Residual Gas Calculation: Hydrogen And Oxygen Reaction

Let's dive into a classic chemistry problem that involves calculating the volume of residual gas after a reaction between hydrogen and oxygen. This problem is a great example of how we can apply the principles of stoichiometry and the concept of limiting reactants. We'll break down the problem step-by-step, making it easy to understand, even if you're new to chemistry. The core of this question is centered on the reaction of hydrogen and oxygen to produce water (in the form of steam), and it is a typical exercise in understanding chemical reactions and the volumes of gases involved.

Understanding the Chemical Reaction

The fundamental equation that governs this reaction is: $2H_{2(g)} + O_{2(g)} ightarrow 2H_2O_{(g)}$. This equation tells us a few crucial things. First, it states that hydrogen gas ($H_2$) reacts with oxygen gas ($O_2$) to produce water in its gaseous form, commonly referred to as steam ($H_2O$). The subscript (g) indicates that the substances are in gaseous form, which is essential for understanding the volume relationships in this problem. Secondly, the coefficients in front of each chemical formula are critical. They tell us the stoichiometric ratio of the reactants and products. Specifically, the balanced equation tells us that 2 moles of hydrogen react with 1 mole of oxygen to produce 2 moles of water. Or, looking at the volumes, if the reaction occurs at the same temperature and pressure (as stated in the standard temperature and pressure or STP, context), this also means that 2 volumes of hydrogen react with 1 volume of oxygen to produce 2 volumes of water. This is based on Avogadro's law, which states that equal volumes of gases at the same temperature and pressure contain the same number of molecules.

Important note: Always ensure that your chemical equation is balanced before starting any calculations. An unbalanced equation will lead to incorrect results.

Identifying the Limiting Reactant

The key to solving this type of problem lies in identifying the limiting reactant. The limiting reactant is the substance that is completely consumed during the reaction, thus determining the amount of product formed. In this case, we have $30 cm^3$ of hydrogen and $20 cm^3$ of oxygen. To determine the limiting reactant, we can use the stoichiometric ratios from the balanced equation. According to the balanced equation, we require 2 volumes of hydrogen to react with 1 volume of oxygen. Let us check the available volumes of hydrogen and oxygen:

• If all $30 cm^3$ of hydrogen reacts, it would require $30 cm^3 / 2 = 15 cm^3$ of oxygen. We have $20 cm^3$ of oxygen, so there is enough oxygen for all the hydrogen to react.
• If all $20 cm^3$ of oxygen reacts, it would require $20 cm^3 * 2 = 40 cm^3$ of hydrogen. However, we only have $30 cm^3$ of hydrogen, so hydrogen will run out first. It is the limiting reactant.

Therefore, hydrogen is the limiting reactant, meaning that all of the hydrogen will be used up in the reaction, and some oxygen will remain unreacted.

Calculating the Volume of Oxygen Reacted and the Residual Gas

Since hydrogen is the limiting reactant, we'll use the volume of hydrogen to calculate how much oxygen is consumed. From the balanced equation, we know that 2 volumes of hydrogen react with 1 volume of oxygen. We have $30 cm^3$ of hydrogen. So, the volume of oxygen that reacts is: $(30 cm^3 H_2) * (1 cm^3 O_2 / 2 cm^3 H_2) = 15 cm^3$ of oxygen reacts.

Now, we can calculate the volume of oxygen that is left over (the residual gas). We started with $20 cm^3$ of oxygen, and $15 cm^3$ reacted. Therefore, the volume of oxygen remaining is: $20 cm^3 - 15 cm^3 = 5 cm^3$.

Determining the Correct Answer

We're asked to find the volume of the residual gas. In this case, the residual gas is the unreacted oxygen. From our calculations, we found that $5 cm^3$ of oxygen remains after the reaction.

Looking at the answer choices:

• A. $50 cm^3$ - Incorrect.
• B. $35 cm^3$ - Incorrect.
• C. $30 cm^3$ - Incorrect.
• D. $25 cm^3$ - Incorrect.

However, from our calculation, the remaining residual gas is $5 cm^3$. There seems to be a mistake in the provided choices.

Therefore, the correct answer, although not listed in the options, is $5 cm^3$ of oxygen.

In Conclusion

This problem elegantly demonstrates the importance of stoichiometry in chemistry. By carefully balancing the chemical equation, identifying the limiting reactant, and using the correct volume ratios, we can accurately predict the outcome of a chemical reaction. Remember to always double-check your calculations and ensure that you understand the fundamental concepts. This type of problem is fundamental to many other calculations in chemistry, so practicing it helps a lot.

Key Takeaways

• Stoichiometry: Use the balanced chemical equation to determine molar or volume ratios.
• Limiting Reactant: Identify the reactant that is completely consumed.
• Volume Calculations: Use the balanced equation to find the volume of reactants that react and the volume of products formed.
• Residual Gas: Calculate the remaining amount of any unreacted reactants.

This problem might seem complex at first, but by breaking it down step-by-step, understanding the underlying principles, and practicing similar problems, you can master these types of calculations and confidently tackle any chemistry challenge that comes your way.

Further Exploration

To solidify your understanding, try variations of this problem with different volumes of reactants or different chemical reactions. You can also explore concepts like the ideal gas law and how it relates to volume, temperature, and pressure. Consider the impact of changing the temperature or pressure on the reaction's outcome. For additional learning and related concepts, you can visit Khan Academy for a wide range of chemistry topics.