๐ What is the Combined Gas Law?
The Combined Gas Law is a single equation that combines Boyle's Law, Charles's Law, and Gay-Lussac's Law. It expresses the relationship between pressure, volume, and temperature for a fixed amount of gas. This law is especially useful when dealing with situations where multiple properties of a gas are changing simultaneously.
๐ History and Background
The Combined Gas Law wasn't discovered by a single person. Instead, it's a culmination of the work of several scientists. Robert Boyle discovered the inverse relationship between pressure and volume, Jacques Charles found the direct relationship between volume and temperature, and Joseph Louis Gay-Lussac established the direct relationship between pressure and temperature. By combining these individual laws, scientists created a single, more comprehensive equation.
๐ Key Principles
- ๐ก๏ธ Temperature Must Be Absolute: Always use Kelvin ($K$) for temperature. To convert Celsius ($^{\circ}C$) to Kelvin, use the formula: $K = {^{\circ}C} + 273.15$.
- ๐ฆ Fixed Amount of Gas: The Combined Gas Law applies only when the amount of gas (number of moles) remains constant.
- โ๏ธ The Equation: The Combined Gas Law is represented by the following equation:
$$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$$
Where:
- ๐ $P_1$ = Initial Pressure
- ๐ $V_1$ = Initial Volume
- ๐ฅ $T_1$ = Initial Temperature (in Kelvin)
- ๐ $P_2$ = Final Pressure
- ๐ $V_2$ = Final Volume
- ๐ฅ $T_2$ = Final Temperature (in Kelvin)
๐งช Real-World Examples
- ๐ Inflating a Tire: As a car tire heats up during driving (increasing temperature), the pressure inside the tire also increases if the volume remains relatively constant.
- ๐ Weather Balloons: As a weather balloon ascends into the atmosphere, the pressure decreases. The balloon expands (volume increases) as it rises, and the temperature also changes, making it a perfect example of the Combined Gas Law in action.
- ๐ Diving: When a scuba diver descends, the pressure increases, compressing the air in their scuba tank. The Combined Gas Law helps to predict how the volume and temperature of the air will change under these conditions.
๐ก Tips for Solving Problems
- โ
Identify Variables: Carefully read the problem to identify the initial and final values for pressure, volume, and temperature.
- โ๏ธ Convert Units: Ensure all units are consistent. Temperature must be in Kelvin. Volume and pressure should be in consistent units (e.g., liters and atmospheres).
- โ Rearrange the Equation: Rearrange the Combined Gas Law equation to solve for the unknown variable.
- ๐ Plug and Solve: Substitute the known values into the rearranged equation and solve for the unknown.
๐งฎ Practice Quiz
Try these practice problems to test your understanding of the Combined Gas Law:
- A gas occupies a volume of 10.0 L at standard temperature and pressure (STP). If the temperature is increased to 100.0 $^\circ$C and the pressure is increased to 2.00 atm, what is the new volume of the gas?
- A balloon contains 5.0 L of air at 25 $^\circ$C and 1.0 atm. If the temperature drops to 10 $^\circ$C and the pressure increases to 1.5 atm, what is the new volume of the balloon?
- A gas in a container has a pressure of 3.0 atm, a volume of 6.0 L, and a temperature of 200 K. If the pressure is decreased to 1.0 atm and the volume is increased to 12.0 L, what is the new temperature of the gas?
Answers:
- V2 = 9.15 L
- V2 = 3.24 L
- T2 = 133 K
๐ Conclusion
The Combined Gas Law is a powerful tool for understanding and predicting the behavior of gases under varying conditions. By mastering this law, you can solve a wide range of chemistry problems and gain a deeper understanding of the properties of gases. Remember to always convert temperature to Kelvin and keep track of your units!