Copper has a density of 8.96 g/cm3. If 75.0 g of copper is added to 50.0 mL of water in a graduated cylinder, to what volume reading will the water level in the cylinder rise
The Correct Answer and Explanation is:
To find the new volume reading in the graduated cylinder after adding 75.0 g of copper to 50.0 mL of water, we must first determine the volume that the copper will occupy.
Step 1: Use the density formula
The formula relating mass, volume, and density is:Density=MassVolume\text{Density} = \frac{\text{Mass}}{\text{Volume}}Density=VolumeMass
We rearrange this formula to solve for volume:Volume=MassDensity\text{Volume} = \frac{\text{Mass}}{\text{Density}}Volume=DensityMass
Step 2: Plug in the known values
Mass of copper=75.0 g\text{Mass of copper} = 75.0\ \text{g}Mass of copper=75.0 gDensity of copper=8.96 g/cm3\text{Density of copper} = 8.96\ \text{g/cm}^3Density of copper=8.96 g/cm3Volume of copper=75.0 g8.96 g/cm3≈8.38 cm3\text{Volume of copper} = \frac{75.0\ \text{g}}{8.96\ \text{g/cm}^3} \approx 8.38\ \text{cm}^3Volume of copper=8.96 g/cm375.0 g≈8.38 cm3
Since 1 cm³ is equal to 1 mL, the volume of copper is about 8.38 mL.
Step 3: Add this volume to the initial water level
Initial water volume=50.0 mL\text{Initial water volume} = 50.0\ \text{mL}Initial water volume=50.0 mLFinal volume reading=50.0 mL+8.38 mL=58.38 mL\text{Final volume reading} = 50.0\ \text{mL} + 8.38\ \text{mL} = 58.38\ \text{mL}Final volume reading=50.0 mL+8.38 mL=58.38 mL
Final Answer:
The water level in the graduated cylinder will rise to approximately 58.38 mL.
Explanation:
This question involves understanding how displacement works. When a solid object like copper is submerged in water, it pushes the water out of the way, causing the water level to rise. The amount of water displaced is equal to the volume of the solid. In this case, copper has a relatively high density, so a 75.0 g sample occupies a small volume of about 8.38 mL. Adding that volume to the initial water level of 50.0 mL gives the total new reading. Because volume and mass are related through density, this calculation is crucial in practical laboratory measurements and illustrates how displacement can be used to determine the volume of irregular solids.
