An 11.5 -mL sample of liquid butane (density =0.573 g / mL ) is evaporated in an otherwise empty

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An 11.5 -mL sample of liquid butane (density =0.573 g / mL )...

An 11.5 -mL sample of liquid butane (density $=0.573 \mathrm{g} / \mathrm{mL}$ ) is evaporated in an otherwise empty container at a temperature of $28.5^{\circ} \mathrm{C}$ . The pressure in the container following evaporation is 892 torr. What is the volume of the container?

Key Concepts

Density and Mass-Volume Conversion

Density relates the mass of a substance to its volume and is a key property used to determine the mass of a liquid or solid when the volume is known. This concept is foundational in converting measured volumes into masses, which can then be used in further calculations such as determining the number of moles of a substance.

Mole Concept and Molar Mass

The mole is a unit that quantifies the amount of a substance by relating its mass to the number of particles, using the molar mass for conversion. This concept is crucial for chemical calculations, as it allows the conversion from mass to the number of moles, which is a central step in applying gas laws to quantify gaseous behavior.

Ideal Gas Law

The ideal gas law, expressed as PV = nRT, connects a gas's pressure, volume, number of moles, the gas constant, and temperature. This relationship is essential for predicting the behavior of gases under various conditions, and is widely used to determine unknown variables when the others are known. It serves as a primary tool in solving problems involving gaseous states resulting from the evaporation of a liquid.

Unit Conversions

Proper unit conversions ensure consistency in equations, particularly when working with the ideal gas law. Converting pressure units (e.g., torr to atmospheres) and temperature from Celsius to Kelvin is critical for maintaining the integrity of the calculations, as the gas constant is defined with specific units that require such standardization.

Phase Change and Vaporization

The process of vaporization involves the transition of a substance from its liquid phase to its gaseous phase. Understanding this phase change is important because it justifies using the ideal gas law, as the substance, once evaporated, behaves like a gas and follows the predictable relationships defined by gas laws.

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