Ch.10 - Gases

Brown - Chemistry: The Central Science 14th Edition

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Brown 14th Edition

Ch.10 - Gases

Problem 40a

Chapter 10, Problem 40a

An aerosol spray can with a volume of 125 mL contains 1.30 g of propane gas (C3H8) as a propellant. (a) If the can is at 25 °C, what is the pressure in the can?

Verified step by step guidance

The volume of the can is 125 mL, which needs to be converted to liters for use in the ideal gas law. The mass of propane is 1.30 g, and the temperature is 25 °C, which needs to be converted to Kelvin.

Convert the volume from mL to L by dividing by 1000. Convert the temperature from Celsius to Kelvin by adding 273.15. Calculate the number of moles of propane using its molar mass (C3H8).

The ideal gas law is given by 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 temperature in Kelvin.

Rearrange the equation to P = (nRT)/V. Substitute the values for n, R, T, and V into the equation.

Perform the calculation to find the pressure in the can, ensuring all units are consistent. The result will be in atmospheres (atm).

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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 units such as atmospheres (atm) or pascals (Pa). In the context of the aerosol can, understanding how temperature and the number of gas molecules affect pressure is crucial for determining the pressure inside the can using the Ideal Gas Law.

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