The density of diamond is 3.51g/cm^3,and the density of platinum is 21.43g/cm^3.If equal masses of diamond and platinum are transferred to equal volumes of water in separate graduated cylinders,which graduated cylinder would have the greatest volume change? Explain or show with a sample calculation
They both sink because they both have density greater than water (about 1 g/cm^3)
Therefore the one with the greater volume will displace a greater volume of water.
If they have the same mass, the one with more volume will be the diamond, because it has lower density.
To determine which graduated cylinder would have the greatest volume change when equal masses of diamond and platinum are transferred to equal volumes of water, we need to compare the densities of diamond and platinum to the density of water, which is approximately 1 g/cm^3.
Let's calculate the volume change for diamond first:
Density of diamond = 3.51 g/cm^3
Mass of diamond = Mass of platinum (since equal masses are transferred)
Density = Mass / Volume
Let's assume the mass of diamond and platinum is "m" grams.
Volume of diamond = Mass of diamond / Density of diamond = m / 3.51 cm^3
Next, let's calculate the volume change for platinum:
Density of platinum = 21.43 g/cm^3
Volume of platinum = m / 21.43 cm^3
Finally, let's compare the volume change with water:
Density of water = 1 g/cm^3
Volume of water = m / 1 cm^3 = m cm^3
Now, let's compare the volume changes for both substances:
For diamond:
Volume change = Volume of diamond - Volume of water
Volume change for diamond = (m / 3.51) cm^3 - m cm^3 = m (1 - 1/3.51) cm^3
For platinum:
Volume change = Volume of platinum - Volume of water
Volume change for platinum = (m / 21.43) cm^3 - m cm^3 = m (1 - 1/21.43) cm^3
Comparing the volume changes, we find that the volume change for diamond is greater than the volume change for platinum:
Volume change for diamond = m (1 - 1/3.51) cm^3
Volume change for platinum = m (1 - 1/21.43) cm^3
Since the value of (1 - 1/3.51) is greater than (1 - 1/21.43), the graduated cylinder with the greatest volume change would be the one holding diamond.
To determine which graduated cylinder would have the greatest volume change, we need to compare the volume of water displaced by equal masses of diamond and platinum.
Given:
Density of diamond = 3.51 g/cm^3
Density of platinum = 21.43 g/cm^3
Let's assume we have 1 gram of diamond and 1 gram of platinum.
To find the volume of the water displaced by the diamond, we can use the density formula:
Density = Mass / Volume
Rearranging the formula, we have:
Volume = Mass / Density
For diamond:
Volume of water displaced by diamond = 1 g / 3.51 g/cm^3 ≈ 0.284 cm^3
Similarly, for platinum:
Volume of water displaced by platinum = 1 g / 21.43 g/cm^3 ≈ 0.047 cm^3
Based on these calculations, the volume change in the graduated cylinder containing diamond would be greater. The diamond would displace a larger volume of water compared to the platinum, as it has a lower density.