What pressure will 800 . \(\mathrm{mL}\) of a gas at \(\mathrm{STP}\) exert when its volume is \(250 . \mathrm{mL}\) at \(30^{\circ} \mathrm{C}\) ?

The ideal gas law is a fundamental principle in chemistry used to explain the relationship between pressure (P), volume (V), temperature (T), and the amount of gas (n) in moles. The law is usually expressed as: PV = nRT It incorporates the universal gas constant (R) and is helpful for solving problems where the amount of gas is constant but other variables change. Understanding the ideal gas law is crucial for grasping more complex gas behavior and advanced topics in physical chemistry. Alongside the combined gas law, the ideal gas law is essential in calculations involving gases. Ensure to consider the units: * Pressure (P) should be in atmospheres (atm), pascals (Pa), or any consistent unit. * Volume (V) typically in liters (L). * Temperature (T) in Kelvin (K). * R has a value of 0.0821 L·atm/mol·K when using atmospheres.

Gas laws describe how gases behave under various conditions. They include Boyle's Law, Charles's Law, and Avogadro's Law. When integrated, they form the combined gas law and the ideal gas law. Boyle's Law states that the volume of a gas is inversely proportional to its pressure when the temperature is constant: PV = k Where k is a constant. Charles's Law shows a direct relationship between volume and temperature at constant pressure: V/T = k Avogadro's Law states that equal volumes of gases, at the same temperature and pressure, contain an equal number of molecules: V/n = k By combining these laws, we arrive at: The Combined Gas Law: (P_1 V_1)/T_1 = (P_2 V_2)/T_2 This formula is especially useful when dealing with gas transitions between different states, as illustrated in our exercise. Familiarity with these laws enhances problem-solving skills in chemistry.

Solving chemistry problems involves a systematic approach. Here are some steps that help: * Identify all given variables and what you need to find. * Convert units to ensure consistency, especially for temperature (use Kelvin). * Choose the appropriate gas law based on the problem's conditions. * Substitute known values into the equation. * Isolate the desired variable and solve algebraically. * Finally, calculate and check if the answer makes sense contextually. In our exercise, we knew the initial and final volumes and temperatures of the gas, and we needed to find the final pressure. By following the steps, we applied the combined gas law and found the final result through systematic calculation. Practice and familiarity with these steps will strengthen your problem-solving skills.

The relationship between temperature and pressure in gases is crucial in gas law problems. According to Gay-Lussac's Law, the pressure of a gas is directly proportional to its temperature when volume is held constant: P/T = k If temperature increases, the pressure will increase, provided the volume does not change. This relationship is embedded within the combined gas law used in the exercise: (P_1 V_1)/T_1 = (P_2 V_2)/T_2 As in the exercise, understanding how changing temperature affects pressure—while also considering volume changes—is foundational for predicting gas behavior. Make sure to convert temperatures to Kelvin for accurate calculations, as Celsius does not measure absolute temperature change in the gas laws.