Problem 65 - A Complete Resource Book in Chemistry for JEE Main

Question

The number of moles of oxygen in one litre of air containing \(21 \%\) oxygen by volume, in standard conditions, is (a) \(0.176 \mathrm{~mol}\) (b) \(0.32 \mathrm{~mol}\) (c) \(0.0093 \mathrm{~mol}\) (d) \(2.20 \mathrm{~mol}\)

Step-by-Step Solution

Answer

The number of moles of oxygen is approximately 0.0093 mol (option c).

Step 1: Understand the Problem

We need to find the number of moles of oxygen in 1 liter of air where air is composed of 21% oxygen by volume under standard temperature and pressure (STP) conditions.

Step 2: Recall STP Conditions for Volume and Moles

Under standard temperature and pressure (STP), 1 mole of any gas occupies 22.4 liters. This will be a key factor in finding out the number of moles from a given volume of oxygen.

Step 3: Calculate the Volume of Oxygen

Since the air contains 21% oxygen by volume, the volume of oxygen in 1 liter of air is \(0.21 \times 1 \text{ L} = 0.21 \text{ L}\).

Step 4: Use Volume-Moles Conversion at STP

We use the conversion factor where 22.4 liters of gas at STP is equivalent to 1 mole. Therefore, the number of moles of oxygen from 0.21 liters is calculated as follows: \[\text{Number of moles of } O_2 = \frac{0.21 \text{ L}}{22.4 \text{ L/mol}}\]

Step 5: Perform the Calculation

By performing the division, we find: \[\frac{0.21}{22.4} \approx 0.009375 \text{ mol}\] Rounding this to significant figures gives approximately 0.0093 mol.

Key Concepts

Stoichiometry

Stoichiometry is the area of chemistry that involves the calculation of reactants and products in chemical reactions. It uses the concept of the mole to determine the proportions of elements and compounds in chemical equations. The mole allows chemists to quantify substances at the atomic level, making it easier to measure things out in the lab. This concept ensures the conservation of mass in a chemical reaction. Stoichiometry is essential because it provides a bridge between the mass of substances and the number of atoms or molecules. This relationship is fundamental to performing chemical calculations accurately.

Gas Laws

Gas laws describe how gases behave under various conditions of temperature, pressure, and volume. The ideal gas law, one of the primary gas laws, is expressed as: \[ PV = nRT \] where \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin.These laws are instrumental in understanding gases at the molecular level:

• Boyle's Law: Pressure inversely proportional to volume
• Charles's Law: Volume directly proportional to temperature
• Avogadro's Law: Volume directly proportional to the number of moles

By using these fundamental principles, we can predict and calculate the behavior of gases under different scenarios.

Standard Temperature and Pressure (STP)

Standard Temperature and Pressure (STP) are conventional conditions used in the laboratory to ensure consistency in measurements and calculations. At STP, the temperature is defined as 0°C or 273.15 K, and the pressure as 1 atm or 101.325 kPa. The significance of STP in gas calculations lies in its definition:

• One mole of any ideal gas occupies 22.4 liters
• Allows for standardized conditions to compare and predict gas behaviors

Using STP simplifies the calculation of gas reactions or the conversion between volume and moles, especially when dealing with different gases and reactions.

Volume to Mole Conversion

Volume to mole conversion is key when dealing with gases, particularly under STP. This conversion is based on the fact that 1 mole of any ideal gas occupies 22.4 liters at STP.To convert volume to moles:1. Measure the volume of the gas.2. Utilize the conversion formula: \[ ext{Moles} = rac{ ext{Volume at STP}}{ ext{Molar Volume (22.4 L/mol)}} \ \]For instance, to find the moles of oxygen in 0.21 liters of air at STP, you divide 0.21 by 22.4:\[ \text{Moles of } O_2 = \frac{0.21 \text{ L}}{22.4 \text{ L/mol}} \approx 0.009375 \text{ mol} \] This simple division technique allows chemists to relate physical measurements with molar quantities seamlessly.