Question

At STP the density of a gas (mol. wt. = 45) in \(\mathrm{g} / \mathrm{L}\) is: (a) \(11.2\) (b) 1000 (c) 2 (d) \(22.4\)

Short answer

The correct answer is (c) 2.

Step-by-step solution

Recall the Ideal Gas Law formula

The Ideal Gas Law can be represented as \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is temperature.

Define standard temperature and pressure (STP) conditions

Standard Temperature and Pressure (STP) are defined as \( 0^\circ C \) or \( 273.15 \text{ K} \) for temperature and \( 1 \text{ atm} \) for pressure. At STP, 1 mole of any ideal gas occupies \( 22.4 \text{ L} \).

Determine moles of gas at STP

With the molar mass of the gas given as \( 45 \text{ g/mol} \), at STP, \( 1 \text{ mole} \) of this gas will occupy \( 22.4 \text{ L} \).

Calculate the density of the gas

Density \( (\rho) \) is mass divided by volume. At STP, the mass of 1 mole (\( 45 \text{ g} \)) occupies \( 22.4 \text{ L} \). Therefore, density \( \rho = \frac{\text{mass}}{\text{volume}} = \frac{45 \text{ g}}{22.4 \text{ L}} \approx 2.01 \text{ g/L} \).

Choose the correct option

The density of the gas at STP is closest to \( 2 \text{ g/L} \). Therefore, option (c) is the correct answer.

Key concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental equation that describes the behavior of ideal gases. It is expressed as \( PV = nRT \), where:

• \( P \) represents pressure of the gas.
• \( V \) is the volume.
• \( n \) stands for the number of moles of the gas.
• \( R \) is the ideal gas constant \( (8.314 \, \text{J/(mol\(\cdot\)K)}) \).
• \( T \) is the temperature measured in Kelvin.

This equation relates the pressure, volume, number of moles, and temperature of a gas, allowing you to predict one property if the others are known. It's crucial to note that the Ideal Gas Law assumes gases behave perfectly with no interactions between molecules. This assumption holds true under many conditions, especially at high temperatures and low pressures.

Molar Mass

Molar mass is a key concept in chemistry that represents the mass of one mole of a given substance. It is usually expressed in grams per mole (\( ext{g/mol} \)). To find molar mass, you simply multiply the atomic mass of each element by the number of its atoms in a molecule and sum up the results.
For instance, a gas with a molar mass of \(45 \text{ g/mol}\) means that one mole of this gas weighs 45 grams. Understanding molar mass helps in identifying substances and predicting how they will behave in chemical reactions.

Standard Temperature and Pressure (STP)

Standard Temperature and Pressure, abbreviated as STP, refers to two specific conditions used as a baseline in scientific calculations. STP is defined as a temperature of \( 0 ^\circ \text{C} \) (or 273.15 K) and a pressure of 1 atmosphere (atm).
Under these conditions, one mole of an ideal gas occupies \(22.4 \text{ L}\). STP is often used as a reference point for gas-related calculations, simplifying the comparison of results and consistency in experiments.

Gas Density at STP

Gas density at STP is an important property used to describe the mass of a gas per unit volume under standard conditions. It is calculated using the formula \( \rho = \frac{\text{mass}}{\text{volume}} \), where density (\( \rho \)) is usually given in grams per liter (\( \text{g/L} \)).
For example, if a gas has a molar mass of \(45 \text{ g/mol}\), its density at STP can be calculated by dividing the molar mass by the molar volume at STP. Thus, \( \rho = \frac{45 \text{ g}}{22.4 \text{ L}} \), providing a density of approximately \(2.01 \text{ g/L}\). This density value offers insight into how much substance is present in a certain volume of space at STP, which is useful in various scientific and industrial applications.