The density of diamond is 3.51 g/cm3 and the density of lead is 11.3 g/cm3. If equal masses of diamond and lead are transferred to equal volumes of water in separate graduated cylinders, which graduated cylinder would have the greatest volume change?
Pick a mass, any mass you choose. Then
mass = volume x density and rearrange to
volume = mass/density
volume = substitute mass and density and see which has the larger volume.
the graduated cylinder with the diamond would have the highest volume reading because its low density would have to account for greater volume
To determine which graduated cylinder would have the greatest volume change when equal masses of diamond and lead are transferred to equal volumes of water, we need to compare the density of the substances with the density of water.
Density is defined as the mass per unit volume. In this case, we can use the formula:
Density = Mass / Volume
Let's start by calculating the volume change for each substance.
For diamond:
Given density of diamond = 3.51 g/cm³
Equal mass is transferred, so let's assume the mass is 1 gram.
Using the formula Density = Mass / Volume, we can rearrange it to calculate the volume:
Volume = Mass / Density
Volume of diamond = 1 gram / 3.51 g/cm³ ≈ 0.284 cm³
For lead:
Given density of lead = 11.3 g/cm³
Equal mass is transferred, so let's assume the mass is also 1 gram.
Using the formula Density = Mass / Volume, we can rearrange it to calculate the volume:
Volume = Mass / Density
Volume of lead = 1 gram / 11.3 g/cm³ ≈ 0.0885 cm³
Now, let's compare the volume changes for diamond and lead when transferred to equal volumes of water.
Since the mass transferred for both substances is equal (1 gram), the volume change would be equal to the initial volume of the substance (diamond or lead) minus the volume of water displaced.
Let's assume the initial volume of water is 100 cm³.
For diamond:
Volume change = Initial volume of diamond - Volume of water displaced
= 0.284 cm³ - 100 cm³
= -99.716 cm³
For lead:
Volume change = Initial volume of lead - Volume of water displaced
= 0.0885 cm³ - 100 cm³
= -99.9115 cm³
Comparing the volume changes, we can see that the volume change for diamond is -99.716 cm³, while the volume change for lead is -99.9115 cm³.
In this case, the cylinder with lead would have the greatest volume change, as the magnitude of -99.9115 is larger than -99.716. However, it is important to note that both substances cause a decrease in volume when transferred to water.