A sailor on a trans-Pacific solo voyage notices one day that if he puts 714. mL of fresh water into a plastic cup weighing 25.0 g, the cup floats in the seawater around his boat with the fresh water inside the cup at exactly fresh water the same level as the seawater outside the cup (see sketch at right). salt water Calculate the amount of salt dissolved in each liter of seawater. Be sure your answer has a unit symbol, if needed, and round it to 2 significant digits. You'll need to know that the density of fresh water at the temperature of the sea around the sailor is 0.999 g/cm. You'll also want to remember Archimedes' Principle, that objects float when they displace a mass of water equal to their own mass.
A sailor on a trans-Pacific solo voyage notices one day that if he puts 714. mL of fresh water into a plastic cup weighing 25.0 g, the cup floats in the seawater around his boat with the fresh water inside the cup at exactly fresh water the same level as the seawater outside the cup (see sketch at right). salt water Calculate the amount of salt dissolved in each liter of seawater. Be sure your answer has a unit symbol, if needed, and round it to 2 significant digits. You'll need to know that the density of fresh water at the temperature of the sea around the sailor is 0.999 g/cm. You'll also want to remember Archimedes' Principle, that objects float when they displace a mass of water equal to their own mass.
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
Related questions
Question
100%
Pls solve accurate pls pls it's important
![### Example Problem: Calculating the Mass of Dissolved Salt in Seawater
A sailor on a trans-Pacific solo voyage notices one day that if he puts 714 mL of fresh water into a plastic cup weighing 25.0 g, the cup floats in the seawater around his boat with the fresh water inside the cup at exactly the same level as the seawater outside the cup (*see sketch at right*).
Calculate the amount of salt dissolved in each liter of seawater. Be sure your answer has a unit symbol, if needed, and round it to 2 significant digits.
#### Key Information
1. The density of fresh water at the temperature of the sea around the sailor is \(0.999 \text{ g/cm}^3\).
2. Archimedes' Principle: Objects float when they displace a mass of water equal to their own mass.
#### Steps to Solve
1. **Determine the mass of the freshwater inside the cup**:
- Volume of fresh water = 714 mL
- Density of fresh water \(= 0.999 \text{ g/cm}^3 \)
- Convert volume to cm\(^3\) (since 1 mL = 1 cm\(^3\)):
\[
714 \text{ mL} = 714 \text{ cm}^3
\]
- Mass of fresh water:
\[
\text{Mass} = \text{Volume} \times \text{Density} = 714 \text{ cm}^3 \times 0.999 \text{ g/cm}^3 = 712.29 \text{ g}
\]
2. **Total mass floating in seawater**:
- Mass of cup \(= 25.0 \text{ g}\)
- Total mass = Mass of cup + Mass of fresh water
\[
\text{Total mass} = 25.0 \text{ g} + 712.29 \text{ g} = 737.29 \text{ g}
\]
3. **Apply Archimedes' Principle**:
- The seawater displaced by the cup with fresh water inside is equal to the total mass floating, which is 737.29 g.
4. **Calculate the density of seawater**:
- Let \(\rho_s\) be the density of](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F398dfb8b-8c41-4715-a697-5c459af04574%2F0a663e3a-951d-49fc-8427-bdc34aaa03af%2Fnsdv7po_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Example Problem: Calculating the Mass of Dissolved Salt in Seawater
A sailor on a trans-Pacific solo voyage notices one day that if he puts 714 mL of fresh water into a plastic cup weighing 25.0 g, the cup floats in the seawater around his boat with the fresh water inside the cup at exactly the same level as the seawater outside the cup (*see sketch at right*).
Calculate the amount of salt dissolved in each liter of seawater. Be sure your answer has a unit symbol, if needed, and round it to 2 significant digits.
#### Key Information
1. The density of fresh water at the temperature of the sea around the sailor is \(0.999 \text{ g/cm}^3\).
2. Archimedes' Principle: Objects float when they displace a mass of water equal to their own mass.
#### Steps to Solve
1. **Determine the mass of the freshwater inside the cup**:
- Volume of fresh water = 714 mL
- Density of fresh water \(= 0.999 \text{ g/cm}^3 \)
- Convert volume to cm\(^3\) (since 1 mL = 1 cm\(^3\)):
\[
714 \text{ mL} = 714 \text{ cm}^3
\]
- Mass of fresh water:
\[
\text{Mass} = \text{Volume} \times \text{Density} = 714 \text{ cm}^3 \times 0.999 \text{ g/cm}^3 = 712.29 \text{ g}
\]
2. **Total mass floating in seawater**:
- Mass of cup \(= 25.0 \text{ g}\)
- Total mass = Mass of cup + Mass of fresh water
\[
\text{Total mass} = 25.0 \text{ g} + 712.29 \text{ g} = 737.29 \text{ g}
\]
3. **Apply Archimedes' Principle**:
- The seawater displaced by the cup with fresh water inside is equal to the total mass floating, which is 737.29 g.
4. **Calculate the density of seawater**:
- Let \(\rho_s\) be the density of
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.Recommended textbooks for you
Chemistry
Chemistry
ISBN:
9781305957404
Author:
Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:
Cengage Learning
Chemistry
Chemistry
ISBN:
9781259911156
Author:
Raymond Chang Dr., Jason Overby Professor
Publisher:
McGraw-Hill Education
Principles of Instrumental Analysis
Chemistry
ISBN:
9781305577213
Author:
Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Publisher:
Cengage Learning
Chemistry
Chemistry
ISBN:
9781305957404
Author:
Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:
Cengage Learning
Chemistry
Chemistry
ISBN:
9781259911156
Author:
Raymond Chang Dr., Jason Overby Professor
Publisher:
McGraw-Hill Education
Principles of Instrumental Analysis
Chemistry
ISBN:
9781305577213
Author:
Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Publisher:
Cengage Learning
Organic Chemistry
Chemistry
ISBN:
9780078021558
Author:
Janice Gorzynski Smith Dr.
Publisher:
McGraw-Hill Education
Chemistry: Principles and Reactions
Chemistry
ISBN:
9781305079373
Author:
William L. Masterton, Cecile N. Hurley
Publisher:
Cengage Learning
Elementary Principles of Chemical Processes, Bind…
Chemistry
ISBN:
9781118431221
Author:
Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:
WILEY