Question
A piece of metal weighing 281.0 g is placed in a graduated cylinder containing 217.7 mL . of water. The volume of water now reads 246.0 ml . From these data calculate the density of the metal. Round your answer to 3 significant digits. density:
Ask by Lynch Chavez. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The density of the metal is 9.93 g/mL.
Solution
To calculate the density of the metal, you can use the formula:
\[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
\]
**Given:**
- Mass of the metal, \( m = 281.0 \) g
- Initial volume of water, \( V_{\text{initial}} = 217.7 \) mL
- Final volume of water with metal, \( V_{\text{final}} = 246.0 \) mL
**Steps:**
1. **Find the Volume of the Metal:**
\[
\text{Volume of metal} = V_{\text{final}} - V_{\text{initial}} = 246.0 \, \text{mL} - 217.7 \, \text{mL} = 28.3 \, \text{mL}
\]
2. **Calculate the Density:**
\[
\text{Density} = \frac{281.0 \, \text{g}}{28.3 \, \text{mL}} \approx 9.93 \, \text{g/mL}
\]
**Final Answer:**
The density of the metal is **9.93 g/mL**.
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Beyond the Answer
To find the density of the metal, you'll first need to determine the volume of the metal itself. You can do this by subtracting the initial water volume from the final water volume, which gives you: Volume of metal = Final water volume - Initial water volume Volume of metal = 246.0 mL - 217.7 mL = 28.3 mL Now that we have the mass and the volume of the metal, we can use the density formula: Density = Mass / Volume Density = 281.0 g / 28.3 mL ≈ 9.92 g/mL Rounding this to three significant digits, the density of the metal is 9.92 g/mL. Now you’re all set with the metal's density!
