Final answer:
To calculate the final pressure in the hot can, Gay-Lussac's Law P_1/T_1 = P_2/T_2 is used, converting temperatures to Kelvin and noting that the pressure of the propellant gas increases with temperature. If the can's initial pressure is 1344 torr at 23 °C, the final pressure can be calculated for the increased temperature of 475 °C.
Step-by-step explanation:
The question involves the application of one of the gas laws, specifically Gay-Lussac's Law, which describes how the pressure of a gas tends to increase as the temperature increases, provided that the volume remains constant. To find the pressure of the propellant gas in the spray can at a higher temperature, we can use the formula P_1/T_1 = P_2/T_2, where P represents pressure and T represents temperature in Kelvin. Given that the initial pressure (P_1) is 1344 torr at 23 °C (which is 296 K), we need to convert the final temperature (475 °C) to Kelvin, which is 748 K. Therefore, the calculation would be P_2 = (P_1 × T_2) / T_1 = (1344 torr × 748 K) / 296 K.
By solving this, we get the final pressure P_2, which tells us how much the pressure will increase in the hot can. It is crucial to remember that such an increase in pressure can be dangerous, which is why aerosol cans come with warnings not to expose them to high temperatures or incinerate them.