Butane (C₄H₈) is an easily compressible gas used in cigarette lighters. It has a melting point of and a boiling point of - 138.4 degree Celsius and a boiling point of 0.5 degree Celsius. Would you expect a butane lighter to work in winter when the temperature outdoors is 25 degree F? Why or why not?

Verified step by step guidance

1. Convert the outdoor temperature from Fahrenheit to Celsius using the formula: $T(\text{degree}C)=\frac{5}{9}(T(\text{degree}F)-32)$.
2. Calculate the Celsius equivalent of 25°F.
3. Compare the converted temperature to the boiling point of butane, which is 0.5°C.
4. Determine if the outdoor temperature is above or below the boiling point of butane.
5. Conclude whether butane will be in the gaseous state and if the lighter will work based on the temperature comparison.

Key Concepts

Phase Changes

Phase changes refer to the transitions between solid, liquid, and gas states of matter, which are influenced by temperature and pressure. For butane, its melting point of -138.4°C indicates that it is a gas at typical outdoor temperatures, while its boiling point of 0.5°C shows that it can exist as a liquid under pressure in a lighter. Understanding these phase changes is crucial to predicting the behavior of butane in varying temperatures.

Temperature and Gas Behavior

Temperature significantly affects the behavior of gases, including their pressure and volume. According to the ideal gas law, as temperature decreases, the pressure of a gas can also decrease if the volume remains constant. In winter, when the outdoor temperature is 25°F (-3.9°C), the butane may not vaporize effectively, leading to reduced pressure in the lighter and potentially causing it to fail.

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid form. For butane, its vapor pressure at 25°F is likely lower than at higher temperatures, meaning that there may not be enough vapor to ignite. This concept is essential for understanding why a butane lighter may struggle to function in cold conditions, as the vapor pressure must be sufficient for the lighter to produce a flame.