Ch.10 - Gases

Problem 41

Chapter 10, Problem 41

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

Verified step by step guidance

Identify the initial and final conditions of the system. Initially, you have solid CO2 at -100 °C, and finally, you have gaseous CO2 at 25 °C in a 5.0 L container.

Convert the mass of CO2 to moles using the molar mass of CO2 (44.01 g/mol). This will help you determine the amount of gas present.

Use the Ideal Gas Law, \( PV = nRT \), to find the pressure. Here, \( P \) is the pressure, \( V \) is the volume (5.0 L), \( n \) is the number of moles of CO2, \( R \) is the ideal gas constant (0.0821 L·atm/mol·K), and \( T \) is the temperature in Kelvin.

Convert the final temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature (25 °C).

Substitute the values for \( n \), \( V \), \( R \), and \( T \) into the Ideal Gas Law equation and solve for \( P \), the pressure inside the container.

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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 is essential for calculating the pressure of gases 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). To find the number of moles of a substance, you can use the formula n = mass (g) / molar mass (g/mol). In this question, knowing the molar mass of CO2 allows us to convert the mass of dry ice into moles, which is necessary for applying the Ideal Gas Law.

Phase Changes and Temperature Effects

Phase changes refer to the transitions between solid, liquid, and gas states of matter, which are influenced by temperature and pressure. In this scenario, solid CO2 (dry ice) sublimates directly into gas as it warms up. Understanding how temperature affects the state of a substance is crucial for predicting the behavior of CO2 in the container as it transitions from solid to gas.

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