Final answer:
To find the Celsius temperature of 212 moles of an ideal gas in a 2.75 L container at 5.86 kPa, use the ideal gas law, converting pressure to atm, rearranging the equation, and then converting Kelvin to Celsius.
Step-by-step explanation:
To determine the temperature in Celsius of 212 moles of an ideal gas in a 2.75 L container at 5.86 kPa, apply the ideal gas law, PV = nRT. Begin by converting the pressure to atmospheres by dividing it by 101.325 kPa/atm.
Rearrange the ideal gas law to isolate temperature (T), yielding T = PV / (nR).
Subsequently, substitute the provided values for pressure (P), volume (V), moles (n), and the gas constant (R) into the equation.
Given the pressure in atmospheres, volume in liters, and moles, use the universal gas constant, R = 0.0821 L·atm/(mol·K). Solve for temperature in Kelvin.
Lastly, convert the obtained temperature from Kelvin to Celsius by subtracting 273.15.
Following these steps will yield the temperature in Celsius for 212 moles of the ideal gas within a 2.75 L container at 5.86 kPa.