CO2 Gas Volume Calculation Using Combined Gas Law
In the realm of chemistry, understanding the behavior of gases under varying conditions is crucial. This article delves into the principles governing gas behavior, specifically focusing on how to calculate the final volume of a carbon dioxide (CO2) gas sample when subjected to changes in temperature and pressure. We'll explore the combined gas law, a fundamental concept in chemistry, and apply it to a practical scenario. Let's embark on this scientific journey together!
Understanding the Combined Gas Law
The combined gas law is a cornerstone of gas behavior studies, elegantly merging Boyle's law, Charles's law, and Gay-Lussac's law into a single, comprehensive equation. This law proves invaluable when dealing with scenarios where the pressure, volume, and temperature of a gas all undergo simultaneous changes, while the amount of gas remains constant. The combined gas law is mathematically expressed as:
(P₁V₁) / T₁ = (P₂V₂) / T₂
Where:
- P₁ = Initial pressure
- V₁ = Initial volume
- T₁ = Initial temperature
- P₂ = Final pressure
- V₂ = Final volume (what we want to find)
- T₂ = Final temperature
This equation highlights the intrinsic relationships between pressure, volume, and temperature. It allows us to predict how a gas will respond to alterations in these conditions, making it an indispensable tool for chemists and scientists alike. By understanding and applying the combined gas law, we can unlock the secrets of gas behavior and solve a wide range of problems.
Boyle's Law: Pressure-Volume Relationship
At the heart of the combined gas law lies Boyle's law, which elucidates the inverse relationship between the pressure and volume of a gas when the temperature and amount of gas remain constant. In simpler terms, as the pressure on a gas increases, its volume decreases proportionally, and vice versa. Imagine squeezing a balloon – the pressure inside increases, causing the volume to shrink. This relationship is mathematically expressed as:
P₁V₁ = P₂V₂
Boyle's law finds applications in various real-world scenarios, from understanding the functioning of scuba diving equipment to predicting the behavior of gases in industrial processes. Its simplicity and elegance make it a fundamental concept in the study of gases.
Charles's Law: Temperature-Volume Relationship
Charles's law unveils the direct proportionality between the volume and temperature of a gas when the pressure and amount of gas are kept constant. This means that as the temperature of a gas increases, its volume expands proportionally, and vice versa. Think of a hot air balloon – heating the air inside causes it to expand, making the balloon buoyant. The mathematical representation of Charles's law is:
V₁ / T₁ = V₂ / T₂
Charles's law is crucial for understanding phenomena like thermal expansion and contraction, and it plays a vital role in designing systems that involve gases at varying temperatures.
Gay-Lussac's Law: Pressure-Temperature Relationship
Gay-Lussac's law reveals the direct relationship between the pressure and temperature of a gas when the volume and amount of gas are held constant. As the temperature of a gas rises, its pressure increases proportionally, and vice versa. Consider the pressure inside a car tire on a hot day – the increased temperature leads to higher pressure. Gay-Lussac's law is expressed mathematically as:
P₁ / T₁ = P₂ / T₂
This law is particularly relevant in applications involving closed containers, where volume is constant, and temperature fluctuations can significantly impact pressure.
Applying the Combined Gas Law: A Step-by-Step Solution
Now, let's apply the combined gas law to solve the problem at hand: determining the final volume of CO2 gas under changing conditions. We are given the following information:
- Initial volume (V₁) = 5.00 L
- Initial temperature (T₁) = 14 °C
- Initial pressure (P₁) = 779 mmHg
- Final temperature (T₂) = 39 °C
- Final pressure (P₂) = 735 mmHg
Our goal is to calculate the final volume (V₂).
Step 1: Convert Temperatures to Kelvin
The combined gas law requires temperatures to be expressed in Kelvin (K), the absolute temperature scale. To convert from Celsius (°C) to Kelvin, we use the following formula:
K = °C + 273.15
Therefore:
- T₁ = 14 °C + 273.15 = 287.15 K
- T₂ = 39 °C + 273.15 = 312.15 K
Converting to Kelvin ensures accurate calculations when using the combined gas law.
Step 2: State the Knowns and Unknowns
Let's clearly list our known and unknown variables:
- Knowns:
- P₁ = 779 mmHg
- V₁ = 5.00 L
- T₁ = 287.15 K
- P₂ = 735 mmHg
- T₂ = 312.15 K
- Unknown:
- V₂ = ?
Organizing the information in this way helps to streamline the problem-solving process.
Step 3: Rearrange the Combined Gas Law Equation to Solve for V₂
To isolate V₂, we need to rearrange the combined gas law equation:
(P₁V₁) / T₁ = (P₂V₂) / T₂
Multiply both sides by T₂:
(P₁V₁T₂) / T₁ = P₂V₂
Now, divide both sides by P₂:
V₂ = (P₁V₁T₂) / (P₁T₁)
This rearranged equation allows us to directly calculate V₂ using the known values.
Step 4: Plug in the Values and Calculate V₂
Substitute the known values into the equation:
V₂ = (779 mmHg * 5.00 L * 312.15 K) / (735 mmHg * 287.15 K)
Perform the calculation:
V₂ ≈ 5.80 L
Therefore, the final volume of the CO2 gas is approximately 5.80 liters.
Result and Discussion
The final volume of the CO2 gas under the given conditions is approximately 5.80 liters. This result demonstrates the application of the combined gas law in predicting gas behavior. By increasing the temperature and decreasing the pressure, the volume of the gas expanded, as expected. This calculation underscores the importance of understanding the relationships between pressure, volume, and temperature in gas systems.
In conclusion, the combined gas law is a powerful tool for analyzing and predicting the behavior of gases under changing conditions. By carefully applying the law and paying attention to unit conversions, we can accurately determine the final volume of a gas in various scenarios. This knowledge is fundamental to many areas of chemistry and related fields, making the combined gas law an essential concept for students and professionals alike.