Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 1: Problem 86

The total volume of ice in the Antarctic is about \(3.01 \times 10^{7} \mathrm{km}^{3} .\) If all the ice in the Antarctic were to melt completely, estimate the rise, \(h,\) in sea level that would result from the additional liquid water entering the oceans. The densities of ice and fresh water are \(0.92 \mathrm{g} / \mathrm{cm}^{3}\) and \(1.0 \mathrm{g} / \mathrm{cm}^{3},\) respectively. Assume that the oceans of the world cover an area, \(A,\) of about \(3.62 \times 10^{8} \mathrm{km}^{2}\) and that the increase in volume of the oceans can be calculated as \(A \times h\).

Short Answer

Expert verified
The sea level would rise approximately 67.32 m if all Antarctic ice were to melt completely.

Step by step solution

01

Calculate the Total Volume of Melted Ice

Since 1 g of ice melts to 1 g of water, and the densities of ice and water are 0.92 g/cm³ and 1.0 g/cm³ respectively, we can find the volume of water produced when all the ice melts by using the formula: \[ V_{water} = V_{ice} \times \frac{Density_{ice}}{Density_{water}} \] where \(V_{water}\) is the volume of water, \(V_{ice}\) is the volume of ice, \(Density_{ice}\) is density of ice and \(Density_{water}\) is the density of water. Heap in mind that initial volume of ice is given in km³ and we need to convert it to cm³ for consistency with density units. 1 km³ = \(10^{15}\) cm³.
02

Calculate the Rise in Sea Level

The volume of the resulting water will spread around the world's oceans and the sea level will rise accordingly. This rise in sea level, \(h\), can be calculated by dividing the volume of water, \(V_{water}\), by the area of the oceans, \(A_ocean\). Hence: \[h = \frac{V_{water}}{A_{ocean}}\] Again, bear in mind the units. The area of the oceans is given in km² , thus we should perform a conversion from km² to cm²: 1 km² = \(10^{10}\) cm² .
03

Substituting values

Now we substitute the given values into formulas outlined in steps 1 and 2 and calculate the final answer. Remembering about all necessary unit conversions.
04

Check the Answer

Finally, as common practice, it's always important to make sure the answer makes sense in the context of the problem. In this case, double-checking whether calculated value for sea level rise does seem plausible given the known data about the Earth's hydrosphere.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Compared with its mass on Earth, the mass of the same object on the moon should be (a) less; (b) more; (c) the same; (d) nearly the same, but somewhat less.

Indicate whether each sample of matter listed is a substance or a mixture; if it is a mixture, indicate whether it is homogeneous or heterogeneous. (a) clean fresh air (b) a silver-plated spoon (c) garlic salt (d) ice

A good example of a homogeneous mixture is (a) a cola drink in a tightly capped bottle (b) distilled water leaving a distillation apparatus (c) oxygen gas in a cylinder used in welding (d) the material produced in a kitchen blender

Blood alcohol content (BAC) is sometimes reported in weight-volume percent and, when it is, a BAC of \(0.10 \%\) corresponds to \(0.10 \mathrm{g}\) ethyl alcohol per \(100 \mathrm{mL}\) of blood. In many jurisdictions, a person is considered legally intoxicated if his or her BAC is 0.10\%. Suppose that a 68 kg person has a total blood volume of 5.4 L and breaks down ethyl alcohol at a rate of 10.0 grams per hour. \(^{*}\) How many 145 mL glasses of wine, consumed over three hours, will produce a BAC of \(0.10 \%\) in this 68 kg person? Assume the wine has a density of \(1.01 \mathrm{g} / \mathrm{mL}\) and is \(11.5 \%\) ethyl alcohol by mass. (* The rate at which ethyl alcohol is broken down varies dramatically from person to person. The value given here for the rate is a realistic, but not necessarily accurate, value.)

Express each value in exponential form. Where appropriate, include units in your answer. (a) speed of sound (sea level): 34,000 centimeters per second (b) equatorial radius of Earth: 6378 kilometers (c) the distance between the two hydrogen atoms in the hydrogen molecule: 74 trillionths of a meter (d) $\frac{\left(2.2 \times 10^{3}\right)+\left(4.7 \times 10^{2}\right)}{5.8 \times 10^{-3}}=$
See all solutions

Recommended explanations on Chemistry Textbooks

The Earths Atmosphere

Read Explanation

Kinetics

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Nuclear Chemistry

Read Explanation

Chemical Analysis

Read Explanation

Physical Chemistry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free