An expandable balloon contains 1400 . L of He at \(0.950\) atm pressure and \(18^{\circ} \mathrm{C}\). At an altitude of 22 miles (temperature \(2.0^{\circ} \mathrm{C}\) and pressure \(4.0\) torr), what will be the volume of the balloon?

Gas laws are a set of rules that describe how gases behave under different conditions of pressure, volume, and temperature. The Combined Gas Law is one of these fundamental rules. It combines three simpler laws: Boyle's Law, Charles's Law, and Gay-Lussac's Law. Boyle's Law states that the pressure of a gas is inversely proportional to its volume when temperature is constant \(P_1V_1=P_2V_2\). Charles's Law states the volume of gas is directly proportional to its temperature in Kelvin if the pressure is constant \(\frac{V_1}{T_1}=\frac{V_2}{T_2}\). Gay-Lussac’s Law states that the pressure of a gas is directly proportional to its temperature in Kelvin if the volume is constant \(\frac{P_1}{T_1}=\frac{P_2}{T_2}\). By combining these, the Combined Gas Law is formed and expressed as \(\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2} \),

The Kelvin temperature scale is fundamental in the study of gases because it provides an absolute reference point for measuring temperatures. Unlike Celsius or Fahrenheit, Kelvin does not have negative values, making it more reliable for scientific calculations. The Kelvin scale starts at absolute zero (-273.15°C), the point where all molecular motion stops. Converting Celsius to Kelvin is straightforward: simply add 273.15. For example, converting 18°C to Kelvin is \(18°C + 273.15 = 291.15K\). Using Kelvin ensures that all values are positive and directly proportional to the energy of the gas, which makes calculations simpler and more accurate.

The relationship between volume and pressure is a key aspect in gas laws. According to Boyle's Law, as pressure increases, volume decreases, provided temperature is constant. This means that if you squeeze a gas, making its container smaller, the pressure inside increases. Conversely, if you let the gas expand, the pressure decreases. The Combined Gas Law leverages this relationship by accounting for changes in both temperature and pressure. This relationship is fundamental in understanding how gases will behave under different conditions and is crucial to solving problems involving gas dynamics.

Unit conversions are vital in chemistry to ensure that measurements are consistent and calculations are accurate. Different scientific disciplines might use different units, so conversion helps standardize these measurements. When dealing with gases, common unit conversions include converting pressure from torr to atmospheres or temperature from Celsius to Kelvin. For example, in the given exercise, pressure is converted from torr to atmospheres using the conversion factor 1 atm = 760 torr. Thus, \(4 \text{ torr} \div 760 \text{ torr/atm} = 0.005263 \text{ atm}\). Mastering unit conversions ensures precision and consistency in scientific calculations.