A graduated cylinder has a mass of 80.4 g when empty. When 20.0 mL of water is added, the graduated cylinder has a mass of 100.4 g. If a stone is added to the graduated cylinder, the water level rises to 43.5 mL and the total mass is now 156.1 g. What is the density of the stone?
2.36
To find the density of the stone, we can use the formula:
Density = Mass / Volume
Step 1: Calculate the mass of the water.
The mass of the water can be found by subtracting the mass of the empty cylinder from the mass of the cylinder with water.
Mass of water = Mass of cylinder with water - Mass of empty cylinder
Mass of water = 100.4 g - 80.4 g
Mass of water = 20.0 g
Step 2: Calculate the volume of the stone.
The volume of the stone can be found by subtracting the initial volume of water (20.0 mL) from the final volume of water with the stone (43.5 mL).
Volume of stone = Final volume - Initial volume
Volume of stone = 43.5 mL - 20.0 mL
Volume of stone = 23.5 mL
Step 3: Convert the volume of the stone to cubic centimeters (cm³).
Since density is typically measured in g/cm³, we need to convert the volume of the stone to cubic centimeters.
1 mL is equal to 1 cm³, so the volume of the stone is already in cm³.
Volume of stone = 23.5 cm³
Step 4: Calculate the density of the stone.
Density = Mass / Volume
Density = 156.1 g / 23.5 cm³
Therefore, the density of the stone is approximately 6.65 g/cm³.
To find the density of the stone, we need to consider the change in mass and volume of the water when the stone is added to the graduated cylinder.
First, let's calculate the mass of the water.
The mass of the graduated cylinder when empty is 80.4 g. When 20.0 mL of water is added, the mass increases to 100.4 g. Therefore, the mass of the water can be calculated by subtracting the mass of the empty graduated cylinder from the mass of the graduated cylinder with water:
Mass of water = Mass of graduated cylinder with water - Mass of empty graduated cylinder
= 100.4 g - 80.4 g
= 20.0 g
Now, let's calculate the mass of the stone.
When the stone is added to the graduated cylinder, the total mass increases to 156.1 g. Therefore, the mass of the stone can be calculated by subtracting the mass of the empty graduated cylinder and the mass of the water from the total mass:
Mass of stone = Total mass - Mass of empty graduated cylinder - Mass of water
= 156.1 g - 80.4 g - 20.0 g
= 55.7 g
Next, let's find the volume of the stone.
The volume of the stone can be calculated by finding the difference in volume of the water before and after the stone is added. The water level rises from 20.0 mL to 43.5 mL, so the volume occupied by the stone is the difference:
Volume of stone = Final volume of water - Initial volume of water
= 43.5 mL - 20.0 mL
= 23.5 mL
Finally, we can use the formula for density to find the density of the stone:
Density = Mass of stone / Volume of stone
= 55.7 g / 23.5 mL
= 2.37 g/mL
Therefore, the density of the stone is 2.37 g/mL.
mass stone=156.1-100.4
volume stone=43.5-20
density=mass/volume