An aerosol spray can with a volume of 125 mL contains 1.30 g of propane gas (C3H8) as a propellant. (c) The can's label says that exposure to temperatures above 50 °C may cause the can to burst. What is the pressure in the can at this temperature?

Verified step by step guidance

1. Convert the volume of the can from milliliters to liters by dividing by 1000, since 1 L = 1000 mL.
2. Use the molar mass of propane (C_3H_8) to convert the mass of propane from grams to moles. The molar mass of C_3H_8 is approximately 44.10 g/mol.
3. Apply the Ideal Gas Law, PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant (0.0821 L·atm/mol·K), and T is the temperature in Kelvin.
4. Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature.
5. Rearrange the Ideal Gas Law to solve for pressure (P) and substitute the known values for n, R, T, and V to find the pressure in the can.

Key Concepts

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for calculating the pressure of gases under varying conditions, allowing us to predict how changes in temperature or volume affect gas behavior.

Molar Mass and Moles

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole. To use the Ideal Gas Law, it is necessary to convert the mass of propane (1.30 g) into moles by dividing by its molar mass (44.1 g/mol), which is crucial for determining the number of moles (n) in the equation.

Gas Pressure and Temperature Relationship

According to Gay-Lussac's Law, the pressure of a gas is directly proportional to its absolute temperature when volume is held constant. This relationship is important for understanding how increasing the temperature of the aerosol can (to 50 °C) will increase the pressure inside the can, potentially leading to a burst.