Final answer:
The warning label on LP-gas cylinders is for safety, as the flammable gas inside can expand and potentially explode at high temperatures. By using the ideal gas law, it is calculated that if the cylinder's temperature rises to 50 °C, the new pressure would be approximately 391.5 kPa.
Step-by-step explanation:
The warning to store LP-gas cylinders at temperatures below 120 °F (48.8 °C) and not to incinerate is due to safety concerns. LP-gas cylinders contain flammable gases which can expand with temperature and, if exposed to excessive heat or open flame, could cause the cylinder to rupture or explode due to the rapid pressure increase.
To calculate the new pressure when the temperature rises to 50 °C, we can use the ideal gas law, which relates pressure, volume, and temperature of an ideal gas in a closed system. Assuming the volume is constant (350 mL) and there is no gas leakage, we can use the formula ΔP=ΔT · (P1/T1); where ΔP is the pressure change, ΔT is the temperature change in Kelvin, P1 is the initial pressure, and T1 is the initial temperature in Kelvin.
Firstly, convert the initial and final temperatures to Kelvin:
- Initial: 24 °C + 273.15 = 297.15 K
- Final: 50 °C + 273.15 = 323.15 K
Using the formula mentioned:
ΔT = 323.15 K - 297.15 K = 26 K
ΔP = 26 K · (360 kPa / 297.15 K)
ΔP = 360 kPa · (26 K / 297.15 K)
ΔP = 360 kPa · 0.0875 = 31.5 kPa (approximately)
Thus, the new pressure, P2, is the initial pressure plus the change in pressure:
P2 = P1 + ΔP = 360 kPa + 31.5 kPa = 391.5 kPa