A piece of dry ice (solid carbon dioxide) with a mass of 22.1 g sublimes (converts from solid to gas) into a large balloon. Assuming that all of the carbon dioxide ends up in the balloon, what is the volume of the balloon at and a pressure of 742 mmHg?

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Identify the given values: mass of CO2 = 22.1 g, pressure = 742 mmHg, temperature = 25°C (which is 298 K).

Convert the mass of CO2 to moles using the molar mass of CO2 (44.01 g/mol).

Use the ideal gas law equation, PV = nRT, to solve for the volume V. Here, P is the pressure in atm, n is the number of moles, R is the ideal gas constant (0.0821 L·atm/mol·K), and T is the temperature in Kelvin.

Convert the pressure from mmHg to atm by dividing by 760 mmHg/atm.

Substitute the values of n, R, T, and P into the ideal gas law equation to solve for V, the volume of the balloon.

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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 volume of a gas when the amount of substance and conditions are known.

Molar Mass of Carbon Dioxide

The molar mass of carbon dioxide (CO2) is essential for converting the mass of dry ice into moles. The molar mass is calculated by adding the atomic masses of its constituent elements: carbon (12.01 g/mol) and oxygen (16.00 g/mol). Since CO2 has one carbon atom and two oxygen atoms, its molar mass is approximately 44.01 g/mol, which is used to determine the number of moles from the given mass.

Gas Volume and Pressure Relationship

The relationship between gas volume and pressure is described by Boyle's Law, which states that at constant temperature, the volume of a gas is inversely proportional to its pressure. This means that if the pressure increases, the volume decreases, and vice versa. Understanding this relationship is crucial for calculating the volume of the balloon when the pressure of the gas is provided.

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Relationship of Volume and Moles Example

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