Problem 7 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Assuming ideal gas behaviour, the ratio of density of ammonia to that of hydrogen chloride at same temperature and pressure is: (Atomic wt. of \(\mathrm{Cl}=35.5 \mathrm{u}\) ) (a) \(1.46\) (b) \(1.64\) (c) \(0.46\) (d) \(0.64\)

Step-by-Step Solution

Answer

The ratio of the density of ammonia to hydrogen chloride is approximately 0.46.

Step 1: Identify the compounds

Identify the chemical formulas for ammonia and hydrogen chloride. Ammonia is NH₃ and hydrogen chloride is HCl.

Step 2: Determine molar masses

Calculate the molar mass for each compound. For NH₃ (Molar mass of N = 14 u, H = 1 u): \(14 + 3 \times 1 = 17\) u. For HCl (Molar mass of H = 1 u, Cl = 35.5 u): \(1 + 35.5 = 36.5\) u.

Step 3: Use ideal gas law relationship

Recall that the density \( \rho \) for gases under ideal conditions at the same temperature and pressure is directly proportional to their molar mass. Therefore, the ratio of densities \( \rho_\text{NH₃} / \rho_\text{HCl} = M_\text{NH₃} / M_\text{HCl} \).

Step 4: Calculate density ratio

Substitute molar masses into the ratio: \( \rho_\text{NH₃} / \rho_\text{HCl} = 17 / 36.5 \approx 0.466\).

Step 5: Compare with given options

Compare the calculated density ratio to the given options. The closest value is 0.46.

Key Concepts

Density Calculation

When solving problems involving gases, understanding how to calculate density can be incredibly handy. In ideal gas conditions, densities of gases at the same temperature and pressure are proportional to their molar masses. This implies that to find the density of a gas, you can use its molar mass and the conditions set by the ideal gas law.
For gases, the ideal gas law states that \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is moles, \( R \) is the gas constant, and \( T \) is temperature.

Density \( \rho \) is defined as mass per unit volume. So, \( \rho = \frac{m}{V} \). With ideal gases, using the molar mass (\( M \)), density can be determined by the formula \( \rho = \frac{PM}{RT} \). However, when temperature and pressure remain constant for two gases, their densities directly relate to their molar masses:
- \( \rho_1/\rho_2 = M_1/M_2 \), where \( \rho_1, \rho_2 \) are densities and \( M_1, M_2 \) are molar masses of the respective gases.

This direct relationship allows you to simplify calculations: find the molar mass and apply it to determine density ratios.

Molar Mass Determination

Molar mass is crucial in many chemistry calculations, especially when working with gases. It represents the mass of one mole of a given substance. For compounds, the molar mass is found by adding the atomic masses of all atoms in a molecule.

For example, in the exercise above:

• Ammonia (NH₃) has one nitrogen atom and three hydrogen atoms. The molar masses are: \( N = 14 \) atomic units, \( H = 1 \) atomic unit. Thus, the molar mass is \( 14 + 3 \times 1 = 17 \) atomic units.
• Hydrogen chloride (HCl) has one hydrogen atom and one chlorine atom. Here, \( H = 1 \) atomic unit, \( Cl = 35.5 \) atomic units, giving a molar mass of \( 1 + 35.5 = 36.5 \) atomic units.

Get familiar with periodic table values to quickly gauge atomic weights, aiding faster calculations in problems involving multiple elements.

Chemical Formulas Identification

Understanding chemical formulas is essential. They give insight into the number and type of atoms in a molecule. This exercise relies on correctly identifying formulas to proceed with mathematical calculations.

Let's dissect ammonia (NH₃) and hydrogen chloride (HCl):

• **Ammonia (NH₃):** Composed of one nitrogen atom and three hydrogen atoms.
• **Hydrogen Chloride (HCl):** Composed of one hydrogen atom and one chlorine atom.

Chemical formulas not only help in stoichiometry and balancing equations but also in understanding gas behavior under various conditions. Recognizing and remembering common molecular compounds such as NH₃ or HCl is fundamental for efficiency in solving chemistry problems. Practice by forming associations and regularly referring to chemical tables to enhance your proficiency.