Final answer:
Under the conditions provided, the temperature at which the gas pressure in an aerosol can will reach 5.0 atm is approximately 720.68°C, calculated using Gay-Lussac's Law.
Step-by-step explanation:
The question is asking to calculate the temperature at which the gas pressure in an aerosol can will increase from 1.5 atm to 5.0 atm, assuming the volume and the amount of gas remain constant. This situation can be approached using Gay-Lussac's Law, which states that the pressure of a gas is directly proportional to its absolute temperature, as long as the volume and the amount of gas remain constant. The formula for Gay-Lussac's Law is P1/T1 = P2/T2, where P1 and T1 are the initial pressure and temperature, and P2 and T2 are the final pressure and temperature.
Firstly, we need to convert the temperatures from Celsius to Kelvin by adding 273.15. Hence, 25°C will be 298.15 K. Using the formula:
P1/T1 = P2/T2
(1.5 atm)/(298.15 K) = (5.0 atm)/T2
Now we solve for T2:
T2 = (5.0 atm) × (298.15 K) / (1.5 atm)
T2 = 993.83 K
To find the temperature in Celsius, we subtract 273.15 from the Kelvin temperature:
Temperature in °C = 993.83 K - 273.15
= 720.68°C
Therefore, the temperature at which the gas will have a pressure of 5.0 atm is approximately 720.68°C.