Problem 27 - A Complete Resource Book in Chemistry for JEE Main

Question

4 grams of an ideal gas occupies \(5.6035\) litres of volume at \(546 \mathrm{~K}\) and 2 atm pressure. What is its molecular weight? (a) 4 (b) 16 (c) 32 (d) 64

Step-by-Step Solution

Answer

The molecular weight of the gas is 16 g/mol, which corresponds to option (b).

Step 1: Identify the Formula Needed

To find the molecular weight of a gas, use the Ideal Gas Law equation in the form: \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is the amount of substance (in moles), \( R \) is the ideal gas constant, and \( T \) is temperature. Molecular weight can be calculated as \( \text{Molecular Weight} = \frac{\text{Mass}}{\text{Moles}} \).

Step 2: Convert Units if Necessary

Ensure all units are consistent. Pressure is given in atm, volume in litres, and temperature in Kelvin—all in standard units, so no conversion is necessary.

Step 3: Calculate Number of Moles

Rearrange the Ideal Gas Law to find the number of moles: \( n = \frac{PV}{RT} \). Given \( P = 2 \), \( V = 5.6035 \), \( T = 546 \), and \( R = 0.0821 \; \frac{\text{L atm}}{\text{mol K}} \), substitute these values into the equation: \[ n = \frac{(2)(5.6035)}{0.0821 \times 546} \approx 0.25 \; \text{moles} \]

Step 4: Calculate Molecular Weight

Use the formula \( \text{Molecular Weight} = \frac{\text{mass}}{\text{moles}} \). Mass is given as \(4 \; \text{grams}\). Substitute the calculated moles \[ \text{Molecular Weight} = \frac{4}{0.25} = 16 \; \text{grams/mol} \]

Step 5: Determine the Correct Answer

Compare the calculated molecular weight of 16 g/mol with the given options. The correct choice is (b) 16.

Key Concepts

Molecular weight calculation

Molecular weight is a crucial concept in chemistry that helps in identifying and characterizing substances. To calculate the molecular weight of a gas, you need to know two key pieces of information: the mass of the gas and the number of moles present. This is often represented by the formula:

• Molecular Weight = \( \frac{\text{Mass in grams}}{\text{Moles}} \)

In the given exercise, we have a mass of 4 grams and a calculated mole count of 0.25 moles. Plugging these values into the formula gives us:\[\text{Molecular Weight} = \frac{4 \, \text{grams}}{0.25 \, \text{moles}} = 16 \, \text{g/mol}\]This calculation shows that each mole of the gas weighs 16 grams, providing us with the molecular weight. Understanding how to determine molecular weight helps in various applications, such as stoichiometry and determining reaction yields.

Gas moles calculation

Calculating the number of moles of a gas is a fundamental skill in chemistry, especially when working with gases. To find the number of moles, we often use the Ideal Gas Law, expressed as:\[ PV = nRT \]where:

• \( P \) is the pressure of the gas
• \( V \) is the volume
• \( n \) is the number of moles
• \( R \) is the ideal gas constant \( (0.0821 \; \frac{\text{L atm}}{\text{mol K}}) \)
• \( T \) is the temperature in Kelvin

This exercise provides the following values: Pressure \( (P) \) = 2 atm, Volume \( (V) \) = 5.6035 L, and Temperature \( (T) \) = 546 K. Replacing these into the equation to solve for \( n \) (number of moles):\[n = \frac{PV}{RT} = \frac{(2)(5.6035)}{0.0821 \times 546} \approx 0.25 \, \text{moles}\]This calculation shows you the precise way to find out the quantity of substance present in the sample. Identifying the amount in moles is essential for further calculations such as determining molecular weight.

Chemistry problem solving

Successful problem solving in chemistry often requires breaking down tasks into simpler parts and employing appropriate formulas. To tackle a problem like this one efficiently, follow these steps: 1. **Identify the equation needed:** Recognize what information the problem provides and what it's asking for. In this case, applying the Ideal Gas Law and molecular weight formula is crucial. 2. **Consistency in units:** Ensure all measurements are in their standard units (atm for pressure, liters for volume, Kelvin for temperature) to avoid errors. This problem gives values in standard units, so conversions are unnecessary. 3. **Mathematical operations:** Perform calculations carefully. Double-check by inserting values correctly into the formulas. Calculating moles first with the Ideal Gas Law followed by molecular weight ensures accuracy. 4. **Check against multiple choice:** By solving step-by-step, check your final answer with the provided options. Here, 16 g/mol is the correct choice in the options given. By approaching chemistry problems systematically, you can streamline problem-solving and ensure reliable results, building a solid understanding essential for more advanced topics in chemistry.