Problem 29 - Chemistry in 30 days

Question

A bottle of 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 center 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 ring forms near the hydrogen chloride bottle.

Step 1: Understand the Problem

We need to determine where the ammonium chloride ring will form when ammonia diffuses from one end of a tube and hydrogen chloride from the other.

Step 2: Consider Diffusion Speeds

The speed of gas diffusion is inversely proportional to the square root of its molar mass according to Graham's law. Ammonia (NH₃) is lighter with a molar mass of approximately 17 g/mol, while hydrogen chloride (HCl) is heavier with a molar mass of about 36.5 g/mol.

Step 3: Apply Graham's Law

According to Graham's law, the rate of effusion ( ext{r}) of a gas is inversely proportional to the square root of its molar mass ( ext{M}): \[ \frac{r_{\text{NH}_3}}{r_{\text{HCl}}} = \sqrt{\frac{M_{\text{HCl}}}{M_{\text{NH}_3}}} \]Plugging in the values:\[ \frac{r_{\text{NH}_3}}{r_{\text{HCl}}} = \sqrt{\frac{36.5}{17}} \approx 1.46 \]This means ammonia diffuses faster than hydrogen chloride.

Step 4: Identify Ring Location

Since ammonia diffuses more rapidly, it travels further down the tube from its source compared to the hydrogen chloride gas. This causes the ammonium chloride ring to form closer to the side where hydrogen chloride is introduced.

Key Concepts

Graham's Law

Graham's Law is a fundamental principle in chemistry that explains how gases diffuse and effuse. This law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass.

• This means lighter gases will effuse more quickly compared to heavier gases.
• The mathematical formula for this law is: \( \frac{r_1}{r_2} = \sqrt{\frac{M_2}{M_1}} \), where \( r \) is the effusion rate and \( M \) is the molar mass of the gases.

Graham's Law helps us predict how different gases will behave when they escape through small openings or diffuse through space. For example, when ammonia and hydrogen chloride are allowed to diffuse toward each other, Graham's Law enables us to determine which gas moves faster and how their meeting point is affected.

Ammonia

Ammonia is a colorless gas with a distinct pungent smell. Its chemical formula is \( NH_3 \). Ammonia plays a vital role in numerous industrial processes and is widely used as a fertilizer.

• It has a lower molar mass of approximately 17 g/mol, making it lighter than many other gases.
• This lower molar mass contributes to its faster diffusion rate, as demonstrated with Graham’s Law.

When ammonia is released in an experiment with hydrogen chloride, it will travel faster. This speed allows it to reach further distances before reacting, influencing where the resulting ammonium chloride forms.

Hydrogen Chloride

Hydrogen chloride, represented by the chemical formula \( HCl \), is a colorless gas known for its strong, acrid smell.

• In its gaseous form, it is more dense and has a molar mass of about 36.5 g/mol, making it heavier than ammonia.
• This heavier molar mass results in a slower diffusion rate under Graham’s Law.

When hydrogen chloride gas comes into contact with ammonia, a chemical reaction occurs to form solid ammonium chloride, which is visible as a white ring in diffusion experiments.

Molar Mass

Understanding molar mass is essential for determining how gases diffuse and react. Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol).

• Lighter gases like ammonia (17 g/mol) diffuse faster due to their smaller mass.
• Heavier gases such as hydrogen chloride (36.5 g/mol) diffuse more slowly.

Using the molar masses of these gases, Graham's Law helps us accurately predict diffusion rates, which, in turn, helps identify where reactions like ammonium chloride formation might occur in experiments involving different gases.

Effusion Rate

The effusion rate of a gas refers to the speed at which gas molecules escape through a small hole into a vacuum. Factors affecting effusion include the molar mass of the gas and the conditions under which effusion occurs.

• Graham's Law dictates that gas effusion rate is inversely proportional to the square root of the gas's molar mass.
• Thus, lighter gases like ammonia, with a lower molar mass, will effuse more rapidly than heavier gases like hydrogen chloride.

By understanding effusion rates, scientists can manipulate and predict how gases behave in experiments, such as determining the position where a reaction will take place along a tube, as with the ammonium chloride ring formation.