Calculating Moles of Propane at STP: A Comprehensive Guide

When dealing with gases, understanding their behavior at standard temperature and pressure (STP) becomes crucial. This article will guide you through the process of calculating the number of moles of propane, CH3CH2CH3, present at STP if the volume is 65.0 liters. We will explore different methods, including the use of the ideal gas law and the concept of the standard molar volume.

Understanding STP and Standard Molar Volume

Standard Temperature and Pressure (STP) are defined as:

Temperature: 0°C (273.15 K) Pressure: 1 atm (101.3 kPa)

At these conditions, one mole of any ideal gas occupies a volume of 22.4 liters. This volume is known as the standard molar volume. This concept is fundamental for calculating the number of moles of a gas given its volume under STP.

Method 1: Using the Standard Molar Volume

The simplest approach to finding the number of moles of propane at STP is by using the standard molar volume. Here’s how:

Step-by-Step Calculation

Given data: Volume of propane, V 65.0 L Standard molar volume at STP, VSTP 22.4 L/mol

Using the formula:

[n frac{V}{V_{STP}}]

Substituting the values:

[n frac{65.0 , text{L}}{22.4 , text{L/mol}} approx 2.89 , text{moles}]

This calculation indicates that approximately 2.89 moles of propane are present at STP.

Method 2: Using the Ideal Gas Law

The ideal gas law, (PV nRT), is another way to determine the number of moles. Here’s how this method works:

Step-by-Step Calculation

Given data: Volume of propane, (text{V} 65.0 , text{L}) Temperature, (text{T} 273.15 , text{K}) Pressure, (text{P} 101.3 , text{kPa}) Gas constant, (text{R} 8.31 , text{kPa L/mol K}) Temperature and pressure at STP do not change.

Rearranging the ideal gas law to solve for moles (n):

[n frac{PV}{RT}]

Substituting the values:

[n frac{101.3 times 65.0}{8.31 times 273.15} approx 2.90 , text{moles}]

Again, this calculation confirms that approximately 2.90 moles of propane are present at STP.

Summary

Both methods yield nearly the same result, which is approximately 2.90 moles of propane at STP. The choice of method depends on your familiarity with the standard molar volume and the ideal gas law, respectively.

Further Reading

For further exploration of gas laws and properties, consider reading about:

The different states of matter and their behavior under varying conditions The laws of thermodynamics and how they apply to gases Real gas behavior and deviations from ideal gas law behavior