Calculating Moles of Helium Gas in a Metal Cylinder: A Step-by-Step Guide

Introduction

Understanding the calculation of gas moles is crucial in various scientific and engineering fields. In this article, we will apply the Ideal Gas Law to determine the moles of helium gas in an 8.5L metal cylinder at a pressure of 20.0 atm and a temperature of 22°C. This process involves several steps, including identifying the correct units and using the Ideal Gas Law formula.

Understanding the Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry and physics that relates the pressure, volume, temperature, and quantity of a gas. The equation is expressed as:

Formula: PV nRT

P Pressure (atm) V Volume (L) n Number of moles (mol) R Ideal Gas Constant (L·atm/K·mol) T Absolute Temperature (K)

Step-by-Step Calculation

To solve for the number of moles of helium gas, we will follow these steps:

Identify the given values and ensure they are in the correct units for the Ideal Gas Law equation. Plug the given values into the Ideal Gas Law equation and solve for n. Round the final answer to the appropriate number of significant figures.

Given Values:

Pressure (P) 20.0 atm Volume (V) 8.5 L Gas Constant (R) 0.082056 L·atm/K·mol Temperature (T) 22°C

Step 1: Convert Temperature to Kelvin

The temperature in Kelvin (K) is calculated by adding 273.15 to the Celsius temperature:

T 22°C 273.15 295.15 K

Step 2: Apply the Ideal Gas Law

The Ideal Gas Law formula is:

n PV/R.T

Substitute the given values into the equation:

n (20.0 atm) × (8.5 L) / (0.082056 L·atm/K·mol) × (295.15 K)

Step 3: Perform the Calculation

n (20.0 × 8.5) / (0.082056 × 295.15) 7.02 mol

Rounding to Two Significant Figures

Since the given values have two significant figures, the final answer should also be rounded to two significant figures:

n 7.0 mol

Final Answer

Therefore, the number of moles of helium gas in an 8.5L metal cylinder at a pressure of 20.0 atm and a temperature of 22°C is approximately 7.0 moles.

Conclusion

The calculation of gas moles using the Ideal Gas Law is a fundamental skill in chemistry and physics. By understanding and properly applying this formula, one can accurately determine the moles of any gas under given conditions. This example demonstrates the step-by-step process of solving for moles using the Ideal Gas Law.