Problem 30 - Chemistry: The Central Science

Question

(a) What conditions are represented by the abbreviation STP? (b) What is the molar volume of an ideal gas at STP? (c) Room temperature is often assumed to be \(25^{\circ} \mathrm{C}\). Calculate the molar volume of an ideal gas at \(25^{\circ} \mathrm{C}\) and 1 atm pressure.

Step-by-Step Solution

Answer

(a) STP represents Standard Temperature and Pressure, with the conditions being 0°C (273.15 K) temperature and 1 atm (101.325 kPa) pressure. (b) The molar volume of an ideal gas at STP is approximately 22.414 L/mol. (c) The molar volume of an ideal gas at 25°C and 1 atm pressure is approximately 24.465 L/mol.

Step 1: Define STP

STP stands for Standard Temperature and Pressure. It is the standard set of conditions that scientists often use to compare gases. The conditions at STP are: 1. Temperature: 0°C (273.15 K) 2. Pressure: 1 atm (101.325 kPa)

Step 2: Determine molar volume at STP

The molar volume of an ideal gas at STP is the volume occupied by one mole of ideal gas under STP conditions. According to the Ideal Gas Law, we have the relationship: \(PV=nRT\) where: P: pressure (atm) V: volume (L) n: number of moles R: ideal gas constant (~0.0821 L⋅atm/mol⋅K) T: temperature (K) At STP, temperature T = 273.15 K, pressure P = 1 atm, and n = 1 mole. Plugging these values into the Ideal Gas Law, we can solve for the molar volume (V): \(V = \frac{nRT}{P} = \frac{1 \times 0.0821 \times 273.15}{1}\)

Step 3: Calculate molar volume at STP

Now that we have the equation set up, we can calculate the molar volume of an ideal gas at STP: \(V = \frac{1 \times 0.0821 \times 273.15}{1} = 22.414\, L/mol\) So, the molar volume of an ideal gas at STP is approximately 22.414 L/mol.

Step 4: Calculate molar volume at 25°C and 1 atm

Now, we are asked to calculate the molar volume of an ideal gas at 25°C (298.15 K) and 1 atm pressure. We can use the Ideal Gas Law again with the new temperature and pressure values: \(V = \frac{nRT}{P} = \frac{1 \times 0.0821 \times 298.15}{1}\)

Step 5: Molar volume at 25°C and 1 atm

Now, we can calculate the molar volume of an ideal gas at 25°C and 1 atm: \(V = \frac{1 \times 0.0821 \times 298.15}{1} = 24.465\, L/mol\) So, the molar volume of an ideal gas at 25°C and 1 atm pressure is approximately 24.465 L/mol.

Key Concepts

STP (Standard Temperature and Pressure)

STP stands for Standard Temperature and Pressure, which is a set of conditions widely used in scientific calculations to evaluate and compare the properties of gases. These standard conditions help scientists and students to have a common reference point. Under STP, the temperature is standardized to 0°C, which is equivalent to 273.15 Kelvin. The pressure is standardized to 1 atmosphere, which corresponds to 101.325 kilopascals. These conditions are crucial in performing chemical experiments and calculations involving gases. By understanding STP, we can easily predict how gases will behave under specified conditions if we assume ideal behavior.

Molar Volume

The molar volume of a gas refers to the volume that one mole of gas occupies under certain conditions of temperature and pressure. At STP, the molar volume of an ideal gas is about 22.414 liters per mole.

This concept is derived from the ideal gas law, which is expressed as:\[ PV = nRT \]

Where:

• \(P\) is the pressure
• \(V\) is the volume
• \(n\) is the number of moles
• \(R\) is the ideal gas constant
• \(T\) is the temperature

To calculate the molar volume at different temperatures and pressures, we can rearrange the ideal gas equation. For example, at 25°C (298.15 K) and 1 atm, the molar volume is calculated as approximately 24.465 liters per mole. By understanding molar volume, we can predict and calculate how a gas will expand or contract under varying conditions.

Ideal Gas Constant

The ideal gas constant, often symbolized as \(R\), is a fundamental part of the Ideal Gas Law equation, \(PV=nRT\). This constant provides a connection between the pressure, volume, temperature, and moles of a gas, allowing these different properties to be interrelated in a meaningful way.

For gases, the value of \(R\) is usually given as 0.0821 liters atm per mole Kelvin (L⋅atm/mol⋅K). This value is consistent when calculations involve the pressure of gases in atmospheres, volume in liters, and temperature in Kelvin.

The ideal gas constant is pivotal in calculations involving the Ideal Gas Law, serving as a bridge between theoretical predictions and real-world applications in chemistry and physics. Understanding \(R\) helps us to predict how gases will behave under { extit{ideal}} conditions, shaping our understanding of the relationships between observed physical properties.