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Height (cm) Diameter (cm) 52. Your laboratory instructor has given you two shiny, light gray metal cylinders. Your assignment is to determine which one is made of aluminum (d = 2.699 g/mL) and which one is made of titanium (d = 4.54 g/mL). The mass of each cylinder was determined on a balance to five significant figures. The volume was determined by immersing the cylinders in a graduated cylinder as shown in Figure P1.90. The initial volume of water was 25.0 mL in each graduated cylinder. The following data were collected: Mass (g) 15.560 5.1 35.536 5.9 Cylinder A Cylinder B (a) Calculate the volume of each cylinder by using the physical dimensions of the cylinder. (b) Calculate the volume of each cylinder from the water displacement method. (c) Which volume determination (part a or b) allows for the greater number of significant figures in the calculated densities? (d) Express the density of each cylinder to the appropriate number of significant figures using the method having greater precision. 40 30 20 103 Cylinder A 40 30 20 10 1.2 1.3 Cylinder B

Height (cm) Diameter (cm) 52. Your laboratory instructor has given you two shiny, light gray metal cylinders. Your assignment is to determine which one is made of aluminum (d = 2.699 g/mL) and which one is made of titanium (d = 4.54 g/mL). The mass of each cylinder was determined on a balance to five significant figures. The volume was determined by immersing the cylinders in a graduated cylinder as shown in Figure P1.90. The initial volume of water was 25.0 mL in each graduated cylinder. The following data were collected: Mass (g) 15.560 5.1 35.536 5.9 Cylinder A Cylinder B (a) Calculate the volume of each cylinder by using the physical dimensions of the cylinder. (b) Calculate the volume of each cylinder from the water displacement method. (c) Which volume determination (part a or b) allows for the greater number of significant figures in the calculated densities? (d) Express the density of each cylinder to the appropriate number of significant figures using the method having greater precision. 40 30 20 103 Cylinder A 40 30 20 10 1.2 1.3 Cylinder B

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
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**Experiment 52: Density Determination of Metal Cylinders** Your laboratory instructor has provided you with two shiny, light gray metal cylinders. Your task is to identify which cylinder is made of aluminum (density = 2.699 g/mL) and which is made of titanium (density = 4.54 g/mL). The mass of each cylinder was measured with a balance, accurate to five significant figures. The volume of each cylinder was determined by immersing it in a graduated cylinder as illustrated in Figure P1.90. The initial volume of water was 25.0 mL in each graduated cylinder. The data collected is as follows: | | Mass (g) | Height (cm) | Diameter (cm) | |-------|----------|-------------|---------------| | Cylinder A | 15.560 | 5.1 | 1.2 | | Cylinder B | 35.536 | 5.9 | 1.3 | ### Tasks: (a) **Calculate the Volume Using Physical Dimensions**: Determine the volume of each cylinder using their physical measurements. (b) **Calculate the Volume Using Water Displacement**: Calculate the volume of each cylinder using the water displacement method. (c) **Significant Figures**: Identify which volume calculation method allows for a greater number of significant figures when determining the cylinders' densities. (d) **Density Calculation**: Calculate the density of each cylinder, adjusting to the appropriate number of significant figures based on the method that provides greater precision. ### Figure P1.90 Explanation: - **Left Image (Cylinder A)**: Shows a graduated cylinder with water level rising from 25.0 mL to around 35.0 mL upon submersion of Cylinder A. - **Right Image (Cylinder B)**: Illustrates a graduated cylinder with water level increasing from 25.0 mL to about 40.0 mL when Cylinder B is submerged. This demonstration aids in understanding the water displacement method for volume determination in density calculations.
Transcribed Image Text:**Experiment 52: Density Determination of Metal Cylinders** Your laboratory instructor has provided you with two shiny, light gray metal cylinders. Your task is to identify which cylinder is made of aluminum (density = 2.699 g/mL) and which is made of titanium (density = 4.54 g/mL). The mass of each cylinder was measured with a balance, accurate to five significant figures. The volume of each cylinder was determined by immersing it in a graduated cylinder as illustrated in Figure P1.90. The initial volume of water was 25.0 mL in each graduated cylinder. The data collected is as follows: | | Mass (g) | Height (cm) | Diameter (cm) | |-------|----------|-------------|---------------| | Cylinder A | 15.560 | 5.1 | 1.2 | | Cylinder B | 35.536 | 5.9 | 1.3 | ### Tasks: (a) **Calculate the Volume Using Physical Dimensions**: Determine the volume of each cylinder using their physical measurements. (b) **Calculate the Volume Using Water Displacement**: Calculate the volume of each cylinder using the water displacement method. (c) **Significant Figures**: Identify which volume calculation method allows for a greater number of significant figures when determining the cylinders' densities. (d) **Density Calculation**: Calculate the density of each cylinder, adjusting to the appropriate number of significant figures based on the method that provides greater precision. ### Figure P1.90 Explanation: - **Left Image (Cylinder A)**: Shows a graduated cylinder with water level rising from 25.0 mL to around 35.0 mL upon submersion of Cylinder A. - **Right Image (Cylinder B)**: Illustrates a graduated cylinder with water level increasing from 25.0 mL to about 40.0 mL when Cylinder B is submerged. This demonstration aids in understanding the water displacement method for volume determination in density calculations.
Expert Solution
Step 1

a.) The volume of cylinder using physical dimension is calculated using formula 

V=πr2h

b) The volume using water displacement is calculated using formula 

V = Final volume of water - Initial volume of water 

c) The volume which would have more number of significant digits will give more precise result for density. 

d) Density would be calculated as :

Density = MassVolume 

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