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Chapter 1: Problem 106

A \(250-\mathrm{mL}\) glass bottle was filled with \(242 \mathrm{~mL}\) of water at \(20^{\circ} \mathrm{C}\) and tightly capped. It was then left outdoors overnight, where the average temperature was \(-5^{\circ} \mathrm{C}\). Predict what would happen. The density of water at \(20^{\circ} \mathrm{C}\) is \(0.998 \mathrm{~g} / \mathrm{cm}^{3}\) and that of ice at \(-5^{\circ} \mathrm{C}\) is $0.916 \mathrm{~g} / \mathrm{cm}^{3}.

Short Answer

Expert verified
The glass bottle will break when the water freezes, because the volume of ice formed (263.5 mL) exceeds the volume of the bottle (250 mL).

Step by step solution

01

Calculate the mass of water

First, find the mass of the water in the bottle before it's left outdoors. Since density (\( \rho \)) is mass (\( m \)) divided by volume (\( V \)), we can rearrange the formula to find mass: \( m = \rho \times V \).The volume of water in the bottle is \( V = 242 \mathrm{~mL} = 242 \mathrm{~cm}^{3}\) (since 1 mL = 1 cm^3), and the density of water at 20^{\circ} \mathrm{C} is \( \rho = 0.998 \mathrm{~g/cm}^{3}\). Thus, the mass of the water is \( m = \rho \times V = 0.998 \mathrm{~g/cm}^{3} \times 242 \mathrm{~cm}^{3} = 241.516 \mathrm{~g} \)
02

Calculate the volume of ice

Now, keep the mass constant and recalculate the volume at -5^{\circ} \mathrm{C} using the density of ice. The density of ice is given as 0.916 \mathrm{~g/cm}^{3}. Using the formula for density \( \rho = m / V \), we can rearrange the formula to find the new volume \( V = m / \rho \). Thus, the volume of the ice is \( V = 241.516 \mathrm{~g} / 0.916 \mathrm{~g/cm}^{3} = 263.5 \mathrm{~cm}^{3}= 263.5 \mathrm{~mL} \).
03

Compare the volumes

Finally, compare the initial volume of the bottle (250 mL) with the volume of the ice (263.5 mL). The volume of ice is more than the volume of the bottle. Therefore, the glass bottle will break when the water freezes to ice.

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Most popular questions from this chapter

Classify each of the following substances as an element or a compound: (a) hydrogen, (b) water, (c) gold, (d) sugar.

Comment on whether each of the following is a homogeneous mixture or a heterogeneous mixture: (a) air in a closed bottle, (b) air over New York City.

Carry out the following conversions: (a) \(22.6 \mathrm{~m}\) to decimeters, (b) \(25.4 \mathrm{mg}\) to kilograms, (c) \(556 \mathrm{~mL}\) to liters, (d) \(10.6 \mathrm{~kg} / \mathrm{m}^{3}\) to \(\mathrm{g} / \mathrm{cm}^{3}\).

Express the answers to the following calculations in scientific notation: (a) \(0.0095+\left(8.5 \times 10^{-3}\right)\) (b) \(653 \div\left(5.75 \times 10^{-8}\right)\) (c) \(850,000-\left(9.0 \times 10^{5}\right)\) (d) \(\left(3.6 \times 10^{-4}\right) \times\left(3.6 \times 10^{6}\right)\)

Define significant figure. Discuss the importance of using the proper number of significant figures in measurements and calculations.
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