a graduated cylinder containing 75.0 mL of water has a mass of 149.86 g. A piece of metal is added to the cylinder and the volume of the water changes to 86.3 mL. The mass of the graduated cylinder, water and metal rises to 218.90 g.
What is the question? Density of the object?
D=mass/volume=(218.8-149.86)/(86.3-75.0)
To find the mass of the metal, we need to subtract the mass of the graduated cylinder and water from the mass of the graduated cylinder, water, and metal.
Let's break down the problem step by step:
1. Mass of the graduated cylinder and water: 149.86 g
2. Volume of water before adding the metal: 75.0 mL
3. Volume of water after adding the metal: 86.3 mL
4. Mass of the graduated cylinder, water, and metal: 218.90 g
Now, let's calculate the mass of the metal:
Step 1: Calculate the mass of the water before adding the metal:
Density of water = mass/volume
Since the density of water is constant, we can calculate the mass of the water using the initial volume.
Density of water = Mass of water / Volume of water before adding the metal
Rearranging the formula, we get:
Mass of water = Density of water * Volume of water before adding the metal
Since the density of water is approximately 1 g/mL, we have:
Mass of water = 1 g/mL * 75.0 mL = 75.0 g
Step 2: Calculate the mass of the water after adding the metal:
Using the same formula as above:
Mass of water = Density of water * Volume of water after adding the metal
Mass of water = 1 g/mL * 86.3 mL = 86.3 g
Step 3: Calculate the mass of the metal:
Mass of metal = Mass of the graduated cylinder, water, and metal - Mass of the graduated cylinder and water
Mass of metal = 218.90 g - 149.86 g = 69.04 g
Thus, the mass of the metal is 69.04 g.