Problem 114 - A Complete Resource Book in Chemistry for JEE Main

Question

What is the correct sequence of active masses in increasing order in gaseous mixture, containing one gram per litre of each of the following? 1\. \(\mathrm{NH}_{3}\) 2\. \(\mathrm{N}_{2}\) 3\. \(\mathrm{H}_{2}\) 4\. \(\mathrm{O}_{2}\) Select the correct answer using the codes given below: (a) \(3,1,4,2\) (b) \(3,4,2,1\) (c) \(2,1,4,3\) (d) \(4,2,1,3\)

Step-by-Step Solution

Answer

The correct sequence is \(3, 1, 4, 2\), so the answer is (a).

Step 1: Understand Active Masses

Active mass refers to the concentration of a substance in moles per liter (mol/L). In a gaseous state, this is equivalent to the number of moles per liter of gas since gas concentration is determined by its volume and number of moles.

Step 2: Calculate Moles for Each Gas

For each gas, we need to calculate the number of moles per liter. Use the molar mass of each gas to convert from grams to moles. 1. \(\text{For } \mathrm{NH}_3: \frac{1\, \text{g}}{17\, \text{g/mol}}\)2. \(\text{For } \mathrm{N}_2: \frac{1\, \text{g}}{28\, \text{g/mol}}\)3. \(\text{For } \mathrm{H}_2: \frac{1\, \text{g}}{2\, \text{g/mol}}\)4. \(\text{For } \mathrm{O}_2: \frac{1\, \text{g}}{32\, \text{g/mol}}\)

Key Concepts

Gaseous Mixture

A gaseous mixture consists of more than one gas occupying the same space. Each component of the mixture behaves independently, and their combined behavior can often be predicted using principles similar to those for ideal gases. This can include gases like nitrogen, hydrogen, and oxygen, each contributing to the overall properties of the mixture, like pressure and volume. Gaseous mixtures are crucial in various chemical processes and everyday applications. For instance, the air we breathe is a gaseous mixture primarily made up of nitrogen and oxygen. Understanding the behavior of each component within a gaseous mixture helps us in calculating and predicting the overall properties of the mixture. Each gas contributes to the total pressure of the mixture as described by Dalton’s Law of Partial Pressures, which states that the total pressure exerted by a mixture of non-reactive gases is equal to the sum of the partial pressures of individual gases.

Moles per Liter

In chemistry, concentration often refers to the amount of a substance within a certain volume. The number of moles per liter, denoted usually as molarity, is a common way to express concentration, especially in solutions. In a gaseous state, avogadro’s law applies, which states that at the same temperature and pressure, equal volumes of gases contain an equal number of molecules. Therefore, concentration in terms of moles per liter can be directly linked to the gas's volume and its molar volume. At standard temperature and pressure (STP), one mole of any gas occupies approximately 22.4 liters. This standard allows chemists to work easily with gas conversions and calculate accordingly to find how many moles exist within a liter of gas.

Molar Mass Calculation

Understanding molar mass is a fundamental aspect of chemistry. It is the mass of one mole of a substance, typically measured in grams per mole (g/mol). This is a crucial conversion factor for determining how many moles of a substance are present when given mass data, as in the case of gases in a mixture. To calculate molar mass, add together the atomic masses of each element in a molecule, utilizing the periodic table for the atomic masses. For example, the molar mass of ammonia (NH extsubscript{3}) is calculated by adding the mass of nitrogen (14 g/mol) with three times the mass of hydrogen (1 g/mol), resulting in a molar mass of 17 g/mol. This concept allows us to interconvert between mass and moles, aiding in solving the problem of determining active masses in the exercise.

Concentration in Gases

Concentration in gases is typically measured in terms of moles per liter. This differs somewhat from liquid solutions since gas concentrations need to consider volume more explicitly due to gas compressibility and diffusibility. In the context of the given problem, concentration affects how we perceive active mass in a chemical reaction. Concentration in gas form is particularly important in stoichiometry and reaction dynamics, as it determines how reactants interact. By using the ideal gas law equation, chemists can determine the necessary parameters to find concentration. Expressing concentration in moles per liter for gases aligns with understanding how gases contribute to reaction conditions in the real world. For reactions involving gases, knowledge of concentration helps direct how reactions progress, ensuring calculations for yields and rates are accurate.