Problem 31 - A Complete Resource Book in Chemistry for JEE Main

Question

At STP the density of a gas \((\mathrm{mol} . \mathrm{wt}=45)\) in \(\mathrm{g} / \mathrm{L}\) is (a) \(11.2\) (b) 1000 (c) 2 (d) 224

Step-by-Step Solution

Answer

The density of the gas at STP is approximately 2 g/L, option (c).

Step 1: Understanding STP Conditions

Before solving the problem, we need to know that STP (standard temperature and pressure) refers to a temperature of 273.15 K (0 °C) and a pressure of 1 atmosphere. Under these conditions, one mole of any gas occupies 22.4 liters.

Step 2: Knowing the Formula for Density

Density is defined as mass per unit volume. For a gas, it can be calculated using the formula: \( \text{density} = \frac{\text{molar mass}}{\text{volume of one mole of gas at STP}} \).

Step 3: Calculating the Density

Substitute the values into the formula for density: the molar mass is 45 g/mol, and the volume occupied by one mole of gas at STP is 22.4 L. Therefore, the density \( \rho = \frac{45}{22.4} \approx 2.0089 \text{ g/L} \).

Step 4: Interpreting the Result

The calculated density of the gas is approximately 2.0089 g/L, which is very close to the option (c) 2 g/L. Based on this approximation, we choose option (c) as the correct answer.

Key Concepts

STP conditions

Standard Temperature and Pressure, or **STP conditions**, are baseline settings agreed upon by scientists for measuring gas properties. These conditions are defined as a temperature of 273.15 Kelvin, which corresponds to zero degrees Celsius, and a pressure of one atmosphere, equivalent to 101.325 kPa.
At such conditions, gases behave predictably and consistently, allowing for easier comparisons and calculations. When dealing with gases, knowing whether the values are measured under STP is crucial, because it directly influences calculations involving volume and density. At STP, one mole of any ideal gas occupies exactly 22.4 liters. This volume function as a standard against which we can calculate other properties such as density, making STP incredibly significant in chemistry and physics.

molar mass of gases

The **molar mass of gases** is a key concept in understanding gas behavior. It refers to the mass of one mole of any gas, measured in grams per mole (g/mol). It essentially links the mass of a substance to the amount of substance when measured in moles.For any gas, knowing the molar mass allows you to calculate its density using the formula: \(\text{Density} = \frac{\text{Molar Mass}}{\text{Volume of one mole of gas at STP}}\)In this specific example, the molar mass is given as 45 g/mol. By plugging this into the equation with the known volume at STP (22.4 L), you can determine the density of the gas.Understanding molar mass is not only crucial for calculating densities but also for determining the ratios in which gases react with each other in chemical equations. It provides a bridge between the macroscopic world of mass and the microscopic world of moles.

volume of gases at STP

The **volume of gases at STP** is a fundamental aspect of gas calculations. At standard temperature and pressure, one mole of an ideal gas occupies a volume of 22.4 liters. This is a constant that emerges from the ideal gas law, where gases are assumed to behave perfectly under the STP conditions. Knowing this 22.4 liters volume per mole is vital because it simplifies the process of calculating the densities of gases. Since density is defined as mass per unit volume, having a fixed volume at STP makes it easier to derive the density if the molar mass is known.

The volume of gas at STP sets a reference point for scientists and students alike, acting as a standardized benchmark in chemistry. It makes complex calculations more manageable and helps in understanding the behavior of gases across different conditions.