i have no idea how to set this problem up! please help!
A 22.19-g sample of a solid is placed in a flask. Toluene, in which the solid is insoluble, is added to the flask so that the total volume of solid and liquid together is 50.0 mL. The solid and toluene together weigh 47.27 g. The density of toluene at the temperature of the experiment is 0.864 g/mL. What is the density of the solid?
total mass: 47.27g
solid mass: 22.19g
so, toluene mass: 25.08g
toluene density is .864g/ml, so toluene volume: 25.08g / 0.864g/ml = 29.03ml
so, solid volume: 20.97ml
solid density: 22.19g/20.97ml = 1.058g/ml
To find the density of the solid, we need to determine its mass and volume. Here is how to set up the problem:
1. Write down the given information:
- Mass of the solid sample = 22.19 g
- Total mass of solid and toluene = 47.27 g
- Volume of solid and toluene mixture = 50.0 mL
- Density of toluene = 0.864 g/mL
2. Determine the mass of toluene:
- Mass of toluene = Total mass of solid and toluene - Mass of solid sample
- Mass of toluene = 47.27 g - 22.19 g
- Mass of toluene = 25.08 g
3. Calculate the volume of toluene:
- Volume of toluene = Volume of solid and toluene mixture - Volume of solid
- Volume of toluene = 50.0 mL - 0 mL (Since the solid is insoluble in toluene)
- Volume of toluene = 50.0 mL
4. Use the formula for density:
- Density = Mass / Volume
- Density of solid sample = Mass of solid sample / Volume of solid sample
- Density of toluene = Mass of toluene / Volume of toluene
5. Plug in the values:
- Density of solid sample = 22.19 g / 0 mL (Since the solid has no volume)
- Density of toluene = 25.08 g / 50.0 mL
6. Simplify the equations:
- Density of solid sample = Undefined (Since the solid has no volume)
- Density of toluene = 25.08 g / 50.0 mL
- Density of toluene = 0.5016 g/mL
Therefore, the density of the solid sample is undefined, while the density of toluene is 0.5016 g/mL.