An aerosol spray can with a volume of 250 mL contains 2.30 g of propane gas (C3H8) as a propellant. a. If the can is at 23°C, what is the pressure in the can?

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Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature. This is necessary because the gas law equations require temperature in Kelvin.

Use the ideal gas law equation, which is PV = nRT. Here, P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant (0.0821 L atm K^{-1} mol^{-1}), and T is the temperature in Kelvin.

Calculate the number of moles of propane (C3H8) by using the molar mass of propane. The molar mass of C3H8 is approximately 44.1 g/mol. Divide the mass of propane given in the problem by its molar mass to find the number of moles.

Substitute the values for n, R, T, and V into the ideal gas law equation to solve for P. Make sure the units are consistent: volume in liters, temperature in Kelvin, and the number of moles as calculated.

Solve for P, the pressure in the can, using the rearranged ideal gas law equation P = \frac{nRT}{V}. This will give you the pressure in atmospheres.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

Molar Mass

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 can be calculated by summing the atomic masses of its constituent elements: carbon (C) and hydrogen (H). Knowing the molar mass is essential for converting grams of a substance to moles, which is necessary for applying the Ideal Gas Law.

Gas Pressure

Gas pressure is the force exerted by gas molecules colliding with the walls of their container. It is typically measured in atmospheres (atm), pascals (Pa), or mmHg. In the context of the aerosol can, understanding how temperature and the number of gas molecules affect pressure is crucial, as higher temperatures or more gas will increase the pressure inside the can according to the Ideal Gas Law.

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