In a room at 24.5 ^∘ C, a balloon is filled with helium gas...

In a room at $24.5{ }^{\circ} \mathrm{C}$, a balloon is filled with helium gas until the pressure inside the balloon is $768.0 \mathrm{~mm} \mathrm{Hg}$. What is the density of the gas in grams per liter and in grams per milliliter?

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Key Concepts

Unit Conversions

Consistent unit conversion is crucial in gas law calculations. Pressure, volume, temperature, and the gas constant must all be in compatible units, which often involves converting temperature from Celsius to Kelvin and pressure from mm Hg or other units to a standard pressure unit like atmospheres or Pascals.

Molar Mass

Molar mass is the mass of one mole of a substance and is a key parameter in connecting the microscopic scale (number of molecules) to macroscopic properties like density. In gas law calculations, the molar mass is used to convert between moles of gas and its corresponding mass.

Ideal Gas Law

The Ideal Gas Law (PV = nRT) is a foundational equation in thermodynamics that relates the pressure, volume, temperature, and number of moles of a gas. This law is extensively used to predict the behavior of gases under different conditions and to derive other important properties, such as density and molar volume.

Gas Density

Gas density is defined as the mass per unit volume of a gas. By combining the ideal gas law with the definition of density, one can derive an expression that relates density to pressure, molar mass, temperature, and the gas constant. This approach is frequently used in problems involving the properties of gases in various environmental conditions.

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