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Chapter 1: Problem 81

Water has a density of \(0.997 \mathrm{~g} / \mathrm{cm}^{3}\) at $25^{\circ} \mathrm{C}\(; ice has a density of \)0.917 \mathrm{~g} / \mathrm{cm}^{3}$ at \(-10^{\circ} \mathrm{C}\). (a) If a soft-drink bottle whose volume is $1.50 \mathrm{~L}\( is completely filled with water and then frozen to \)-10^{\circ} \mathrm{C},$ what volume does the ice occupy? (b) Can the ice be contained within the bottle?

Short Answer

Expert verified
(a) The ice occupies a volume of \(1630.74 \, \text{cm}^3\). (b) No, the ice cannot be contained within the bottle as its volume is larger than the bottle's volume.

Step by step solution

01

Calculate the mass of the water

The volume of the soft-drink bottle is 1.50 L. First, convert the volume to cubic centimeters: \(1.50 \,\text{L} \times \frac{1000 \,\text{cm}^3}{1\,\text{L}} = 1500 \,\text{cm}^3\) Using the formula for density, which is, \(\text{density} = \frac{\text{mass}}{\text{volume}}\), we can calculate the mass of the water in the bottle: \(\text{mass}_{\text{water}} = \text{density}_{\text{water}} \times \text{volume}_{\text{water}}\) Where \(\text{density}_{\text{water}} = 0.997\frac{\text{g}}{\text{cm}^3}\) and \(\text{volume}_{\text{water}} = 1500 \,\text{cm}^3\) \(\text{mass}_{\text{water}}= (0.997\frac{\text{g}}{\text{cm}^3})(1500 \, \text{cm}^3) = 1495.50\, \text{g} \)
02

Calculate the volume of the ice

Now, we can calculate the volume of the ice that would be formed from this mass of water. Using the formula for density, we have: \(\text{volume}_{\text{ice}} = \frac{\text{mass}_{\text{water}}}{\text{density}_{\text{ice}}}\) Where \(\text{density}_{\text{ice}} = 0.917\frac{\text{g}}{\text{cm}^3}\) (Note: we use ice density since we're calculating ice volume) \(\text{volume}_{\text{ice}} = \frac{1495.50\,\text{g}}{0.917\frac{\text{g}}{\text{cm}^3}} = 1630.74 \, \text{cm}^3 \)
03

Compare the volume of the ice in the bottle

Now, let's compare the volume of the ice formed (\(1630.74 \, \text{cm}^3\)) to the volume of the bottle (\(1500 \, \text{cm}^3\)): \(1630.74 \, \text{cm}^3\) is larger than \(1500 \, \text{cm}^3\). This means that the volume of ice formed is greater than the volume of the bottle.
04

Answer

(a) The ice occupies a volume of \(1630.74 \, \text{cm}^3\). (b) No, the ice cannot be contained within the bottle as its volume is larger than the bottle's volume.

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Most popular questions from this chapter

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