Chemistry
10th Edition
ISBN: 9781305957404
Author: Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Related questions
Concept explainers
Question
![### Solving Applications of Boyle's Law
**Problem:**
A marine biologist is preparing a deep-sea submersible for a dive. The sub stores breathing air under high pressure in a spherical air tank that measures 78.0 cm wide.
The biologist estimates she will need 1400 L of air for the dive. Calculate the pressure to which this volume of air must be compressed in order to fit into the air tank. Write your answer in atmospheres. Round your answer to 3 significant digits.
**Solution Steps:**
1. **Determine the Volume of the Spherical Tank:**
- Given the diameter of the tank is 78.0 cm, the radius \( r \) is half of the diameter:
\[
r = \frac{78.0 \, \text{cm}}{2} = 39.0 \, \text{cm}
\]
- Volume \( V \) of a sphere is given by the formula:
\[
V = \frac{4}{3}\pi r^3
\]
- Converting the radius to meters for standard units (1 cm = 0.01 m):
\[
r = 39.0 \, \text{cm} \times 0.01 \, \text{m/cm} = 0.39 \, \text{m}
\]
- Calculating the volume:
\[
V = \frac{4}{3}\pi (0.39 \, \text{m})^3
\]
\[
V \approx 0.249 \, \text{m}^3
\]
\( 1 \, \text{m}^3 = 1000 \, \text{L} \), so
\[
V \approx 249 \, \text{L}
\]
2. **Apply Boyle’s Law:**
Boyle’s Law states that \( P_1 V_1 = P_2 V_2 \).
- Assuming the initial pressure \( P_1 = 1 \, \text{atm} \),
\[
1 \, \text{atm} \times 1400 \, \text{L} = P_2 \times 249 \, \text{L}
\]
- Sol](https://content.bartleby.com/qna-images/question/19406573-6a1e-471a-ba9f-f1bcf97fa675/e2059b8d-c043-4f6a-943f-2673d2f4f7e0/yka2nna.png)
Transcribed Image Text:### Solving Applications of Boyle's Law
**Problem:**
A marine biologist is preparing a deep-sea submersible for a dive. The sub stores breathing air under high pressure in a spherical air tank that measures 78.0 cm wide.
The biologist estimates she will need 1400 L of air for the dive. Calculate the pressure to which this volume of air must be compressed in order to fit into the air tank. Write your answer in atmospheres. Round your answer to 3 significant digits.
**Solution Steps:**
1. **Determine the Volume of the Spherical Tank:**
- Given the diameter of the tank is 78.0 cm, the radius \( r \) is half of the diameter:
\[
r = \frac{78.0 \, \text{cm}}{2} = 39.0 \, \text{cm}
\]
- Volume \( V \) of a sphere is given by the formula:
\[
V = \frac{4}{3}\pi r^3
\]
- Converting the radius to meters for standard units (1 cm = 0.01 m):
\[
r = 39.0 \, \text{cm} \times 0.01 \, \text{m/cm} = 0.39 \, \text{m}
\]
- Calculating the volume:
\[
V = \frac{4}{3}\pi (0.39 \, \text{m})^3
\]
\[
V \approx 0.249 \, \text{m}^3
\]
\( 1 \, \text{m}^3 = 1000 \, \text{L} \), so
\[
V \approx 249 \, \text{L}
\]
2. **Apply Boyle’s Law:**
Boyle’s Law states that \( P_1 V_1 = P_2 V_2 \).
- Assuming the initial pressure \( P_1 = 1 \, \text{atm} \),
\[
1 \, \text{atm} \times 1400 \, \text{L} = P_2 \times 249 \, \text{L}
\]
- Sol
*Note: The diagram shows a cylinder filled with gas and a piston applying force to the gas.*
Calculate the pressure of the gas inside the cylinder. Write your answer in units of kilopascals. Round your answer to 2 significant digits.
---
#### Input Section:
- Label: **kPa**
- Additional Options:
- Multiplication factor (×10)
- Undo
- Help
---
### Instructions for Calculation:
1. Calculate the area of the piston.
2. Use the formula \( \text{Pressure} = \frac{\text{Force}}{\text{Area}} \) to find the pressure.
3. Convert the pressure to kilopascals (kPa).
4. Round your answer to 2 significant digits.
---
##### Example Calculation:
1. **Calculate the Area (A):**
- Area of a circle = \( \pi r^2 \), where radius \( r = \frac{d}{2} = \frac{2.4 \, \text{cm}}{2} = 1.2 \, \text{cm} \)
- \( A = \pi (1.2 \, \text{cm})^2 = \pi \times 1.44 \, \text{cm}^2 = 4.52 \, \text{cm}^2 \)
2. **Convert Area to m²:**
- \( 4.52 \, \text{cm}^2 = 4.52 \times 10^{-4} \, \text{m}^2 \)
3. **Calculate the Pressure (P):**
- \( P = \frac{F}{A} = \frac{13 \, \text{N}}{4.52 \times 10^{-4} \, \text{m}^2} = 2.88 \times 10^4 \, \text{Pa} \)
4. **Convert](https://content.bartleby.com/qna-images/question/19406573-6a1e-471a-ba9f-f1bcf97fa675/e2059b8d-c043-4f6a-943f-2673d2f4f7e0/f4gm13j.png)
Transcribed Image Text:---
### GASES
## Interconverting pressure and force
A cylinder measuring **2.4 cm wide** and **2.9 cm high** is filled with gas. The piston is pushed down with a steady force measured to be **13 N**.
*Note: The diagram shows a cylinder filled with gas and a piston applying force to the gas.*
Calculate the pressure of the gas inside the cylinder. Write your answer in units of kilopascals. Round your answer to 2 significant digits.
---
#### Input Section:
- Label: **kPa**
- Additional Options:
- Multiplication factor (×10)
- Undo
- Help
---
### Instructions for Calculation:
1. Calculate the area of the piston.
2. Use the formula \( \text{Pressure} = \frac{\text{Force}}{\text{Area}} \) to find the pressure.
3. Convert the pressure to kilopascals (kPa).
4. Round your answer to 2 significant digits.
---
##### Example Calculation:
1. **Calculate the Area (A):**
- Area of a circle = \( \pi r^2 \), where radius \( r = \frac{d}{2} = \frac{2.4 \, \text{cm}}{2} = 1.2 \, \text{cm} \)
- \( A = \pi (1.2 \, \text{cm})^2 = \pi \times 1.44 \, \text{cm}^2 = 4.52 \, \text{cm}^2 \)
2. **Convert Area to m²:**
- \( 4.52 \, \text{cm}^2 = 4.52 \times 10^{-4} \, \text{m}^2 \)
3. **Calculate the Pressure (P):**
- \( P = \frac{F}{A} = \frac{13 \, \text{N}}{4.52 \times 10^{-4} \, \text{m}^2} = 2.88 \times 10^4 \, \text{Pa} \)
4. **Convert
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 nowThis is a popular solution!
Step by stepSolved in 2 steps with 2 images
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.Similar questions
- A marine biologist is preparing a deep-sea submersible for a dive. The sub stores breathing air under high pressure in a spherical air tank that measures 66.0 cm wide. The biologist estimates she will need 6800. L of air for the dive. Calculate the pressure to which this volume of air must be compressed in order to fit into the air tank. Write your answer in atmospheres. Round your answer to 3 significant digits. atm x10arrow_forwardCalculate the new volume of the balloon. Round your answer to 3 significant digits.arrow_forwardHow many gas molecules are present in 727 mL of propane (C3H8) at 27 °C and 494 torr pressure? Enter using scientific notation. How many atoms are present? Enter using scientific notation. What would the volume of the sample be at STP? Enter using decimal notation.arrow_forward
- Calculate the pressure to which this volume of air must be compressed in order to fit into the air tank. Write your answer in atmospheres. Be sure your answer has the correct number of significant digits.arrow_forwardAn arctic weather balloon is filled with 40.8 L of helium gas inside a prep shed. The temperature inside the shed is 14. °C. The balloon is then taken outside, where the temperature is 43. °C. Calculate the new volume of the balloon. You may assume the pressure on the balloon stays constant at exactly 1 atm. Round your answer to 3 significant digits.arrow_forwardA particular gas has an initial volume of 5.29 L and an initial temperature of 213.3 K. If the volume changes to 38.2 L, calculate the new temperature in K.arrow_forward
- A balloon contains 0.154 mol of gas and has a volume of 2.61 L . If an additional 0.200 mol of gas is added to the balloon (at the same temperature and pressure), what will its final volume be? Express your answer in liters to three significant figures.arrow_forwardA sample of nitrogen gas occupies a volume of 250. mL at 25.0°C. What volume will it occupy at 95.0°C? O a. 65.8 mL O b. 309 mL O c. 905 mL O d. 202 mL O e. 278 mL е. 80 45X-5X iw bas motaya gaiwolloi odt ovlo2 (.AIarrow_forwardA gas occupying a volume of 622.0 mL at a pressure of 0.860 atm is allowed to expand at constant temperature until its pressure reaches 0.547 atm. What is its final volume? Be sure your answer has the correct number of significant digits. mL Xarrow_forward
- A heliox deep-sea diving mixture contains 2.0 g of oxygen to every 98.0 g of helium. What is the partial pressure of oxygen when this mixture is delivered at a total pressure of 7.9 atm? Express your answer in atmospheres using two significant figures.arrow_forwardA gas sample initially at 1 atm increases in pressure to 4.51 atm as the volume shrinks to 5.6 L. What was the initial volume? Show work on your paper. In the box below, enter your numeric answer only.arrow_forwardA marine biologist is preparing a deep-sea submersible for a dive. The sub stores breathing air under high pressure in a spherical air tank that measures 62.0cm wide.The biologist estimates she will need 3100.L of air for the dive. Calculate the pressure to which this volume of air must be compressed in order to fit into the air tank. Write your answer in atmospheres. Round your answer to 3 significant digits. atmarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- ChemistryChemistryISBN:9781305957404Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCostePublisher:Cengage Learning
ChemistryChemistryISBN:9781259911156Author:Raymond Chang Dr., Jason Overby ProfessorPublisher:McGraw-Hill Education
Principles of Instrumental AnalysisChemistryISBN:9781305577213Author:Douglas A. Skoog, F. James Holler, Stanley R. CrouchPublisher:Cengage Learning 
Organic ChemistryChemistryISBN:9780078021558Author:Janice Gorzynski Smith Dr.Publisher:McGraw-Hill Education
Chemistry: Principles and ReactionsChemistryISBN:9781305079373Author:William L. Masterton, Cecile N. HurleyPublisher:Cengage Learning
Elementary Principles of Chemical Processes, Bind...ChemistryISBN:9781118431221Author:Richard M. Felder, Ronald W. Rousseau, Lisa G. BullardPublisher:WILEY
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