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Ch.10 - Gases
Brown - Chemistry: The Central Science 14th Edition
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Capitolo 10, Problema 39

A scuba diver's tank contains 2.50 kg of O2 compressed into a volume of 11.0 L. (b) What volume would this oxygen occupy at 25 °C and 101.33 kPa?

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Identify the given values: mass of O2 = 2.50 kg, initial volume = 11.0 L, temperature = 25 °C, and pressure = 101.33 kPa.
Convert the mass of O2 from kilograms to grams for easier calculations: 2.50 kg = 2500 g.
Calculate the number of moles of O2 using the molar mass of O2 (32.00 g/mol): \( n = \frac{\text{mass}}{\text{molar mass}} \).
Use the Ideal Gas Law to find the volume at the given conditions: \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is moles, \( R \) is the ideal gas constant (8.314 J/(mol·K)), and \( T \) is temperature in Kelvin.
Convert the temperature from Celsius to Kelvin: \( T = 25 + 273.15 \). Substitute the known values into the Ideal Gas Law equation and solve for \( V \).

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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 predict how gases behave under different conditions.
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Ideal Gas Law Formula

Molar Mass and Moles

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). To find the number of moles of a gas, you can use the formula n = mass (g) / molar mass (g/mol). In this question, knowing the molar mass of O2 (approximately 32 g/mol) is essential for converting the mass of oxygen into moles, which is necessary for applying the Ideal Gas Law.
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Molar Mass Concept

Gas Behavior under Different Conditions

Gases expand to fill their containers and their behavior can change with variations in temperature and pressure. According to the Ideal Gas Law, if the temperature increases or the pressure decreases, the volume of the gas will increase, and vice versa. Understanding how these variables interact is crucial for calculating the new volume of oxygen at the specified conditions of 25 °C and 101.33 kPa.
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Ideal Gas Conditions Example
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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?

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