
- Calculate the molar mass of benzene (C₆H₆): (6 * 12.01) + (6 * 1.01) = 78.12 g/mol
- Convert moles of benzene to grams: 0.25 mol * 78.12 g/mol = 19.53 g C₆H₆
So, 19.53 grams of benzene are required.
Conclusion
Calculating the mass of dichlorobenzene produced from benzene and chlorine involves understanding the balanced chemical equation, converting volumes to moles, using stoichiometric ratios, and calculating molar masses. By following these steps carefully, you can solve stoichiometry problems with confidence. Remember to avoid common mistakes and practice regularly to strengthen your skills. We've also explored the real-world applications of dichlorobenzene, highlighting its importance in various industries.
Keep practicing, and you'll become a pro at stoichiometry in no time! If you have any questions, feel free to ask. Happy calculating, guys!
