Calculating the Temperature of Methane Gas Using the Ideal Gas Law

Introduction

The ideal gas law is a fundamental principle in physics and chemistry that describes the behavior of gases based on a few key parameters. One common application of the ideal gas law is to calculate the temperature of a gas given its pressure, volume, and the amount of substance in moles. This article will walk you through the steps to calculate the temperature of 118.5 grams of methane (CH4) gas occupying 13.5 liters at a pressure of 2.50 atmospheres.

Understanding the Ideal Gas Law

The ideal gas law is given by the equation:

$$ P V n R T $$ where - P is the pressure (in atm), - V is the volume (in liters), - n is the number of moles of the gas, - R is the ideal gas constant, and - T is the temperature in Kelvin.

Given Data and Required Calculations

The following data are given:

Mass of methane (CH4): 118.5 grams Volume of methane: 13.5 liters Pressure: 2.50 atm

First, we need to find the number of moles of methane using its molar mass. The molar mass of CH4 can be calculated as:

$$ M_{CH4} 12.011 , text{g/mol (for C)} 4 times 1.008 , text{g/mol (for H)} 16.043 , text{g/mol} $$

Next, we can calculate the moles of methane:

$$ n_{CH4} frac{text{mass}}{text{molar mass}} frac{118.5 , text{g}}{16.043 , text{g/mol}} 7.3864 , text{mol} $$

Solving for Temperature

Using the ideal gas law, we can now solve for the temperature:

$$ T frac{P V}{n R} $$

Substituting the known values:

$$ T frac{2.50 , text{atm} times 13.5 , text{L}}{7.3864 , text{mol} times 0.082057 , text{L atm/(K mol)}} $$

Performing the calculation in the correct order, we get:

$$ T frac{33.75 , text{L atm}}{0.6085 , text{L atm/(K mol)}} 55.53 , text{K} $$

By rounding to three significant figures, the temperature is:

$$ T approx 55.7 , text{K} $$

Therefore, the temperature under the given conditions would be approximately 55.7 Kelvin.

Additional Information on the Ideal Gas Law

Methane (CH4) is a simple yet important gas in various applications, from natural gas to industrial processes. Calculating the temperature of gases like methane is crucial for understanding and predicting their behavior under different conditions. The ideal gas law is not only a fundamental concept in thermodynamics but also an indispensable tool in many scientific fields.

For a more detailed understanding, you can explore further applications of the ideal gas law to different gases and under varying conditions. This basic calculation is a stepping stone to more complex thermodynamic problems and real-world applications.