1.4 Density (3)
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1.
Define density in terms of mass and volume. State the formula relating density (ρ), mass (m), and volume (V).
Definition: Density is defined as the mass of an object divided by its volume.
Formula: ρ = m / V, where:
- ρ (rho) represents density (units: kg/m³ or g/cm³)
- m represents mass (units: kg or g)
- V represents volume (units: m³ or cm³)
2.
Question 2
A student uses a graduated cylinder to determine the volume of an irregularly shaped stone. They initially fill the cylinder with 25.0 cm³ of water. When the stone is added, the water level rises to 32.5 cm³. The mass of the stone is 65.0 g. Calculate the density of the stone.
1. Calculate the volume of the stone:
Volume of stone = Final volume - Initial volume = 32.5 cm³ - 25.0 cm³ = 7.5 cm³
2. Calculate the density of the stone:
Density = Mass / Volume = 65.0 g / 7.5 cm³ = 8.67 g/cm³ (rounded to two significant figures)
| Volume of water displaced: 7.5 cm³ |
3.
Question 1
Describe how to determine the density of a liquid, a regularly shaped solid and an irregularly shaped solid which sinks in a liquid, using the method of volume by displacement. Include appropriate calculations.
Determining the Density of a Liquid:
- Measure the mass of the liquid using a balance. Record this as 'm'.
- Measure the volume of the container used to hold the liquid. This can be done using a graduated cylinder. Record this as 'V'.
- Calculate the density using the formula: Density = Mass / Volume (ρ = m/V). Ensure the units are consistent (e.g., g/cm³).
Determining the Density of a Regularly Shaped Solid:
- Measure the mass of the solid using a balance. Record this as 'm'.
- Use calipers or a ruler to accurately measure the dimensions of the solid (length, width, height).
- Calculate the volume of the solid using the appropriate formula for its shape (e.g., Volume of a cube = lwh, Volume of a cuboid = lwh). Record this as 'V'.
- Calculate the density using the formula: Density = Mass / Volume (ρ = m/V). Ensure the units are consistent (e.g., g/cm³).
Determining the Density of an Irregularly Shaped Solid (Volume by Displacement):
- Fill a graduated cylinder partially with a known volume of liquid (e.g., water). Record this initial volume as 'V1'.
- Carefully lower the solid into the graduated cylinder, ensuring it is fully submerged and does not touch the sides.
- Record the new volume of the liquid in the cylinder as 'V2'.
- Calculate the volume of the solid by subtracting the initial volume from the final volume: Volume of solid = V2 - V1.
- Measure the mass of the solid using a balance. Record this as 'm'.
- Calculate the density using the formula: Density = Mass / Volume (ρ = m/V). Ensure the units are consistent (e.g., g/cm³).