An aerosol spray can with a volume of 250 mL contains 2.30 g of propane gas (C3H8) as a propellant. c. The can’s label says that exposure to temperatures above 130°F may cause the can to burst. What is the pressure in the can at this temperature?

검증된 단계별 안내

Step 1: Convert the temperature from Fahrenheit to Kelvin. The formula to convert Fahrenheit to Kelvin is K = (F - 32) * 5/9 + 273.15.

Step 2: Convert the mass of propane gas into moles. The molar mass of propane (C3H8) is approximately 44.1 g/mol. Use the formula n = m/M, where n is the number of moles, m is the mass and M is the molar mass.

Step 3: Convert the volume of the aerosol can from milliliters to liters. 1 L = 1000 mL.

Step 4: Use the ideal gas law equation, P = nRT/V, to calculate the pressure. In this equation, P is the pressure, n is the number of moles, R is the ideal gas constant (0.0821 L·atm/(K·mol) for this problem), T is the temperature in Kelvin, and V is the volume in liters.

Step 5: Plug in the values obtained from the previous steps into the ideal gas law equation to calculate the pressure. Remember, the pressure will be in atmospheres (atm) because of the units of the gas constant we used.

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주요 개념

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Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. This law allows us to calculate the pressure of a gas when its volume, temperature, and amount are known.

Conversion of Temperature

In gas law calculations, temperature must be expressed in Kelvin rather than Celsius or Fahrenheit. To convert Fahrenheit to Kelvin, use the formula K = (°F - 32) × 5/9 + 273.15. This conversion is crucial because the gas laws are derived based on absolute temperature, ensuring accurate calculations of gas behavior under varying conditions.

Molar Mass and Moles

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For propane (C3H8), the molar mass is approximately 44.1 g/mol. To find the number of moles of propane in the aerosol can, divide the mass of propane by its molar mass. This value is essential for applying the Ideal Gas Law to determine the pressure in the can.