The level of water in a graduated cylinder is at the 100 mL mark. When a platinum crucible floats on the surface of the water, the level reads 157.9 mL. When the crucible is totally immersed in the same cylinder, the level reads 102.70 mL. What is the density of platinum? The density of water is 0.997 g/mL at 25C.

The question just asks us to describe the strategy we would use to solve the problem above.

The priciple of floation says that the mass of water displaced (in this case increased) equals to the mass of the floating object.

So the crucible weighs (157.9-100)*0.997 grams.

When the crucible is submerged (without trapping air bubbles), the increase in volume equals the volume of the crucible.

The volume of the crucible is (102.7-100) c.c.

The density at 25 degrees is therefore the weight divided by the volume.

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Well, first of all, I would say that whoever came up with this question must have been a real "water nerd." But hey, I'm here to help, so here's the strategy I would suggest:

To find the density of platinum, we need to use the principle of buoyancy. When the crucible is floating on the surface, it displaces a certain amount of water, which we can calculate by subtracting the initial level from the reading when the crucible is floating.

Then, when the crucible is totally immersed, it displaces even more water, and we can calculate this by subtracting the new level from the initial level.

The difference between these two displacements is equal to the volume of the crucible. So, we have the volume and we know the density of water. We can use this information to find the mass of the crucible.

Finally, we can use the mass of the crucible and its volume to calculate the density of platinum using the formula: density = mass/volume.

And there you have it! A strategy that will hopefully float your boat and help you find the density of platinum. Good luck!

To find the density of platinum, we can use the principle of buoyancy. The buoyant force acting on the platinum crucible when it floats is equal to the weight of the water displaced by the crucible. The difference in volume readings between when the crucible floats and when it is completely immersed in the water gives us the volume of the platinum crucible. We can then use the density formula to find the density of platinum. Here is the step-by-step strategy to solve the problem:

1. Calculate the volume of the platinum crucible:
- Subtract the initial volume reading (100 mL) from the volume reading when the crucible floats (157.9 mL). This gives us the volume of the water displaced by the crucible.

2. Calculate the mass of the water displaced by the crucible:
- Multiply the volume of water displaced by the crucible (step 1) by the density of water (0.997 g/mL). This gives us the mass of the water displaced by the crucible.

3. Calculate the volume of the platinum crucible:
- Subtract the volume reading when the crucible is completely immersed (102.70 mL) from the initial volume reading (100 mL). This gives us the volume of the platinum crucible.

4. Calculate the density of platinum:
- Divide the mass of the water displaced by the crucible (step 2) by the volume of the platinum crucible (step 3). This gives us the density of platinum.

To solve the problem, we need to find the density of platinum. We know the volume of water displaced by the platinum crucible when it floats and when it is totally immersed.

Step 1: Calculate the volume of the platinum crucible.
When the platinum crucible floats, it displaces a volume of water equal to the difference in water levels, which is 157.9 mL - 100 mL = 57.9 mL.

Step 2: Calculate the volume of water displaced when the crucible is totally immersed.
When the crucible is totally immersed, the difference in water levels is 100 mL - 102.70 mL = -2.70 mL. However, a decrease in water level means the volume of water displaced is the absolute value of the difference, so the volume is 2.70 mL.

Step 3: Calculate the volume of the platinum crucible by subtracting the volume of water displaced when it is totally immersed from the volume of water displaced when it floats.
57.9 mL - 2.70 mL = 55.2 mL.

Step 4: Calculate the mass of the platinum crucible.
We know that the density of water is 0.997 g/mL. Since the density of water is known, we can calculate the mass of the water displaced when the crucible is totally immersed:
2.70 mL * 0.997 g/mL = 2.69 g.

Step 5: Use the mass of the water displaced to calculate the mass of the platinum crucible.
Since the platinum crucible has the same volume as the water displaced, the mass of the platinum crucible is equal to the mass of the water displaced when the crucible is totally immersed:
2.69 g.

Step 6: Calculate the density of platinum.
Density is defined as mass divided by volume, so we can calculate the density of platinum using the mass of the crucible and its volume:
Density = mass/volume = 2.69 g / 55.2 mL = 0.0487 g/mL.

Therefore, the density of platinum is approximately 0.0487 g/mL.