The ideal gas law is a fundamental equation in chemistry that relates pressure (P), volume (V), temperature (T), and the number of moles (n) of a gas through the equation PV = nRT, where R is the ideal gas constant. In practical applications, such as determining how changes in volume affect temperature at constant pressure, we can derive a simplified formula.

In a scenario where a sample of sulfur hexachloride gas occupies 8.30 liters at 202 degrees Celsius, and we want to find the temperature required to reduce the volume to 5.25 liters while keeping pressure constant, we can follow a systematic approach. First, we identify the variables involved: the initial volume (V₁ = 8.30 L), the initial temperature (T₁ = 202 °C), and the final volume (V₂ = 5.25 L). The final temperature (T₂) is what we need to determine.

Since pressure is constant, we can use the relationship derived from the ideal gas law, which simplifies to V₁/T₁ = V₂/T₂. To solve for T₂, we rearrange the equation to T₂ = (V₂ * T₁) / V₁.

Before performing calculations, it is crucial to convert temperatures to Kelvin, as the ideal gas law requires absolute temperature. The conversion from Celsius to Kelvin is done by adding 273.15. Thus, T₁ becomes 202 + 273.15 = 475.15 K.

Substituting the known values into the rearranged equation gives us:

T₂ = (5.25 L * 475.15 K) / 8.30 L

Calculating this yields T₂ = 300.55 K. Finally, to convert back to degrees Celsius, we subtract 273.15, resulting in T₂ = 27.40 °C.

In summary, when working with the ideal gas law, always ensure to convert temperatures to Kelvin during calculations, and only focus on the variables that change while keeping constants in mind. This methodical approach will help in solving various problems related to gas laws effectively.