Problem 3 - Chemistry The Molecular Science

Question

What is the volume occupied by \(1 \mathrm{~mol}\) of an ideal gas at STP?

Step-by-Step Solution

Answer

The volume is 22.414 L.

Step 1: Understanding STP

STP stands for Standard Temperature and Pressure. In chemistry, STP is defined as a temperature of 273.15 K (0°C) and a pressure of 1 atm.

Step 2: Using the Ideal Gas Law

The ideal gas law is given by \[ PV = nRT \]where:- \( P \) is the pressure,- \( V \) is the volume,- \( n \) is the number of moles,- \( R \) is the ideal gas constant (0.0821 L atm K⁻¹ mol⁻¹),- \( T \) is the temperature.

Step 3: Substituting Values

At STP, substitute the values into the ideal gas law: - \( P = 1 \text{ atm} \),- \( n = 1 \text{ mol} \),- \( R = 0.0821 \text{ L atm K}^{-1} \text{ mol}^{-1} \),- \( T = 273.15 \text{ K} \).This gives us \[ 1 \text{ atm} \times V = 1 \text{ mol} \times 0.0821 \text{ L atm K}^{-1} \text{ mol}^{-1} \times 273.15 \text{ K} \].

Step 4: Calculating the Volume

Solve for \( V \) by doing the multiplication on the right side of the equation. \[ V = 0.0821 \times 273.15 \approx 22.414 \text{ L} \].

Key Concepts

Standard Temperature and Pressure (STP)

Standard Temperature and Pressure, commonly abbreviated as STP, is a crucial reference point in chemistry for conditions under which experiments and calculations are often made.

STP is defined by specific values:

• Temperature: 273.15 Kelvin (K), which is equivalent to 0 degrees Celsius (°C).
• Pressure: 1 atmosphere (atm), where 1 atm is the pressure exerted by the atmosphere at sea level.

These conditions are significant because they simplify measurements and discussions about gas volumes and reactions. Under STP, gases exhibit predictable behaviors described by the ideal gas law, making it a useful baseline for scientists and students alike when exploring gas properties.

Mole concept

The mole concept is a fundamental idea in chemistry that serves as a bridge between the micro world of atoms and molecules and the macro world of grams and liters. A mole represents a quantity of substance, specifically Avogadro's number, which is approximately 6.022 x 10²³ entities (like atoms or molecules).

This concept allows us to:

• Express amounts of a chemical substance in a practical way.
• Perform stoichiometric calculations in chemical equations, helping predict the amount of products and reactants.
• Relate masses of different substances to the number of particles they contain.

In the context of gas laws like the Ideal Gas Law, one mole of any gas at STP occupies a standard volume, typically around 22.414 liters, which simplifies many calculations.

Gas constant

The gas constant, denoted as R, is a fundamental constant featured in the ideal gas law. Its value in these calculations is 0.0821 L atm K⁻¹ mol⁻¹.

The gas constant is critical for:

• Linking pressure, volume, temperature, and number of moles in the ideal gas equation: \[ PV = nRT \]
• Ensuring unit consistency in calculations involving gases. Its units match those typically used in gas law problems.

The consistent use of R helps bridge the gap between theoretical calculations and real-world chemical and physical phenomena. Understanding the role of the gas constant allows scientists and students to predict how changes in one property of a gas will affect others under ideal conditions.