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When we talk about the specific volume on a mass basis, we're referring to how much volume a certain mass of a substance occupies. It's calculated by dividing the volume of the substance by its mass. This concept is particularly useful when you need to assess how much space a material or gas occupies per unit of mass.

• Formula: The specific volume on a mass basis is expressed as \( v = \frac{V}{m} \).
• Units: In the provided exercise, the specific volume is expressed in \( \text{m}^3/\text{kg} \).

To calculate this, you need to know both the total volume and the mass of the substance. Once you have these values, simply divide the volume by the mass. This will help you understand the space efficiency of the material by kilogram.
In our example, with 500 liters converted to 0.5 cubic meters and a mass of 1 kg, the specific volume is found to be 0.5 \( \text{m}^3/\text{kg} \). This tells us for every kilogram of diatomic oxygen, half a cubic meter is occupied.

Specific volume on a mole basis deals with how much volume is occupied by one mole of a substance. This is primarily used in chemistry to understand gases and reactions at a molecular level.

• Formula: It is expressed as \( \bar{v} = \frac{V}{n} \).
• Units: In the given problem, it is in \( \text{m}^3/\text{mol} \).

This concept helps in understanding how a volume changes with the number of moles, which is significant in reactions and stoichiometry.
The given exercise presents a specific volume on a mole basis as approximately 0.016 \( \text{m}^3/\text{mol} \), indicating that each mole of diatomic oxygen takes up about 0.016 cubic meters. This is valuable for visualizing how tightly or loosely a substance/molecules pack under certain conditions.

Molar mass is the mass of a given substance divided by the amount of substance, measured in moles. It is an essential concept in chemistry because it relates the mass of a substance to the number of moles.

• Definition: Molar mass \( M \) is typically expressed in \( \text{g/mol} \).

For practical purposes, the molar mass enables conversions between the mass and the number of molecules in a sample.
In our problem with diatomic oxygen, the molar mass is 32 g/mol. This value is crucial for determining the number of moles from a given mass, like when converting 1000 g of oxygen to 31.25 moles. This conversion is a pivotal step in finding the specific volume on either a mass or mole basis.

The number of moles represents how many moles of a substance are present in a given sample. It connects physical mass to a chemical amount of substance.

• Formula: It is determined by \( n = \frac{m}{M} \), where \( m \) is mass and \( M \) is molar mass.
• Usage: It's vital for stoichiometry, chemical equations, and understanding molecular interactions.

By knowing a material's molar mass and its mass, you can easily find the number of moles. This is key in chemical equations and calculations. In the exercise, with 1000 grams of oxygen and a molar mass of 32 g/mol, the number of moles is 31.25. Recognizing the amount in moles helps in figuring out how much space the substance will take, which then aids in calculating specific volume on the mole basis.