To find the volume of water at 80 degrees Celsius, we can use the relationship between mass, density, and volume. The formula for density (ρ) is:
ρ = mass/volume
Given the density of water at 20°C is 998 kg/m³, and we have 2000 ml (which is equivalent to 2 kg of mass, as the density of water is approximately 1 kg/L), we can calculate the volume of this mass at 80°C where the density is 972 kg/m³.
First, we determine the mass of the water:
- Mass = Volume × Density = 2 L × 998 kg/m³ = 2 kg
Next, we use the density at 80°C to find the volume:
- Volume = Mass / Density = 2 kg / 972 kg/m³ = 0.002058 m³ = 2058 ml
So, at 80 degrees Celsius, 2000 ml of water at 20 degrees Celsius will occupy approximately 2058 ml.
Now, regarding the second part of the question:
To compare the number of water molecules in 1.0 L of water at different temperatures, we first recognize that the number of molecules is determined by the amount of substance (in moles) and is influenced by density.
At 20 degrees Celsius, the density of water is 998 kg/m³, while at 80 degrees Celsius it is 972 kg/m³. This means that 1.0 L (1000 ml) of water at 20 degrees Celsius contains more mass:
- Mass at 20°C = 1.0 L × 998 kg/m³ = 0.998 kg
- Mass at 80°C = 1.0 L × 972 kg/m³ = 0.972 kg
Since the number of molecules is proportional to the mass, 1.0 L of water at 20 degrees Celsius contains more water molecules than the same volume at 80 degrees Celsius.