The density of diamond is 3.51 g/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.
if the masses are equal, the diamond has more volume because it is less dense.
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 calculate the volume change for each material.
The volume change can be determined using the density formula:
Density = Mass / Volume
For diamond, the given density is 3.51 g/cm^3. Let's assume the mass of the diamond transferred to the water is 'm' grams, and the change in volume is 'V' cm^3.
Using the density formula for diamond, we have:
3.51 g/cm^3 = m g / V cm^3
Rearranging the equation to solve for V:
V cm^3 = m g / (3.51 g/cm^3)
V cm^3 = m / 3.51
Now let's calculate the equivalent volume change for the platinum. The given density of platinum is 21.43 g/cm^3. Using the same mass 'm' and volume change 'V' as before, we have:
21.43 g/cm^3 = m g / V cm^3
Rearranging the equation to solve for V:
V cm^3 = m g / (21.43 g/cm^3)
V cm^3 = m / 21.43
Comparing the two equations, we can see that the volume change for diamond (V = m / 3.51) would be greater than the volume change for platinum (V = m / 21.43) because the density of diamond is lower than that of platinum.
Therefore, the graduated cylinder with the diamond would have the greatest volume change when equal masses of diamond and platinum are transferred to equal volumes of water.
To determine which graduated cylinder would have the greatest volume change, we need to compare the density of each substance with the density of water.
The density of water is approximately 1 g/cm^3.
Let's calculate the volume change for diamond first:
Given that the density of diamond is 3.51 g/cm^3 and its mass is equal to the mass of platinum, we can assume that the volume of diamond is also equal to the volume of platinum.
Let's assume the mass of both diamond and platinum is 100 g.
So, the volume of diamond is:
Volume = mass / density = 100 g / 3.51 g/cm^3 ≈ 28.49 cm^3
Next, let's calculate the volume change for platinum:
Given that the density of platinum is 21.43 g/cm^3 and the mass is 100 g (equal to the mass of diamond), we can use the same formula to find the volume.
Volume = mass / density = 100 g / 21.43 g/cm^3 ≈ 4.67 cm^3
Comparing the two calculated volumes, we can see that the volume change for diamond is greater than the volume change for platinum.
Therefore, if equal masses of diamond and platinum are transferred to equal volumes of water in separate graduated cylinders, the graduated cylinder containing diamond will have the greatest volume change.