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Chapter 2: Problem 138

When a 16.74-g rubber stopper is placed in a graduated cylinder containing \(25.46 \mathrm{~mL}\) of water, the water level rises to \(37.42 \mathrm{~mL}\). What is the density of the stopper in grams per milliliter?

Short Answer

Expert verified
The density of the rubber stopper is approximately \(1.40~g/mL\).

Step by step solution

01

Determine the volume of the rubber stopper

To find the volume of the rubber stopper, we will subtract the initial volume of water from the final volume of water when the rubber stopper is submerged. The difference will give us the volume of the rubber stopper. Initial volume of water: \(25.46~mL\) Final volume of water (with rubber stopper): \(37.42~mL\) Volume of rubber stopper: \(37.42-25.46~mL\)
02

Calculate the volume of the rubber stopper

Now, subtract the initial volume of the water from the final volume of the water to get the volume of the rubber stopper. Volume of rubber stopper: \(37.42~mL - 25.46~mL = 11.96~mL\)
03

Calculate the density of the rubber stopper

To find the density of the rubber stopper, divide the mass of the rubber stopper by its volume. In this case, we have: Mass of rubber stopper: \(16.74~g\) Volume of rubber stopper: \(11.96~mL\) Density of rubber stopper: \(\frac{16.74~g}{11.96~mL}\)
04

Find the density of the rubber stopper

Finally, divide the mass of the rubber stopper by its volume to determine the density in grams per milliliter: Density of rubber stopper: \(\frac{16.74~g}{11.96~mL} = 1.40~g/mL\) The density of the rubber stopper is approximately \(1.40~g/mL\).

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