Gas Laws and Ideal Behavior: A Reflective Analysis
How can we apply the ideal gas law to determine the volume of a gas under different conditions?
Given: Initial volume of Cl₂ gas = 15.0 L
Initial pressure = 1.50 atm
Initial temperature = 23°C
Final pressure = 3.50 atm
Final temperature = 286°C
Using the ideal gas equation [tex]PV=nRT[/tex], how can we calculate the final volume of the gas?
Answer:
The ideal gas law can be applied to calculate the volume of a gas under different conditions by using the formula [tex]V=\\frac{nRT}{P}[/tex].
In this case, the initial volume of Cl₂ gas is 15.0 L at a pressure of 1.50 atm and a temperature of 23°C.
By rearranging the ideal gas equation and calculating the value of nR, we find that the volume of the gas at 3.50 atm and 286°C is 12.14 L.
The ideal gas law provides a useful framework for understanding the behavior of gases in different conditions. By combining Boyle's law, Charles's law, and Avogadro's law into a single equation, we can predict how gases will behave under changing pressure, volume, and temperature.
For this specific example with Cl₂ gas, we started with an initial volume of 15.0 L, a pressure of 1.50 atm, and a temperature of 23°C. By calculating the number of moles, we determined that the initial volume of the gas was 0.927 moles.
When the pressure is increased to 3.50 atm and the temperature to 286°C, we can use the ideal gas equation to calculate the final volume of the gas. Plugging in the values for pressure, temperature, moles, and the gas constant, we find that the gas will occupy 12.14 L under these new conditions.
Understanding how to apply the ideal gas law allows us to make predictions about gas behavior and determine how gases will respond to changes in their environment. By utilizing these principles, scientists and engineers can design systems that rely on the predictable behavior of gases to achieve specific outcomes.