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

(c) 0.0093 mol

Step 1: Determine the Volume of Oxygen

Since the air contains 21% oxygen by volume, calculate the volume of oxygen in 1 litre of air. This is done by multiplying the percentage by the total volume. Volume of oxygen = 0.21 x 1 litre = 0.21 litres.

Step 2: Convert Volume to Moles Using Ideal Gas Law

At standard conditions (0°C and 1 atm), 1 mole of an ideal gas occupies 22.4 litres. Use this information to convert the volume of oxygen to moles.Number of moles = \( \frac{0.21 \text{ litres}}{22.4 \text{ litres/mol}} \).

Step 3: Calculate the Number of Moles

Perform the division to find the number of moles.\( \frac{0.21}{22.4} \approx 0.009375 \mathrm{~mol} \).This approximately equals 0.0093 mol when rounded to four significant figures.

Key Concepts

Moles of Gas

In chemistry, we often talk about moles when dealing with gases. But what is a mole? Simply put, a mole is a way to count large numbers of tiny particles like atoms or molecules. - One mole of any substance contains Avogadro's number, which is approximately \( 6.022 \times 10^{23} \) particles.- For gases, we often use moles to relate to the volume they occupy under certain conditions. When dealing with gases, the Ideal Gas Law is especially useful. It states that a fixed amount of gas at a constant temperature and pressure has a consistent ratio of pressure, volume, and temperature, typically expressed as \( PV = nRT \). Here, \( n \) stands for the number of moles of the gas, \( R \) is the universal gas constant, and \( T \) is the temperature in Kelvin. In our problem, focusing on oxygen in air, we're interested in finding how many moles a specific volume comprises under set conditions.

Standard Conditions

Standard conditions refer to a set of guidelines scientists use to allow for comparisons between different sets of data. For gases, this usually means Standard Temperature and Pressure (STP), which is 0°C (or 273.15 K) and 1 atm pressure. - At STP, one mole of an ideal gas occupies 22.4 liters. - These conditions provide a baseline for many calculations because they simplify the math related to the behavior of gases. - Though real gases may deviate slightly from these conditions, they are often assumed to behave ideally for simplicity. This assumption is very handy in problems like the one we have. In our example, knowing the volume one mole of gas occupies at STP allows us to easily convert a given volume to moles.

Volume to Moles Conversion

Converting volume to moles of gas is a common task in chemistry, especially in exercises that use the Ideal Gas Law. With the information provided by STP, such calculations become straightforward.To convert the volume of a gas to moles:1. Determine the volume of gas available. In our problem, we found this to be 0.21 liters of oxygen.2. Use the fact that at standard conditions, 1 mole of gas occupies 22.4 liters to calculate the number of moles: \[ \text{Number of moles} = \frac{\text{Volume of gas in liters}}{\text{Volume of one mole in liters at STP}} = \frac{0.21}{22.4} \approx 0.009375 \text{ moles} \]3. The calculation shows that the number of moles rounds to 0.0093 moles when considering significant figures.This conversion is crucial for understanding how much substance you're actually dealing with in reactions or when studying gas properties at the atomic level.