Problem 51 - A Complete Resource Book in Chemistry for JEE Main

Question

In the reaction, \(\mathrm{CH}_{4}+2 \mathrm{O}_{2} \longrightarrow \mathrm{CO}_{2}+2 \mathrm{H}_{2} \mathrm{O}\), the amount of oxygen needed to completely bum \(4.0 \mathrm{~g}\) of \(\mathrm{CH}_{4}\) is (a) 4 (b) \(8 \mathrm{~g}\) (c) \(16 \mathrm{~g}\) (d) \(32 \mathrm{~g}\)

Step-by-Step Solution

Answer

(c) 16 g

Step 1: Convert Given Mass to Moles

First, we need to determine the number of moles of CH extsubscript{4}. The molar mass of CH extsubscript{4} is 12.01 g/mol (carbon) plus 4 x 1.01 g/mol (hydrogen), which equals approximately 16.05 g/mol. To find moles, use the formula: \( ext{moles} = \frac{ ext{mass}}{ ext{molar mass}} \). With a mass of 4.0 g of CH extsubscript{4}, the moles of CH extsubscript{4} is \( \frac{4.0 ext{ g}}{16.05 ext{ g/mol}} \approx 0.25 \) moles.

Step 2: Use Stoichiometry to Find Moles of O

According to the balanced chemical equation, 1 mole of CH extsubscript{4} requires 2 moles of O extsubscript{2}. Therefore, if you have 0.25 moles of CH extsubscript{4}, the moles of O extsubscript{2} needed are: \( 0.25 \text{ moles of CH extsubscript{4}} \times \frac{2 \text{ moles of O extsubscript{2}}}{1 \text{ mole of CH extsubscript{4}}} = 0.50 \text{ moles of O extsubscript{2}} \).

Step 3: Convert Moles of O to Grams

Now convert moles of O extsubscript{2} to grams. The molar mass of O extsubscript{2} is 32.00 g/mol. So, \( 0.50 \text{ moles} \times 32.00 \text{ g/mol} = 16.00 \text{ g} \) of O extsubscript{2} is needed.

Key Concepts

Molar Mass Calculation

To solve chemistry problems, the molar mass is a key concept. It tells us the mass of one mole of a substance. You can think of it as the recipe that tells you how much of each ingredient you need. In the molar mass calculation for methane (\(\text{CH}_4\)), we start by adding the atomic mass of the atoms in the molecule. Methane has one carbon atom and four hydrogen atoms. The atomic mass of carbon is about 12.01 g/mol and hydrogen is 1.01 g/mol. So, adding these up gives a molar mass of \(16.05\) g/mol for methane.

• This is important for converting between grams and moles.
• Knowing molar masses helps you compare different substances.

When you know the mass of a substance, you can use its molar mass to find out how many moles you have. Divide the mass you have by the molar mass to get the number of moles. This forms the basis of many calculations in stoichiometry.

Chemical Reactions

Chemical reactions are processes where reactants transform into products. Each reaction can be described by a chemical equation, like this one: \(\text{CH}_4 + 2\ \text{O}_2 \rightarrow \text{CO}_2 + 2\ \text{H}_2\text{O}\). In this equation, methane reacts with oxygen to produce carbon dioxide and water.In a balanced chemical reaction, the number of atoms of each element is the same on both sides of the equation. This balance shows the conservation of mass. For methane reacting with oxygen, each molecule of methane uses 2 molecules of oxygen. This relationship is essential for figuring out the exact amounts of reactants needed or products formed.

• Balancing equations ensures mass is not lost or gained.
• Helps in calculating how much of each reactant is used and product formed.

By understanding these relationships, we can predict how changing one part of a chemical reaction affects the outcome, which is crucial in both chemistry experiments and industrial processes.

Mole Concept

The mole concept offers a bridge between the microscopic world of atoms and the macroscopic world we observe. A mole is a convenient way to talk about very large numbers of atoms or molecules. One mole of any substance contains Avogadro's number of particles, which is approximately \(6.022 \times 10^{23}\) particles.When you calculate moles, you change the focus from individual atoms or molecules to a collective measure. This simplifies calculations. In chemistry, the mole concept helps us keep track of quantities in chemical reactions. For example, in the equation \(\text{CH}_4 + 2\ \text{O}_2 \rightarrow \text{CO}_2 + 2\ \text{H}_2\text{O}\), using the mole concept means understanding that 1 mole of methane reacts with 2 moles of oxygen.

• This allows you to scale reactions up or down.
• Makes it easier to translate between mass and quantities of atoms or molecules.

Understanding moles improves your ability to predict reaction outcomes, balance chemical equations, and make informed decisions in the lab.