Problem 96 - 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 \(\mathrm{N}\), gas at \(\mathrm{STP}\) (c) \(0.5 \mathrm{~g}\) of \(\mathrm{H}_{2}\) gas (d) \(10 \mathrm{~g}\) of \(\mathrm{O}_{2}\) gas

Step-by-Step Solution

Answer

Option (a) has the most molecules with 0.67 moles of \(\text{H}_2\).

Step 1: Understanding Standard Temperature and Pressure (STP)

STP refers to a temperature of 273.15 K (0°C) and a pressure of 1 atm. At STP, 1 mole of any ideal gas occupies a volume of 22.4 L. This information helps in converting the volume of gas to moles when given in liters.

Step 2: Convert Gas Volumes to Moles for Options (a) and (b)

For option (a), convert 15 L of \(\text{H}_2\) to moles: \[ \text{moles of } \text{H}_2 = \frac{15 \, \text{L}}{22.4 \, \text{L/mol}} \approx 0.67 \text{ mol} \]For option (b), convert 5 L of \(\text{N}_2\) to moles: \[ \text{moles of } \text{N}_2 = \frac{5 \, \text{L}}{22.4 \, \text{L/mol}} \approx 0.22 \text{ mol} \]

Step 3: Convert Mass to Moles for Options (c) and (d)

For option (c), given 0.5 g of \(\text{H}_2\) with molar mass approximately \(2 \, \text{g/mol}\): \[ \text{moles of } \text{H}_2 = \frac{0.5 \, \text{g}}{2 \, \text{g/mol}} = 0.25 \text{ mol} \]For option (d), given 10 g of \(\text{O}_2\) with molar mass approximately \(32 \, \text{g/mol}\): \[ \text{moles of } \text{O}_2 = \frac{10 \, \text{g}}{32 \, \text{g/mol}} \approx 0.31 \text{ mol} \]

Step 4: Compare the Number of Moles

Compare the moles for each option: - Option (a) \( \text{H}_2\): 0.67 mol- Option (b) \( \text{N}_2\): 0.22 mol- Option (c) \( \text{H}_2\): 0.25 mol- Option (d) \( \text{O}_2\): 0.31 mol \ The greatest number of moles, and thus molecules, is found in option (a) with 0.67 moles.

Key Concepts

Standard Temperature and Pressure (STP)

The concept of Standard Temperature and Pressure, commonly abbreviated as STP, is a fundamental reference point in chemistry and physics. STP is characterized by a specific set of conditions: a temperature of 273.15 Kelvin (K) or 0°C (Celsius) and a pressure of 1 atmosphere (atm). At these conditions, 1 mole of any ideal gas occupies a volume of 22.4 liters (L). This standardization allows scientists to easily compare and perform calculations involving gaseous substances.

Using STP is particularly useful when dealing with gases because gas volume can change with temperature and pressure. With STP, we have a common ground to understand gas behavior and perform calculations. For example, when given a specific volume of gas at STP, you can directly convert this volume to moles of the gas, using the ideal gas law relationship that 1 mole equals 22.4 L. This relationship becomes invaluable in chemical reactions and stoichiometry, where knowing the mole-to-mole ratio is crucial.

Gas Volume to Moles Conversion

Converting gas volumes to moles is a critical skill in chemistry, particularly under Standard Temperature and Pressure (STP). This conversion helps in understanding the quantities involved in chemical reactions. At STP, as mentioned earlier, 1 mole of a gas takes up 22.4 liters. This makes the calculation straightforward: divide the given volume of the gas by 22.4 L to find the number of moles.

Let's take a practical example from the exercise: To convert 15 liters of hydrogen gas (H_{2}) to moles, you use the formula:
\[\text{moles of } \text{H}_2 = \frac{15 \, \text{L}}{22.4 \, \text{L/mol}} \approx 0.67 \text{ mol}\]

This straightforward method provides the moles directly, which are then used to infer the number of molecules involved in a reaction. It simplifies the process of comparing different gases under fixed conditions of temperature and pressure.

Molecular Calculations

In the realm of chemistry, molecular calculations are essential for quantifying the substances involved in chemical reactions. Once you have the number of moles from volume or mass conversions, the next step is determining the number of molecules. This is done using Avogadro’s number, which is \(6.022 \times 10^{23}\) molecules per mole.

For instance, once you've found that 15 L of hydrogen at STP is approximately 0.67 moles, you can determine the number of molecules as follows:
\[\text{Number of molecules} = 0.67 \, \text{mol} \times 6.022 \times 10^{23} \text{ (molecules/mol)}\]

This powerful tool allows chemists to connect macro-level measurements (like grams or liters) with micro-level quantities (the number of molecules), facilitating deeper insights into chemical processes and reactions. By understanding the molecular makeup, chemists can predict how different substances will interact during a chemical reaction.