Product Ratio In Reaction: $CO_2$ Vs $H_2O$

ightarrow 14 CO_2 + 6 H_2O$

Hey guys! Let's dive into this chemical reaction and figure out the correct product ratio. We're dealing with the combustion of benzoic acid ($C_6H_5COOH$), and it's crucial to understand the stoichiometry to get the right answer. Stoichiometry, in simple terms, is the study of the quantitative relationships or ratios between two or more substances undergoing a physical change or a chemical reaction. For our purposes, it's about understanding how many molecules of reactants turn into how many molecules of products.

The Balanced Equation: Our Starting Point

The backbone of solving any stoichiometry problem is a balanced chemical equation. Thankfully, we already have that:

$2 C_6 H_5 COOH + 15 O_2 ightarrow 14 CO_2 + 6 H_2O$

This equation tells us a whole lot. It tells us that two molecules of benzoic acid react with fifteen molecules of oxygen to produce fourteen molecules of carbon dioxide and six molecules of water. It's like a recipe! If you double the ingredients, you double the output. This balanced equation ensures the law of conservation of mass is obeyed, meaning that the number of atoms of each element is the same on both sides of the equation. You can double-check this by counting the number of carbon, hydrogen, and oxygen atoms on both the reactant (left) and product (right) sides.

Breaking Down the Equation:

• Reactants: We have benzoic acid ($C_6H_5COOH$) and oxygen ($O_2$). These are the substances that are reacting with each other.
• Products: We have carbon dioxide ($CO_2$) and water ($H_2O$). These are the substances that are formed as a result of the reaction.
• Coefficients: The numbers in front of the chemical formulas (2, 15, 14, and 6) are called stoichiometric coefficients. These are super important! They tell us the molar ratio in which the reactants react and the products are formed. They are the key to understanding the proportions in which the substances participate in the reaction.

So, let’s recap. The balanced equation is our roadmap. It tells us the exact proportions in which everything reacts. Now, let's use this information to figure out the product ratio.

Decoding the Product Ratio: $CO_2$ vs. $H_2O$

Alright, let's zoom in on what the question is asking: the ratio of carbon dioxide ($CO_2$) to water ($H_2O$). This is where those stoichiometric coefficients we talked about become our best friends. Remember, these coefficients tell us the relative amounts of each substance involved in the reaction. So, we need to extract the information about $CO_2$ and $H_2O$ from our balanced equation.

Looking back at the equation:

$2 C_6 H_5 COOH + 15 O_2 ightarrow 14 CO_2 + 6 H_2O$

We can see that 14 molecules of $CO_2$ are produced for every 6 molecules of $H_2O$ produced. This directly translates to a ratio. Think of it as a simple comparison: for every 14 units of $CO_2$, we get 6 units of $H_2O$. That’s it!

Expressing the Ratio:

The initial ratio we’ve identified is 14:6. But, like any good mathematical ratio, we want to express it in its simplest form. This means finding the greatest common divisor (GCD) of 14 and 6 and dividing both numbers by it. The GCD of 14 and 6 is 2. So, we divide both sides of the ratio by 2:

• $14 ext{ divided by } 2 = 7$
• $6 ext{ divided by } 2 = 3$

Therefore, the simplified ratio of $CO_2$ to $H_2O$ is 7:3. This means for every 7 molecules of carbon dioxide produced, 3 molecules of water are produced. This simplified ratio maintains the same proportion as the original 14:6 ratio but is expressed in smaller, whole numbers, making it easier to understand and compare. Understanding how to simplify ratios is a handy skill not only in chemistry but also in everyday life when dealing with proportions and comparisons.

Why Ratios Matter:

Understanding product ratios is super important in chemistry for a few key reasons:

• Predicting Yields: Ratios help us predict how much of a product we can expect to form from a given amount of reactants. This is crucial in industrial processes where maximizing yield is essential for economic efficiency. For example, if you know you're starting with a certain amount of benzoic acid, you can calculate the theoretical maximum amount of carbon dioxide you can produce based on the 7:3 ratio.
• Optimizing Reactions: By understanding the ratios, we can optimize reaction conditions to favor the formation of desired products and minimize the formation of unwanted byproducts. This could involve adjusting temperature, pressure, or the amounts of reactants used. If a side reaction is producing an unwanted product, adjusting the reactant ratios might suppress that side reaction.
• Balancing Equations: As we saw earlier, balanced equations are all about maintaining the correct ratios between reactants and products. This ensures that the law of conservation of mass is obeyed.

So, ratios aren't just abstract numbers; they are the language of chemistry, allowing us to understand and control chemical reactions.

Identifying the Correct Option: Putting It All Together

Okay, we've done the hard work of understanding the reaction and calculating the product ratio. Now comes the satisfying part: matching our findings to the answer choices provided. This step is crucial because it ensures we've correctly interpreted the question and applied our knowledge.

Let’s revisit the original question and the options:

Question: For the reaction $2 C_6 H_5 COOH + 15 O_2 ightarrow 14 CO_2 + 6 H_2O$, which of the following options gives the correct product:product ratio?

A. $CO_2 : H_2O = 14:6$ B. $CO_2 : H_2O = 6:14$ C. $CO_2 : H_2O = 1:1$ D. (Other options, which we don’t need to consider yet)

Matching the Ratio:

Remember, we determined that the ratio of $CO_2$ to $H_2O$ is 14:6 (which simplifies to 7:3). Now, we simply scan the options and see which one matches our calculated ratio.

• Option A: $CO_2 : H_2O = 14:6$ – This is a direct match to the ratio we initially derived from the balanced equation! So, this looks promising.
• Option B: $CO_2 : H_2O = 6:14$ – This is the inverse of our ratio. It's important to pay attention to the order in which the products are mentioned in the ratio. This option is incorrect because it flips the relationship between carbon dioxide and water.
• Option C: $CO_2 : H_2O = 1:1$ – This suggests an equal amount of carbon dioxide and water, which is clearly not the case based on our balanced equation. This option is incorrect.

The Correct Answer:

It’s pretty clear now that Option A is the winner. The ratio $CO_2 : H_2O = 14:6$ perfectly matches the stoichiometric relationship we extracted from the balanced chemical equation. We've successfully identified the correct product ratio!

Double-Checking (Always a Good Idea!):

Even when you're confident, it's always a good idea to quickly double-check your work. In this case, we can mentally simplify 14:6 to 7:3 and ensure that this simplified ratio still makes sense in the context of the balanced equation. Since it does, we can be extra sure of our answer.

So, the final answer is A. $CO_2 : H_2O = 14:6$

Key Takeaways: Mastering Stoichiometry

Woohoo! We nailed it! But more importantly, we've learned some crucial principles of stoichiometry along the way. Let's recap the key takeaways to solidify our understanding:

1. Balanced Equations are King: A balanced chemical equation is the foundation of any stoichiometry problem. It provides the essential stoichiometric coefficients that dictate the relationships between reactants and products. Always make sure your equation is balanced before proceeding.
2. Stoichiometric Coefficients are Your Friends: These numbers tell you the molar ratios in which substances react and are formed. They are the key to calculating product ratios, predicting yields, and optimizing reactions.
3. Ratios Express Proportions: Product ratios, like 14:6 or 7:3, express the proportions in which products are formed. Understanding these proportions is crucial for predicting how much of each product will be generated.
4. Simplify When Possible: Simplifying ratios to their lowest terms (like changing 14:6 to 7:3) makes them easier to understand and compare.
5. Double-Check Everything: Always take a moment to double-check your work, especially in exams or critical situations. A quick review can catch simple errors and ensure accuracy.

Level Up Your Stoichiometry Skills:

Now that you've grasped the basics of product ratios, here are some ways to level up your stoichiometry skills:

• Practice, Practice, Practice: The more you work through different stoichiometry problems, the more comfortable you'll become with the concepts and calculations. Look for practice problems in textbooks, online resources, or old exams.
• Work with Different Reaction Types: Stoichiometry applies to all types of chemical reactions, from simple synthesis reactions to complex redox reactions. Challenge yourself by working with a variety of reactions.
• Explore Limiting Reactants: In many reactions, one reactant will be completely consumed before the others. This is called the limiting reactant, and it determines the maximum amount of product that can be formed. Learning about limiting reactants is a crucial next step in mastering stoichiometry.
• Tackle Percent Yield Problems: Percent yield compares the actual amount of product obtained in a reaction to the theoretical yield (the maximum amount that could be formed). These problems introduce real-world considerations into stoichiometric calculations.

So there you have it! By understanding balanced equations, stoichiometric coefficients, and product ratios, you're well on your way to becoming a stoichiometry master. Keep practicing, and you'll be solving even the trickiest chemistry problems in no time! Go get 'em, guys!