Problem 74 - A Complete Resource Book in Chemistry for JEE Main

Question

\(0.24 \mathrm{~g}\) of a volatile gas upon vaporization gives \(45 \mathrm{~mL}\) vapour at NTP. What will be the vapour density of the substances? (density of \(\mathrm{H}_{2}=1\) ) (a) \(95.39\) (b) \(5.973\) (c) \(95.93\) (d) \(59.73\)

Step-by-Step Solution

Answer

The vapor density of the substance is 59.73, so the correct option is (d) 59.73.

Step 1: Understand the Given Data and Terms

We are given that a volatile gas weighs 0.24 g and occupies 45 mL when vaporized at Normal Temperature and Pressure (NTP). We need to find the vapor density of the gas. Vapor density is defined as half of the molar mass of a gaseous substance. The density of hydrogen is 1, which means its molar mass is approximately 2 g/mol.

Step 2: Convert Volume to Molar Volume at NTP

At NTP, 1 mole of an ideal gas occupies 22.4 L (or 22400 mL). Therefore, to find the number of moles of the gas, we divide the volume of the gas by the molar volume at NTP. The formula is:\[\text{Number of moles} = \frac{\text{Volume at NTP}}{22400 \text{ mL}}\]So, \( n = \frac{45}{22400} \approx 0.0020089 \text{ moles} \).

Step 3: Determine the Molar Mass of the Gas

Using the relationship between mass, moles, and molar mass:\[\text{Molar Mass} = \frac{\text{Mass of the gas}}{\text{Number of moles}}\]we have \( M = \frac{0.24}{0.0020089} \approx 119.45 \text{ g/mol} \).

Step 4: Calculate Vapour Density

Vapour density is defined as half of the molar mass:\[\text{Vapour Density} = \frac{\text{Molar Mass}}{2}\]Thus, \( \text{Vapour Density} = \frac{119.45}{2} = 59.725 \approx 59.73 \).

Step 5: Compare with the Given Options

The calculated vapor density is 59.73. We compare this with the given options and see that option (d) 59.73 is the correct choice.

Key Concepts

Volatile Gas

When you hear the term "volatile gas," think about a gas that easily vaporizes.
Volatility in chemistry refers to the readiness of a substance to transition from a liquid to a gas state. This means such substances have low boiling points and evaporate quickly.

Examples of volatile gases include:

• Alcohol (ethanol)
• Ammonia
• Benzene

For a study of vapor density, it's essential to understand that volatile gases can significantly impact the calculations because they change their state under standard conditions and pressures.

Molar Mass

Molar mass is a fundamental concept in chemistry and describes the mass of a mole of a substance.
It tells us how much one mole of a given substance weighs, usually expressed in grams per mole (g/mol).

For gases, determining molar mass is crucial for understanding characteristics like vapor density. This concept comes into play heavily when predicting how a gas will behave under various conditions.
For example, you can calculate the molar mass by dividing the mass of a sample by the number of moles in the sample:\[\text{Molar Mass} = \frac{\text{Mass of the gas}}{\text{Number of moles}}\]Understanding molar mass helps us comprehend how gases compare to each other in terms of their physical and chemical properties.

Normal Temperature and Pressure (NTP)

Normal Temperature and Pressure, abbreviated as NTP, is a condition used as a standard for scientific measurements.
This standard condition helps in making accurate and consistent comparisons and calculations.

NTP specifies:

• Temperature: 20°C (293.15 K)
• Pressure: 1 atmosphere (101.325 kPa)

Under these conditions, gases behave predictably, allowing chemists to standardize their measurements. When working with gases, knowing the volume occupied by a gas at NTP is critical for calculating its molar volume and, subsequently, other properties like molar mass and vapor density.

Ideal Gas

The ideal gas concept helps in simplifying the study of gases.
An ideal gas follows specific theoretical conditions: it makes certain assumptions about gas particles, such as having no volume and no interactions with each other.

While no real gas is perfectly ideal, this model is useful for:

• Predicting gas behaviors under various conditions
• Simplifying equations like the ideal gas law
• Making calculations involving molar volume at standard conditions

When we talk about gases at NTP or use the ideal gas law, we often make assumptions based on the idea that the gas behaves "ideally." This allows for easier calculation and understanding of gas properties, such as vapor density and molar mass calculations.