Ch.10 - Gases

Brown - Chemistry: The Central Science 14th Edition

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Brown 14th Edition

Ch.10 - Gases

Problem 39

Chapter 10, Problem 39

A scuba diver's tank contains 2.50 kg of O2 compressed intoa volume of 11.0 L. (b) What volume would this oxygen occupy at25 °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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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 predict how gases behave under different conditions.

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.

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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Textbook Question

(b) The adult blue whale has a lung capacity of 5.0 * 103 L. Calculate the mass of air (assume an average molar mass of 28.98 g>mol) contained in an adult blue whale's lungs at 0.0 °C and 101.33 kPa, assuming the air behaves ideally.

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Textbook Question

(b) Carbon dioxide makes up approximately 0.04% of Earth's atmosphere. If you collect a 2.0-L sample from the atmosphere at sea level (101.33 kPa) on a warm day 127 °C2, how many CO2 molecules are in your sample?

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Textbook Question

Chlorine is widely used to purify municipal water supplies and to treat swimming pool waters. Suppose that the volume of a particular sample of Cl₂ gas is 8.70 L at 119.3 kPa and 24 °C. (b) What volume will the Cl₂occupy at STP?

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Textbook Question

(a) If the pressure exerted by ozone, O3, in the stratosphere is 304 Pa and the temperature is 250 K, how many ozone molecules are in a liter?

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Textbook Question

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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Textbook Question

A 50.0 g sample of solid CO2 (dry ice) is added at -100 °C toan evacuated (all of the gas removed) container with a volumeof 5.0 L. If the container is sealed and then allowed to warmto room temperature 125 °C2 so that the entire solid CO2 isconverted to a gas, what is the pressure inside the container?

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