Final answer:
By converting the given temperatures to Kelvin and using Gay-Lussac's Law, it's calculated that the final pressure of the gas at 27°C is 4.2 atm when the initial pressure is 7 atm at 227°C and volume and amount of gas remain constant.
Step-by-step explanation:
The student's question concerns the change in pressure of a gas due to a temperature change, keeping the volume and amount of gas constant. This falls into the realm of Chemistry, specifically into gas laws, and is typically covered in high school. To calculate the final pressure of a gas after a temperature change, you can use Gay-Lussac's Law, which is P1/T1 = P2/T2, where P is pressure and T is the temperature in Kelvin.
First, we must convert the temperatures from Celsius to Kelvin, which is done by adding 273 to the Celsius temperature. Thus, the initial temperature, 227°C, becomes 227 + 273 = 500 K, and the final temperature, 27°C, becomes 27 + 273 = 300 K.
Next, we use the initial conditions to find the final pressure: P2 = P1 * (T2/T1), where P1 is 7 atm, T1 is 500 K, and T2 is 300 K. Substituting the values we get P2 = 7 atm * (300 K / 500 K) = 4.2 atm. Thus, the final pressure of the gas at 27°C is 4.2 atm.