Answer:
Step-by-step explanation:
To solve this problem, we can use the ideal gas law, which relates the pressure, volume, temperature, and number of moles of a gas:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.
First, we need to convert the initial temperature of 25 °C to Kelvin:
T1 = 25 °C + 273.15 = 298.15 K
Then, we can use the initial conditions to find the number of moles of gas:
n = PV/RT1
where we can assume that the pressure is atmospheric pressure (1 atm) and R is the ideal gas constant (0.0821 L·atm/mol·K).
n = (1 atm)(0.5 L)/(0.0821 L·atm/mol·K)(298.15 K) = 0.0204 mol
Next, we can use the final temperature of 54 °C (327.15 K) to find the final volume:
V2 = nRT2/P
V2 = (0.0204 mol)(0.0821 L·atm/mol·K)(327.15 K)/(1 atm) = 0.551 L
Finally, we can subtract the initial volume from the final volume to find the potential volume increase:
ΔV = V2 - V1 = 0.551 L - 0.5 L = 0.051 L
Therefore, if the aerosol can is heated to 54 °C, the potential volume of the gas contained in the can would increase by approximately 0.051 L. However, this increase in volume would cause a corresponding increase in pressure, which could lead to an explosion if the can is not designed to withstand the increased pressure.