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Chapter 1: Problem 65

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

Short Answer

Expert verified
The density of the metal can be calculated using the formula Density = Mass / Volume. First, find the volume of the metal pellets by subtracting the initial water volume (12.7 mL) from the final water volume (21.6 mL), which gives 8.9 mL. Then, divide the mass of the metal pellets (33.42 g) by the volume (8.9 mL) to find the density: \(Density \approx \frac{33.42 \mathrm{~g}}{8.9 \mathrm{~mL}} \approx 3.754 \mathrm{~g/mL}\).

Step by step solution

01

Calculate the Volume of Metal Pellets

Since the volume change in the graduated cylinder is due to the added metal pellets, we can find the volume of the metal pellets by subtracting the initial volume of water from the final volume of water. Volume of Metal Pellets = Final Volume - Initial Volume Volume of Metal Pellets = 21.6 mL - 12.7 mL Now, perform the subtraction: Volume of Metal Pellets = 8.9 mL
02

Calculate the Density of the Metal

Now that we've found the volume of the metal pellets, we can find the density of the metal using the formula: Density = Mass / Volume We have the mass of the metal (33.42 g) and the volume of the metal pellets (8.9 mL). Plug these values into the formula: Density = 33.42 g / 8.9 mL Now, perform the division: Density ≈ 3.754 g/mL The density of the metal is approximately 3.754 g/mL.

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