Determine the Volume of a Gas at STP Using the Combined Gas Law

Understanding how to determine the volume of a gas at standard temperature and pressure (STP) is crucial in various scientific and engineering applications. The combined gas law is a powerful tool for such a calculation, allowing us to relate the initial and final states of a gas given changes in pressure, volume, or temperature. This article will guide you through the process using a specific example, followed by a detailed explanation of the combined gas law and its practical applications.

Example Problem

Given a gas with an initial volume of 480 mL at a pressure of 1000 mmHg and a temperature of 40°C, we want to determine the volume of the gas at STP (Standard Temperature and Pressure).

Step 1: Convert all values to the appropriate units

Initial Volume: ( V_1 480 , text{mL} ) Initial Pressure: ( P_1 1000 , text{mmHg} ) Initial Temperature: ( T_1 40^circ text{C} ) - Convert to Kelvin: ( T_1 40 273.15 313.15 , text{K} ) Final Pressure: ( P_2 760 , text{mmHg} ) (STP) Final Temperature: ( T_2 0^circ text{C} ) - Convert to Kelvin: ( T_2 0 273.15 273.15 , text{K} )

Step 2: Write and solve the combined gas law equation

The combined gas law states:

[frac{P_1 V_1}{T_1} frac{P_2 V_2}{T_2}]

Where:

( P_1 ) Initial pressure ( V_1 ) Initial volume ( T_1 ) Initial temperature in Kelvin ( P_2 ) Final pressure at STP ( V_2 ) Final volume at STP ( T_2 ) Final temperature at STP in Kelvin

Plug in the values:

[frac{1000 , text{mmHg} times 480 , text{mL}}{313.15 , text{K}} frac{760 , text{mmHg} times V_2}{273.15 , text{K}}]

Solve for ( V_2 ):

[V_2 frac{1000 times 480 times 273.15}{313.15 times 760}]

Calculate ( V_2 ):

[V_2 approx 550.78 , text{mL}]

Therefore, the volume of the gas at STP is approximately 550.78 mL.

Practical Applications of the Combined Gas Law

The combined gas law has numerous practical applications in chemistry and physics, including:

Chemistry Experiments: In laboratory settings, scientists often need to predict the behavior of gases under different conditions. The combined gas law helps them to calculate the volume of a gas at STP, ensuring accurate experimental results. Industries: In industries that deal with gases, such as compressed gas suppliers, the combined gas law can be used to ensure safe and efficient storage and handling of gases. Engineering: Engineers use the combined gas law to design and optimize systems involving gases, such as gas turbines and air conditioning systems.

Conclusion

The combined gas law is a fundamental principle in thermodynamics and gas dynamics. By understanding how to apply this law, scientists, engineers, and technicians can solve complex problems related to the behavior of gases. Whether in a laboratory, in industry, or in engineering, the combined gas law is an essential tool for anyone dealing with gaseous systems.

Frequently Asked Questions

Q: What is STP in the context of the combined gas law?
A: STP stands for Standard Temperature and Pressure, which is 0°C (273.15 K) and 1 atm (760 mmHg) respectively. Q: How do you convert Celsius to Kelvin?
A: To convert Celsius to Kelvin, add 273.15 to the Celsius temperature. Q: Why is the combined gas law important for engineers?
A: The combined gas law allows engineers to predict and control the behavior of gases in various systems, ensuring reliability and efficiency in design.