Problem 19 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The minimum number of moles of \(\mathrm{O}_{2}\) required for complete combustion of 1 mole of propane and 2 moles of butane is [Main Sep. 05, 2020 [I)]

Step-by-Step Solution

Answer

The minimum number of moles of \(\text{O}_2\) required is 18 moles.

Step 1: Write the Balanced Combustion Equation for Propane

The balanced chemical equation for the complete combustion of propane (\(\text{C}_3\text{H}_8\)) is:\[ \text{C}_3\text{H}_8 + 5\text{O}_2 \rightarrow 3\text{CO}_2 + 4\text{H}_2\text{O} \]From this equation, 1 mole of propane requires 5 moles of \(\text{O}_2\) for complete combustion.

Step 2: Write the Balanced Combustion Equation for Butane

The balanced chemical equation for the complete combustion of butane (\(\text{C}_4\text{H}_{10}\)) is:\[ \text{C}_4\text{H}_{10} + \frac{13}{2}\text{O}_2 \rightarrow 4\text{CO}_2 + 5\text{H}_2\text{O} \]This equation shows that 1 mole of butane requires 6.5 moles of \(\text{O}_2\) for complete combustion.

Step 3: Calculate Moles of \(\text{O}_2\) for Given Quantities of Propane and Butane

Given that there is 1 mole of propane and 2 moles of butane:- 1 mole of propane requires 5 moles of \(\text{O}_2\).- 2 moles of butane require \(2 \times 6.5 = 13\) moles of \(\text{O}_2\).Sum the total moles of \(\text{O}_2\) needed:\[ 5 + 13 = 18 \]

Step 4: Conclude the Total Minimum Moles of \(\text{O}_2\) Required

To find the minimum number of moles of \(\text{O}_2\) required for the complete combustion of the given quantities, add the moles of \(\text{O}_2\) from propane and butane.The total minimum moles of \(\text{O}_2\) needed is 18 moles.

Key Concepts

Chemical Equations

Chemical equations are essential for understanding chemical reactions, as they depict the substances involved and their proportions in a reaction. These equations not only show which substances react but also the products that form. Writing a correct chemical equation involves balancing it, ensuring that the number of atoms for each element is the same on both sides of the equation. This law of conservation of mass must be maintained, which means in our propane combustion, \[ \text{C}_3\text{H}_8 + 5\text{O}_2 \rightarrow 3\text{CO}_2 + 4\text{H}_2\text{O} \] all carbon, hydrogen, and oxygen atoms in propane and oxygen gas are accounted for in carbon dioxide and water.
When balanced correctly, chemical equations provide a clear and concise representation of chemical reactions, allowing us to use them as a reliable means for further calculations in stoichiometry.

Stoichiometry

Stoichiometry is the section of chemistry that involves calculating the relative quantities of reactants and products in chemical reactions. By understanding the balanced chemical equations, stoichiometry allows us to quantitatively analyze reactions.

• It involves using relationships from the balanced equations to determine the amount of each substance consumed or produced.
• In our example of propane and butane combustion, stoichiometry helps us determine how many moles of oxygen are necessary for a complete reaction.

In the combustion of butane, \[ \text{C}_4\text{H}_{10} + \frac{13}{2}\text{O}_2 \rightarrow 4\text{CO}_2 + 5\text{H}_2\text{O} \], for instance, stoichiometric coefficients guide us to know 6.5 moles of oxygen are needed for every mole of butane. Such calculations are crucial for both theoretical and practical chemistry applications, ensuring that reactions can proceed effectively without wastage or leftover reactants.

Moles Calculation

Moles calculation is a fundamental aspect of chemistry that involves converting between the mass of a substance and the number of moles, which reflects the number of particles present. The mole is a standard scientific unit for measuring large quantities of very small entities such as atoms, molecules, or other specified particles.

• In combustion reactions, knowing the moles of reactants gives precise information on the stoichiometry of the reaction.
• A balanced chemical equation provides all necessary stoichiometric relationships, allowing us to calculate the exact moles needed.

For example, in the reaction of burning 1 mole of propane, it clearly requires 5 moles of oxygen. In the case of 2 moles of butane, the equation informs us we need 2 times 6.5, resulting in 13 moles of oxygen. Summing up these calculated moles for both propane and butane aids in determining how much oxygen to supply for complete combustion. This method ensures precise and efficient calculations, which is why mastery of moles and their conversions is vital for students.