A piece of dry ice (solid carbon dioxide) with a mass of 20.0 g isplaced in a 25.0-L vessel that already contains air at 50.66 kPaand 25 °C. After the carbon dioxide has totally sublimed, whatis the partial pressure of the resultant CO2 gas, and the totalpressure in the container at 25 °C?

Verified step by step guidance

Calculate the number of moles of CO2 using the formula: \( n = \frac{m}{M} \), where \( m \) is the mass of CO2 and \( M \) is the molar mass of CO2.

Use the ideal gas law to find the partial pressure of CO2: \( PV = nRT \). Rearrange to solve for \( P \): \( P = \frac{nRT}{V} \).

Substitute the known values into the ideal gas law equation: \( n \) from step 1, \( R = 8.314 \text{ J/(mol K)} \), \( T = 298 \text{ K} \) (since 25 °C = 298 K), and \( V = 25.0 \text{ L} \).

Calculate the partial pressure of CO2 using the values from step 3.

Add the partial pressure of CO2 to the initial pressure of the air (50.66 kPa) to find the total pressure in 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 relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for calculating the behavior of gases under various conditions, allowing us to determine the pressure exerted by the gas in the vessel after sublimation.

Partial Pressure

Partial pressure is the pressure that a single gas in a mixture would exert if it occupied the entire volume alone. According to Dalton's Law of Partial Pressures, the total pressure in a container is the sum of the partial pressures of all gases present, which is crucial for finding the total pressure after the dry ice sublimates.

Sublimation

Sublimation is the phase transition of a substance from solid to gas without passing through the liquid state. In this scenario, the dry ice (solid CO2) sublimates into gaseous CO2, contributing to the total pressure in the vessel, and understanding this process is key to solving the problem.

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