Problem 43 - A Complete Resource Book in Chemistry for JEE Main

Question

A bottle of dry ammonia and a bottle of dry hydrogen chloride connected through a long tube are opened simultaneously at both ends, the white ammonium chloride ring first formed will be (a) at the centre of the tube (b) near the hydrogen chloride bottle (c) near the ammonia bottle (d) throughout the length of the tube

Step-by-Step Solution

Answer

The ammonium chloride ring first forms near the hydrogen chloride bottle (option b).

Step 1: Understanding the Reaction

When ammonia (\text{NH}_3) and hydrogen chloride (\text{HCl}) gases mix, they react to form ammonium chloride (\text{NH}_4\text{Cl}) according to the chemical equation: \[\text{NH}_3 (\text{g}) + \text{HCl} (\text{g}) \rightarrow \text{NH}_4\text{Cl} (\text{s})\] This reaction forms a white solid ring of ammonium chloride at the point where the gases meet inside the tube.

Step 2: Analyzing Gas Diffusion

In the given scenario, the gases diffuse along a tube. The rate at which they diffuse is related to their molar masses. According to Graham's law of diffusion, gas with a lower molar mass will diffuse faster. - Molar mass of \(\text{NH}_3 = 14 + (3\times1) = 17 \text{ g/mol}\)- Molar mass of \(\text{HCl} = 1 + 35.5 = 36.5 \text{ g/mol}\)

Step 3: Applying Graham's Law of Effusion

According to Graham's Law, the relative rate of diffusion of two gases is inversely proportional to the square root of their molar masses:\[\frac{\text{Rate of diffusion of NH}_3}{\text{Rate of diffusion of HCl}} = \sqrt{\frac{M_{HCl}}{M_{NH_3}}}\]Substitute the molar masses into the equation:\[\frac{\text{Rate of diffusion of NH}_3}{\text{Rate of diffusion of HCl}} = \sqrt{\frac{36.5}{17}} \approx 1.47\] This means \(\text{NH}_3\) diffuses faster than \(\text{HCl}\).

Step 4: Determining the Location of the White Ring

Because \(\text{NH}_3\) diffuses faster, it will travel a longer distance in the same amount of time compared to \(\text{HCl}\). Therefore, the ammonium chloride ring will be closer to the hydrogen chloride bottle as \(\text{NH}_3\) travels further inside the tube before meeting \(\text{HCl}\).

Key Concepts

Ammonium Chloride Formation

When ammonia (\(\text{NH}_3\)) and hydrogen chloride (\(\text{HCl}\)) come into contact in their gaseous states, a fascinating reaction occurs. They react to form ammonium chloride (\(\text{NH}_4\text{Cl}\)), which is a solid. This substance forms as a white ring within the tube that connects two containers of these gases. The process can be broken down with the chemical equation: \[\text{NH}_3 (\text{g}) + \text{HCl} (\text{g}) \rightarrow \text{NH}_4\text{Cl} (\text{s})\]. Here, the "g" indicates the gases, and the "s"sign indicates a solid. The \(\text{NH}_4\text{Cl}\) forms where the two gases meet.

Rate of Gas Diffusion

The concept of gas diffusion is critical in understanding how the ammonium chloride is formed in the experiment. According to Graham's Law of Diffusion, gases with lower molar mass will diffuse faster than those with higher molar mass. Molar mass is basically the weight of one mole of a given chemical substance.

• For ammonia (\(\text{NH}_3\)), its molar mass is 17 g/mol,
• whereas for hydrogen chloride (\(\text{HCl}\)), it is 36.5 g/mol.

By calculating the diffusion rates according to Graham's Law:\[\frac{\text{Rate of diffusion of NH}_3}{\text{Rate of diffusion of HCl}} = \sqrt{\frac{M_{HCl}}{M_{NH_3}}}\], we establish that ammonia diffuses approximately 1.47 times faster than hydrogen chloride.

Chemical Reactions in Gases

Chemical reactions involving gases, such as this one between ammonia and hydrogen chloride, often involve diffusional mixing. In a gas-phase reaction, because of the gases’ mobility, reactants can easily intermingle, allowing them to react efficiently with each other.
**Why is diffusion significant?**

• Diffusion allows gases to travel and meet each other, thus permitting reactions.
• Without diffusion, gases in separate containers would never react unless stirred vigorously or heated.

Establishing conditions like that in the long tube designed for the experiment allows these gases to meet in a controlled manner, leading to the formation of the noticeable ammonium chloride ring. Understanding these reactions can open doors to many practical applications, like in the synthesis of other chemical products and in industrial processes where gas reactions are harnessed to procure desired substances.