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Chapter 1: Problem 98

A \(25.00-g\) sample of a solid is placed in a graduated cylinder, and then the cylinder is filled to the \(50.0-\mathrm{mL}\) mark with benzene. The mass of benzene and solid together is \(58.80 \mathrm{~g}\). Assuming that the solid is insoluble in benzene and that the density of benzene is \(0.880 \mathrm{~g} / \mathrm{cm}^{3}\), calculate the density of the solid.

Short Answer

Expert verified
The density of the solid is approximately \(2.16 \mathrm{~g} / \mathrm{cm}^{3}\).

Step by step solution

01

Calculate the mass of benzene

First, we need to find the mass of benzene alone. We have the total mass of benzene and the solid together, which is 58.80 g. We also have the mass of the solid, which is 25.00 g. Subtract the mass of the solid from the total mass to find the mass of benzene: Mass of benzene = Total mass - Mass of solid = 58.80 g - 25.00 g = 33.80 g
02

Calculate the volume of benzene

Now, we use the density of benzene to calculate its volume. The density of benzene is given as 0.880 g/cm³. To find the volume, divide the mass of benzene by its density: Volume of benzene = Mass of benzene / Density of benzene = 33.80 g / 0.880 g/cm³ ≈ 38.41 cm³ Since 1 cm³ is equivalent to 1 mL, the volume of benzene is also 38.41 mL.
03

Calculate the volume of the solid

We know that the graduated cylinder is filled to the 50.0 mL mark with the solid and benzene. To find the volume of the solid, subtract the volume of benzene from the total volume: Volume of solid = Total volume - Volume of benzene = 50.0 mL - 38.41 mL ≈ 11.59 mL Since 1 mL is equivalent to 1 cm³, the volume of the solid is also 11.59 cm³.
04

Calculate the density of the solid

Finally, to find the density of the solid, divide its mass by its volume: Density of solid = Mass of solid / Volume of solid = 25.00 g / 11.59 cm³ ≈ 2.16 g/cm³ The density of the solid is approximately 2.16 g/cm³.

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Most popular questions from this chapter

Which of the following describes a chemical property? a. The density of iron is \(7.87 \mathrm{~g} / \mathrm{cm}^{3}\). b. A platinum wire glows red when heated. c. An iron bar rusts. d. Aluminum is a silver-colored metal.

The scientific method is a dynamic process. What does this mean?

Perform the following unit conversions. a. Congratulations! You and your spouse are the proud parents of a new baby, born while you are studying in \(\Omega\) country that uses the metric system. The nurse has informed you that the baby weighs \(3.91 \mathrm{~kg}\) and measures \(51.4 \mathrm{~cm}\). Convert your baby's weight to pounds and ounces and her length to inches (rounded to the nearest quarter inch). b. The circumference of the earth is \(25,000 \mathrm{mi}\) at the equator. What is the circumference in kilometers? in meters? c. A rectangular solid measures \(1.0 \mathrm{~m}\) by \(5.6 \mathrm{~cm}\) by \(2.1 \mathrm{dm}\). Express its volume in cubic meters, liters, cubic inches, and cubic feet.

When a marble is dropped into a beaker of water, it sinks to the bottom. Which of the following is the best explanation? a, The surface area of the marble is not large enough to be held up by the surface tension of the water. b. The mass of the marble is greater than that of the water. c. The marble weighs more than an equivalent volume of the water. d. The force from dropping the marble breaks the surface tension of the water. e. The marble has greater mass and volume than the water. Justify your choice, and for choices you did not pick, explain what is wrong about them.

Convert the following Celsius temperatures to Kelvin and to Fahrenheit degrees. a. the temperature of someone with a fever, \(39.2^{\circ} \mathrm{C}\) b. a cold wintery day, \(-25^{\circ} \mathrm{C}\) c. the lowest possible temperature, \(-273^{\circ} \mathrm{C}\) d. the melting-point temperature of sodium chloride, \(801^{\circ} \mathrm{C}\)
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