Problem 40 - A Complete Resource Book in Chemistry for JEE Main

Question

The maximum number of molecules is present in (a) \(15 \mathrm{~L}\) of \(\mathrm{H}_{2}\) gas at STP (b) \(5 \mathrm{~L}\) of \(\mathrm{N}_{2}\) gas at STP (c) \(1.5 \mathrm{~g}\) of \(\mathrm{H}_{2}\) gas (d) \(5 \mathrm{~g}\) of \(\mathrm{O}_{2}\) gas

Step-by-Step Solution

Answer

Option (c), 1.5 g of H2, contains the maximum number of molecules with 0.75 moles.

Step 1: Understand Standard Temperature and Pressure (STP)

STP is defined as a temperature of 273.15 K (0 °C) and a pressure of 1 atm. Under these conditions, 1 mole of an ideal gas occupies 22.4 L.

Step 2: Calculate Moles of Gas Under STP for 15 L of H2

Using the molar volume, calculate the moles of gas in 15 L of hydrogen: \[ \text{Moles of } H_2 = \frac{15 \text{ L}}{22.4 \text{ L/mol}} \approx 0.67 \text{ mol} \]

Step 3: Calculate Moles of Gas Under STP for 5 L of N2

Similarly, calculate the moles of nitrogen gas in 5 L: \[ \text{Moles of } N_2 = \frac{5 \text{ L}}{22.4 \text{ L/mol}} \approx 0.22 \text{ mol} \]

Step 4: Calculate Moles of H2 from Mass

Molecular weight of \(H_2 = 2 \text{ g/mol}\). Calculate moles in 1.5 g: \[ \text{Moles of } H_2 = \frac{1.5 \text{ g}}{2 \text{ g/mol}} = 0.75 \text{ mol} \]

Step 5: Calculate Moles of O2 from Mass

Molecular weight of \(O_2 = 32 \text{ g/mol}\). Calculate moles in 5 g: \[ \text{Moles of } O_2 = \frac{5 \text{ g}}{32 \text{ g/mol}} \approx 0.16 \text{ mol} \]

Step 6: Compare Number of Moles

Compare moles of each option: 0.67 mol (a), 0.22 mol (b), 0.75 mol (c), 0.16 mol (d). The option with the most moles has the most molecules.

Key Concepts

Standard Temperature and Pressure (STP)

Standard Temperature and Pressure, commonly abbreviated as STP, are predefined conditions that allow chemists to make consistent comparisons across different experiments and calculations. These specific conditions are set at a temperature of 273.15 Kelvin (equivalent to 0 degrees Celsius) and a pressure of 1 atmosphere. An important aspect of these conditions is that they create an environment where various gas laws can be uniformly applied.

STP simplifies calculations in chemistry, especially when working with gases. This is because at STP, one mole of any ideal gas occupies a volume of 22.4 liters. This notion of a 'molar volume' allows for the easy conversion between the number of moles of a gas and its physical volume, given that the gas behaves ideally. It's important to remember that deviations might occur with real gases under certain conditions, but these are usually negligible at STP.

Understanding STP is crucial for solving gas-related problems, as it provides a base comparison for different gases, helping predict how they will react under other conditions.

Molar Volume

Molar volume is a key concept linked closely with STP and is essential to understanding the behavior of gases in chemistry. It refers to the volume occupied by one mole of a gas at a specified temperature and pressure. At STP, this volume is 22.4 liters for an ideal gas. This concept aids in visualizing how much space a set amount of gas will occupy, which is particularly useful in laboratory and industrial processes where gas calculations and measurements are frequent.

• This is known as the standard molar volume.
• The value changes if the conditions deviate from STP, which is why knowing the exact conditions is vital when conducting real-world calculations.

Altering the conditions of temperature and pressure can affect the molar volume, but the constant factor at STP is beneficial for consistency. By using molar volume, we can easily determine how many moles of a gas are present in a known volume, which in turn helps in calculating the number of molecules using Avogadro's number.

Molecular Weight

Molecular weight, also referred to as molecular mass, is a central concept in chemistry that pertains to the mass of a single molecule of an element or compound. It is usually expressed in atomic mass units (amu) or grams per mole (g/mol). Knowing the molecular weight of a substance is crucial for converting between the mass of a substance and the number of moles.

To calculate molecular weight, sum the atomic weights of all the atoms present in the molecule. For instance, the molecular weight of hydrogen (\(H_2\)u0002) is calculated by summing the atomic weights of the two hydrogen atoms, which is approximately 2 g/mol.

• In the same manner, for oxygen (\(O_2\)u0002), the molecular weight is approximately 32 g/mol.
• This information is invaluable when determining how many moles are in a given mass, as shown in exercises involving mass-to-mole conversions.

Understanding molecular weight allows chemists to make accurate predictions about chemical reactions, including how much of each reactant is needed to produce a desired product. It's a fundamental concept for any student studying chemistry or involved in fields requiring detailed chemical knowledge.