Question

Find the density of a given molecule (solid state).

Answer 1

To find the density of a solid-state molecule:

Density (\( \rho \)) is a physical property that describes how much mass is packed into a given volume. To calculate the density of a solid-state molecule, you need to know two key pieces of information:

• The molecular weight of the molecule.
• The volume of the solid-state molecule.

Density formula:

The density (\( \rho \)) of a substance is defined as its mass (\( m \)) divided by its volume (\( V \)), which is expressed mathematically as:

\( \rho = \frac{m}{V} \)

Step 1: Measure or obtain the mass of the molecule.
The mass can be determined in two ways:

• By directly weighing the sample using a balance or scale.
• By calculating the mass from the molecular weight (if you know the number of molecules in the sample). The molecular weight gives you the mass of a single molecule, and by multiplying it by the number of molecules present, you can find the total mass.

Step 2: Measure or obtain the volume of the solid-state molecule.
The volume of the molecule can be determined using different methods:

• By measuring the volume directly using displacement techniques (such as water displacement for small solid objects).
• If the molecule is a regular solid (e.g., a cube or sphere), its dimensions can be used to calculate the volume (e.g., using the formula \( V = l^3 \) for a cube or \( V = \frac{4}{3} \pi r^3 \) for a sphere, where \( l \) is the side length and \( r \) is the radius).

Step 3: Ensure consistent units.
Before calculating the density, make sure that the units for mass and volume are consistent. Typically, mass is measured in grams (g) and volume in cubic centimeters (cm³) for solid-state molecules, but you should adjust the units if necessary (e.g., kg for mass and m³ for volume in SI units).

Step 4: Calculate the density.
Once you have the mass and volume, you can calculate the density using the formula:

\( \rho = \frac{m}{V} \)

For example, if the mass of the molecule is 10 grams and its volume is 5 cm³, the density would be:

\( \rho = \frac{10 \, \text{g}}{5 \, \text{cm}^3} = 2 \, \text{g/cm}^3 \)

Note: If you have a specific molecular weight and volume for the solid-state molecule you're interested in, feel free to provide those values, and I can help you with the detailed calculation of its density.