This question is also confusing me…
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.
Thank you so much…last question promise!
The problem says equal masses so make up a number, say 10 grams.
Then mass = volume x density or
v = mass/density. Using the 10 g and density of each, calculate volume of each.
That will be the volume occupied by the 10 g sample of each. The largest volume will displace the most water from a graduated cylinder.
To determine which graduated cylinder would have the greatest volume change, we need to compare the volumes of water displaced by the equal masses of diamond and platinum.
Here's a step-by-step calculation to help explain the answer:
1. Let's assume we have an equal mass of each substance, say 10 grams.
2. First, we need to determine the volume of the diamond and platinum using their respective densities.
- For diamond, the density is 3.51 g/cm³. So, the volume of diamond can be calculated as:
Volume of diamond = Mass of diamond / Density of diamond
= 10 g / 3.51 g/cm³
≈ 2.85 cm³
- For platinum, the density is 21.43 g/cm³. So, the volume of platinum can be calculated as:
Volume of platinum = Mass of platinum / Density of platinum
= 10 g / 21.43 g/cm³
≈ 0.47 cm³
3. Now, let's compare the volume change by subtracting the initial volume of water in the graduated cylinders from the calculated volumes of the substances.
- For diamond: Volume change = Volume of water displaced - Initial volume of water
= 2.85 cm³ - Initial volume of water
- For platinum: Volume change = Volume of water displaced - Initial volume of water
= 0.47 cm³ - Initial volume of water
4. Comparing the Volume Changes:
- Since the volume of diamond (2.85 cm³) is greater than the volume of platinum (0.47 cm³), the graduated cylinder with the diamond would have a greater volume change.
In conclusion, the graduated cylinder with the diamond would have the greatest volume change when equal masses of diamond and platinum are transferred to separate graduated cylinders of water.
To determine which graduated cylinder would have the greatest volume change when equal masses of diamond and platinum are transferred, we need to compare the volume of water displaced by each substance.
Density is defined as mass divided by volume. So, we can rearrange this equation to solve for volume:
Volume = Mass / Density
For the diamond:
Given density = 3.51 g/cm^3
Equal masses of diamond and platinum are transferred, so let's assume the mass is M.
Volume of water displaced by diamond = M / (3.51 g/cm^3)
For the platinum:
Given density = 21.43 g/cm^3
Equal masses of diamond and platinum are transferred, so the mass is still M.
Volume of water displaced by platinum = M / (21.43 g/cm^3)
To compare the volume changes, we need to determine the ratio of the volume of water displaced by platinum to the volume of water displaced by diamond:
Volume ratio = (M / (21.43 g/cm^3)) / (M / (3.51 g/cm^3))
= (M * (3.51 g/cm^3)) / (M * (21.43 g/cm^3))
= 3.51 g/cm^3 / 21.43 g/cm^3
= 0.164
Therefore, the volume ratio is approximately 0.164.
This means that the volume change of the graduated cylinder containing platinum would be approximately 0.164 times the volume change of the graduated cylinder containing diamond.
Since the density of platinum is significantly greater than the density of diamond, the volume change of the graduated cylinder containing platinum will be smaller than the volume change of the graduated cylinder containing diamond.