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The combined gas law is a handy equation used in chemistry to understand how gases behave under different conditions of pressure, volume, and temperature. This law combines three fundamental gas laws: Boyle's Law, Charles's Law, and Gay-Lussac's Law. These individual laws describe how one variable affects the other two, assuming the third is constant. However, the combined gas law integrates all three, providing a more comprehensive formula:\[ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \]In this formula:- \(P_1\) and \(P_2\) are the initial and final pressures.- \(V_1\) and \(V_2\) are the initial and final volumes.- \(T_1\) and \(T_2\) are the initial and final temperatures, always in Kelvin.This law allows you to calculate the new state of a gas when it undergoes changes in more than one of these conditions, such as when a weather balloon rises to a higher altitude as seen in our exercise.

Weather balloons are a key tool in meteorology, used to gather data from high altitudes. They rise into the atmosphere, expanding as they go because the atmospheric pressure decreases with altitude. In the given problem, we calculated how the volume of a weather balloon changes from an initial state to a new state at higher altitudes. Initially, the balloon has a volume of 45.0 liters at ground level. As it ascends, both the outside pressure and temperature change, affecting the balloon's volume. By applying the combined gas law, we can predict that the balloon's volume increases to approximately 141.9 liters at 10,000 meters, demonstrating how significant pressure and temperature changes can alter a gas's volume.

When studying the behavior of gases, it's crucial to understand how pressure and temperature changes affect them. As a weather balloon rises, these parameters change drastically - the temperature typically decreases, and the pressure drops. In our exercise: - The initial pressure is 745 mm Hg and decreases to 178 mm Hg as the balloon rises. - The initial temperature is 25.0°C and converts to 298.15 K. It decreases even further to 225 K at 10,000 meters. These conditions simulate real-life scenarios when gases expand during ascent, which is critical for meteorological studies. Lower pressure at higher altitudes allows the gas inside the balloon to expand, increasing its volume.

The Kelvin scale is an absolute temperature scale often used in gas law calculations because it starts at absolute zero. This is crucial because temperature in Kelvin is directly proportional to the energy of the thermodynamic system. To convert Celsius to Kelvin, you use the formula:\[T(K) = T(°C) + 273.15\]For our initial condition, the temperature is 25°C:\[T_1 = 25.0 + 273.15 = 298.15 \text{ K}\]Kelvin is used in the combined gas law calculations to ensure accurate results. Always remember that the Kelvin scale must be used in gas law problems as they require absolute temperatures, avoiding negative values that are nonsensical in physical equations.