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Chapter 1: Problem 75

A sample containing 33.42 g of metal pellets is poured into a graduated cylinder initially containing 12.7 mL of water, causing the water level in the cylinder to rise to 21.6 mL. Calculate the density of the metal.

Short Answer

Expert verified
The density of the metal can be calculated using the formula: Density = Mass / Volume. After adding the metal pellets into the graduated cylinder, the water level rises from 12.7 mL to 21.6 mL, which means the volume of the metal pellets is 21.6 mL - 12.7 mL = 8.9 mL. Given the mass of the metal pellets is 33.42 g, we can now find the density: Density = 33.42 g / 8.9 mL ≈ 3.76 g/mL.

Step by step solution

01

Determine the volume of the metal pellets

To find the volume of the metal pellets, we need to subtract the initial volume of the water in the graduated cylinder from the final volume of the water after the metal was added. This is because the change in water volume will be equal to the volume of the metal pellets. Initial water volume: 12.7 mL Final water volume: 21.6 mL Volume of metal pellets = Final water volume - Initial water volume
02

Calculate the volume of the metal pellets

Now we'll subtract the initial water volume from the final water volume to find the volume of the metal pellets. Volume of metal pellets = 21.6 mL - 12.7 mL = 8.9 mL
03

Calculate the density of the metal

Now that we have the mass and volume of the metal pellets, we can calculate the density using the following formula: Density = Mass / Volume We are given the mass of the metal pellets (33.42 g) and have calculated the volume (8.9 mL). Now, we can plug these values into the formula: Density = 33.42 g / 8.9 mL = 3.76 g/mL The density of the metal is approximately 3.76 g/mL.

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