Photosynthesis: Water's Role In CO2 Reaction

Hey guys! Let's dive into a classic chemistry question that's super important for understanding how plants make their food through photosynthesis. We're going to figure out how much water is needed to react completely with a specific amount of carbon dioxide ($CO_2$). This is a fundamental concept, and once you get the hang of it, you'll be able to solve similar problems with ease. The photosynthesis reaction is a core process to life on Earth and is represented by a chemical equation that dictates the relationship between the reactants and the products. Understanding the ratio of reactants is essential for calculating the quantities required for a complete reaction. This problem not only involves stoichiometry calculations but also reinforces your understanding of the relationship between mass, moles, and chemical equations. Getting the hang of these concepts is crucial for chemistry. So, let’s get started.

We know that the balanced chemical equation for photosynthesis is:

$6 CO_2 + 6 H_2O ightarrow C_6H_{12}O_6 + 6 O_2$

This equation tells us that for every 6 molecules (or moles) of carbon dioxide ($CO_2$) that react, 6 molecules (or moles) of water ($H_2O$) are required. This is the stoichiometric ratio that we'll be using. Keep in mind that the coefficients in the balanced equation give us the mole ratio, which is the key to solving this problem. You should always balance the chemical equation first before calculating. The key here is to use the molar masses to convert between grams and moles, and then use the mole ratio from the balanced equation. We will be using the concepts of stoichiometry and molar mass to find our answer. The stoichiometric ratio from the balanced chemical equation is very important for solving this problem correctly. This kind of problem often appears in exams, so understanding it will be very useful. The ability to perform these calculations is a basic skill that every chemistry student should possess. The balanced chemical equation is the foundation for all stoichiometric calculations. By mastering this concept, you can solve a wide range of chemistry problems and improve your overall understanding of chemical reactions. Let's start with the given mass of $CO_2$ and convert it into moles using the molar mass. Then, use the mole ratio from the balanced equation to find the moles of $H_2O$ required. Finally, convert the moles of $H_2O$ back into mass using the molar mass of water. Pretty straightforward, right?

Step-by-Step Calculation

1. Convert grams of $CO_2$ to moles

We're given that we have 157.35 g of $CO_2$. The molar mass of $CO_2$ is 44.01 g/mol. To convert grams to moles, we divide the mass by the molar mass:

Moles of $CO_2$ = (Mass of $CO_2$) / (Molar mass of $CO_2$)

Moles of $CO_2$ = 157.35 g / 44.01 g/mol ≈ 3.575 mol

So, we have approximately 3.575 moles of $CO_2$. It is important to remember the units during the calculations. Always include the units, and make sure that you do the correct conversion. This step is a fundamental aspect of stoichiometric calculations. Converting the mass of a substance to moles is a necessary step in many chemical calculations, as chemical reactions are governed by the number of moles of reactants and products, rather than their masses. Remember that the molar mass provides the link between mass and moles, allowing us to perform this conversion. Make sure you understand the concept of the mole and the use of molar mass. Keep your units consistent throughout your calculations to make sure you will get the correct answer. The use of molar mass allows us to convert between the mass of a substance and the number of moles. Therefore, it is important to understand the concept of the mole and the use of molar mass. Without correctly converting the grams of carbon dioxide into moles, we cannot proceed with the stoichiometry calculations. Make sure to understand this key step to solve the problem.

2. Use the mole ratio to find moles of $H_2O$

From the balanced equation, we know that 6 moles of $CO_2$ react with 6 moles of $H_2O$. This gives us a 1:1 mole ratio. Therefore, the moles of $H_2O$ required will be equal to the moles of $CO_2$:

Moles of $H_2O$ = Moles of $CO_2$ × (6 mol $H_2O$ / 6 mol $CO_2$)

Moles of $H_2O$ = 3.575 mol × (6 / 6) = 3.575 mol

So, 3.575 moles of water are required to react with 3.575 moles of $CO_2$. In this step, we use the stoichiometry of the balanced chemical equation to find the relationship between the number of moles of $CO_2$ and $H_2O$. The mole ratio from the balanced chemical equation is the key to converting between the amount of reactants in a chemical reaction. The mole ratio is derived from the coefficients in the balanced chemical equation. By using the mole ratio, we are able to calculate how many moles of one substance will react with a certain number of moles of another substance. It’s like a recipe where we need a specific ratio of ingredients to make a product. In this case, our product is the result of the photosynthesis process. Always double-check that you are using the correct mole ratio from the balanced chemical equation. This step is a critical component of solving the problem, as it correctly relates the number of moles of reactants and products. Understanding the mole ratio is essential for accurate stoichiometric calculations.

3. Convert moles of $H_2O$ to grams

We know that we need 3.575 moles of $H_2O$. The molar mass of $H_2O$ is 18.02 g/mol. To convert moles to grams, we multiply the number of moles by the molar mass:

Mass of $H_2O$ = Moles of $H_2O$ × Molar mass of $H_2O$

Mass of $H_2O$ = 3.575 mol × 18.02 g/mol ≈ 64.42 g

Therefore, 64.42 grams of water are required to react completely with 157.35 g of $CO_2$. This step completes the calculation. After determining the moles of water required, we convert this value to mass using the molar mass of water. Ensure you have the correct molar mass for the substance in question. This conversion is crucial for obtaining the final answer in the desired unit. The correct use of molar mass ensures that we accurately convert between moles and grams. Make sure to include the units in your final answer. By correctly performing these calculations, you can solve a wide range of stoichiometry problems and improve your understanding of chemical reactions.

Conclusion

So there you have it, guys! We've successfully calculated the mass of water required to react with a given amount of carbon dioxide in the photosynthesis reaction. Remember, the key steps are to convert grams to moles, use the mole ratio from the balanced equation, and then convert moles back to grams. Keep practicing these types of problems, and you'll become a pro in no time! Understanding the concepts of stoichiometry and the mole ratio is fundamental in chemistry. This problem is just one example of the many types of chemical reactions you can analyze. The more you practice, the more comfortable you will become with these types of calculations. This approach can be applied to many other chemical reactions, so mastering this method is very valuable. By applying these methods, you will gain a deeper understanding of chemical reactions and how to analyze them quantitatively. Keep working hard, and you will see the results!