The density of pure copper is 8.96 at 20°C. If 6.50 g of pure copper pellets is added to a graduated cylinder containing 13.4 mL of water, to what volume level will the water in the cylinder rise
copper sinks so volume is increased by copper volume.
volume of copper = 6.5 g * 1 mL/8.96 g
= .725 mL
so
.725 + 13.4 = 14.1 mL
To determine the volume level to which the water in the cylinder will rise after adding the copper pellets, we need to consider the difference in density between copper and water.
Step 1: Calculate the mass of water displaced by the copper pellets.
Density of water = 1 g/mL
Mass of water = density of water * volume of water
Mass of water = 1 g/mL * 13.4 mL
Mass of water = 13.4 g
Step 2: Calculate the volume of copper pellets from its mass.
Density of copper = 8.96 g/mL
Volume of copper = mass of copper / density of copper
Volume of copper = 6.50 g / 8.96 g/mL
Volume of copper = 0.726 g/mL
Step 3: Subtract the volume of copper pellets from the initial volume of water in the graduated cylinder to find the volume level to which the water will rise.
Volume level = initial volume of water - volume of copper
Volume level = 13.4 mL - 0.726 mL
Volume level = 12.674 mL
Therefore, the water in the cylinder will rise to a volume level of approximately 12.674 mL.
To find the volume level to which the water in the graduated cylinder will rise after adding the copper pellets, we need to consider the difference in density between copper and water.
Here's how you can solve it step-by-step:
1. Determine the density of water: The density of water is approximately 1 g/mL.
2. Find the mass of water in the graduated cylinder: The mass of water can be calculated using its density and volume:
Mass of water = Density of water × Volume of water
Mass of water = 1 g/mL × 13.4 mL
Mass of water = 13.4 g
3. Add the mass of copper and water: The total mass after adding the copper pellets can be obtained by summing the mass of copper and the initial mass of water:
Total mass = Mass of copper + Mass of water
Total mass = 6.50 g + 13.4 g
Total mass = 19.90 g
4. Determine the volume of the mixture: The volume of the mixture can be calculated using the total mass and the density of the mixture:
Density of the mixture = Total mass / Volume of the mixture
Since we are trying to find the volume of the mixture (which includes both water and copper), re-arrange the formula:
Volume of the mixture = Total mass / Density of the mixture
Density of the mixture is the ratio between the mass of the mixture and its volume:
Density of the mixture = (Mass of copper + Mass of water) / Volume of the mixture
5. Rearrange the formula to solve for the volume of the mixture:
Volume of the mixture = Total mass / Density of the mixture
Volume of the mixture = 19.90 g / Density of the mixture
6. Substitute the density of copper into the formula:
Density of copper = 8.96 g/mL
Volume of the mixture = 19.90 g / (8.96 g/mL)
7. Calculate the volume of the mixture:
Volume of the mixture = 2.22 mL
Therefore, after adding the copper pellets, the water level in the graduated cylinder will rise to approximately 2.22 mL.