Moles Of Oxygen Required Reaction With 1.67 Mol Of Hydrogen

The formation of water from hydrogen and oxygen is a fundamental chemical reaction, crucial to understanding stoichiometry and chemical calculations. This article will delve into the balanced chemical equation representing this reaction, $2 H_2 + O_2 \rightarrow 2 H_2O$, and explore how to determine the number of moles of oxygen required to react completely with a given amount of hydrogen. This is a practical application of stoichiometry, the branch of chemistry that deals with the quantitative relationships between reactants and products in chemical reactions. Stoichiometry is essential for chemists and anyone working in related fields, as it allows for precise calculations in chemical processes.

Understanding the stoichiometry of water formation involves interpreting the mole ratios from the balanced equation. The coefficients in the balanced equation represent the number of moles of each substance involved in the reaction. In this case, 2 moles of hydrogen ($H_2$) react with 1 mole of oxygen ($O_2$) to produce 2 moles of water ($H_2O$). This 2:1 mole ratio between hydrogen and oxygen is the key to solving the problem presented.

Moreover, mastering stoichiometric calculations is not just about solving textbook problems. It is a critical skill in many real-world applications, including industrial chemistry, environmental science, and even cooking. In industrial settings, stoichiometric calculations are used to optimize chemical reactions for maximum yield and efficiency. In environmental science, they are used to understand and manage pollution and other chemical processes. Even in cooking, understanding mole ratios can help ensure that recipes turn out as expected. Therefore, understanding the stoichiometry of simple reactions like water formation provides a stepping stone for understanding more complex chemical processes.

The balanced equation, $2 H_2 + O_2 \rightarrow 2 H_2O$, encapsulates the law of conservation of mass, a cornerstone of chemistry. This law states that matter cannot be created or destroyed in a chemical reaction. The balanced equation reflects this law by ensuring that the number of atoms of each element is the same on both sides of the equation. In this case, there are 4 hydrogen atoms and 2 oxygen atoms on both the reactant and product sides.

To determine the number of moles of oxygen required to react completely with 1.67 moles of hydrogen, we use the mole ratio derived from the balanced equation. The balanced equation, $2 H_2 + O_2 \rightarrow 2 H_2O$, clearly indicates that 2 moles of $H_2$ react with 1 mole of $O_2$. This relationship serves as a crucial conversion factor in stoichiometric calculations. Therefore, the mole ratio between $H_2$ and $O_2$ is 2:1. This ratio means that for every 2 moles of hydrogen, we need 1 mole of oxygen for a complete reaction. This understanding is fundamental in solving the given problem.

Applying this mole ratio, we can set up a proportion to calculate the moles of $O_2$ needed. If 2 moles of $H_2$ react with 1 mole of $O_2$, then 1.67 moles of $H_2$ will react with 'x' moles of $O_2$. This can be expressed as:

$\frac{2 ext{ moles } H_2}{1 ext{ mole } O_2} = \frac{1.67 ext{ moles } H_2}{x ext{ moles } O_2}$

Solving for 'x' involves cross-multiplication and division. Cross-multiplying gives us:

$2 ext{ moles } H_2 imes x ext{ moles } O_2 = 1 ext{ mole } O_2 imes 1.67 ext{ moles } H_2$

$2x = 1.67$

Dividing both sides by 2, we find:

$x = \frac{1.67}{2} = 0.835 ext{ moles } O_2$

Therefore, 0.835 moles of $O_2$ are required to react completely with 1.67 moles of $H_2$.

This calculation showcases a fundamental principle in stoichiometry: the ability to convert between moles of different substances in a chemical reaction using mole ratios from the balanced equation. This conversion is a cornerstone of chemical calculations and is essential for accurately predicting the amounts of reactants and products involved in chemical reactions. Mastering this skill is crucial for anyone studying chemistry or working in related fields.

It's also important to note the significance of the term 'completely' in the question. Complete reaction implies that all of the limiting reactant (in this case, hydrogen) is consumed, and the reaction proceeds until one of the reactants is entirely used up. This concept is crucial in industrial chemistry, where maximizing the conversion of reactants to products is a primary goal. Understanding complete reactions and how to ensure they occur is therefore a vital aspect of chemical engineering and process design.

To recap, we've calculated the amount of oxygen needed for the reaction in a methodical way. The answer is derived directly from the balanced equation and the mole ratio it implies.

• Step 1: Identify the balanced chemical equation: $2 H_2 + O_2 \rightarrow 2 H_2O$

• Step 2: Determine the mole ratio between $H_2$ and $O_2$. From the equation, 2 moles of $H_2$ react with 1 mole of $O_2$, giving a ratio of 2:1.

• Step 3: Set up a proportion using the given moles of $H_2$ (1.67 mol) and the mole ratio:

  $\frac{2 ext{ moles } H_2}{1 ext{ mole } O_2} = \frac{1.67 ext{ moles } H_2}{x ext{ moles } O_2}$

• Step 4: Solve for x:

  $x = \frac{1.67 ext{ moles } H_2 imes 1 ext{ mole } O_2}{2 ext{ moles } H_2} = 0.835 ext{ moles } O_2$

The correct answer is A. 0.835 mol $O_2$. This means that 0.835 moles of oxygen are required to react completely with 1.67 moles of hydrogen in the formation of water.

The balanced chemical equation is the foundation of all stoichiometric calculations. Without a balanced equation, it is impossible to accurately determine the mole ratios between reactants and products. Balancing chemical equations ensures that the law of conservation of mass is upheld, meaning that the number of atoms of each element remains constant throughout the reaction. This is critical for predicting the amounts of substances involved in a chemical reaction. For instance, in the water formation reaction, if the equation were not balanced (e.g., if it were written as $H_2 + O_2 \rightarrow H_2O$), the mole ratios would be incorrect, leading to inaccurate calculations of reactant and product amounts.

Moreover, balancing equations often involves trial and error and a deep understanding of chemical formulas and valencies. It is not simply a mathematical exercise but requires a solid grasp of chemical principles. For example, knowing that oxygen typically exists as a diatomic molecule ($O_2$) is essential for balancing the equation for water formation. Similarly, understanding the charges and bonding capacities of different elements is crucial for balancing more complex chemical equations. Therefore, the ability to balance chemical equations accurately is a fundamental skill in chemistry.

Furthermore, balanced equations provide a wealth of information beyond just mole ratios. They also implicitly convey information about the conservation of energy and charge in chemical reactions. While energy changes are not explicitly shown in a balanced equation, they are an integral part of the reaction. Similarly, for reactions involving ions, the balanced equation reflects the conservation of charge. In redox reactions, for example, balancing the equation often requires careful consideration of the electron transfer process.

The principles of stoichiometry are not confined to the laboratory; they have vast real-world applications across various industries and fields. One of the most significant applications is in the chemical industry, where stoichiometric calculations are essential for optimizing chemical processes. Chemical engineers use stoichiometry to determine the correct amounts of reactants needed to produce a desired amount of product, minimizing waste and maximizing efficiency. This is particularly crucial in large-scale industrial processes, where even small improvements in efficiency can translate to significant cost savings.

In the pharmaceutical industry, stoichiometry plays a vital role in drug synthesis. The accurate calculation of reactant quantities is essential for producing drugs with the desired purity and potency. Incorrect stoichiometric calculations can lead to the formation of byproducts or incomplete reactions, which can compromise the quality and safety of the drug. Therefore, pharmaceutical chemists rely heavily on stoichiometric principles to ensure the consistent and reliable production of medications.

Stoichiometry is also critical in environmental science and engineering. It is used to understand and mitigate pollution, design wastewater treatment plants, and develop strategies for environmental remediation. For example, stoichiometric calculations are used to determine the amount of chemicals needed to neutralize acidic or alkaline waste, to estimate the amount of pollutants released into the atmosphere, and to design systems for removing pollutants from water and air. Understanding the chemical reactions and the quantities involved is crucial for effective environmental management.

While stoichiometric calculations are relatively straightforward, there are several common mistakes that students and even experienced chemists can make. Avoiding these errors is crucial for accurate and reliable results. One of the most common mistakes is using an unbalanced equation. As emphasized earlier, a balanced equation is the foundation of all stoichiometric calculations. Using an unbalanced equation will lead to incorrect mole ratios and, consequently, incorrect answers.

Another common mistake is confusing mole ratios with mass ratios. The coefficients in a balanced equation represent the mole ratios, not the mass ratios. To convert between moles and mass, the molar mass of each substance must be used. Failing to make this conversion can lead to significant errors in calculations. For example, in the water formation reaction, the mole ratio between $H_2$ and $O_2$ is 2:1, but the mass ratio is different due to the different molar masses of hydrogen and oxygen.

Finally, another common error is neglecting to identify the limiting reactant. In a chemical reaction, the limiting reactant is the reactant that is completely consumed first, thereby determining the amount of product that can be formed. If the amounts of reactants are not in the exact stoichiometric ratio, one reactant will be the limiting reactant, and the other will be in excess. Failing to identify the limiting reactant can lead to an overestimation of the amount of product that can be formed. Therefore, it is essential to determine the limiting reactant before performing stoichiometric calculations.

In conclusion, understanding the stoichiometry of chemical reactions, as exemplified by the formation of water, is a fundamental skill in chemistry. The ability to interpret balanced chemical equations and use mole ratios to calculate reactant and product quantities is crucial for solving a wide range of chemical problems. From basic calculations like determining the amount of oxygen needed to react with a given amount of hydrogen, to more complex applications in industrial chemistry, pharmaceutical science, and environmental engineering, stoichiometry is an indispensable tool.

The balanced equation $2 H_2 + O_2 \rightarrow 2 H_2O$ serves as a simple yet powerful illustration of stoichiometric principles. It highlights the importance of mole ratios, the law of conservation of mass, and the need for accurate calculations in chemistry. By mastering these principles, students and professionals can confidently tackle a variety of chemical problems and contribute to advancements in various fields.