Table of contents

1. Matter and Measurements4h 31m
2. Atoms and the Periodic Table5h 23m
3. Ionic Compounds2h 18m
4. Molecular Compounds2h 18m
5. Classification & Balancing of Chemical Reactions3h 17m
6. Chemical Reactions & Quantities2h 27m
7. Energy, Rate and Equilibrium3h 46m
8. Gases, Liquids and Solids3h 25m
9. Solutions4h 10m
10. Acids and Bases3h 29m
11. Nuclear Chemistry56m
BONUS: Lab Techniques and Procedures1h 38m
BONUS: Mathematical Operations and Functions47m
12. Introduction to Organic Chemistry1h 34m
13. Alkenes, Alkynes, and Aromatic Compounds2h 12m
14. Compounds with Oxygen or Sulfur1h 6m
15. Aldehydes and Ketones1h 1m
16. Carboxylic Acids and Their Derivatives1h 11m
17. Amines39m
18. Amino Acids and Proteins1h 51m
19. Enzymes1h 37m
20. Carbohydrates1h 41m
21. The Generation of Biochemical Energy2h 8m
22. Carbohydrate Metabolism2h 22m
23. Lipids2h 26m
24. Lipid Metabolism1h 45m
25. Protein and Amino Acid Metabolism1h 37m
26. Nucleic Acids and Protein Synthesis2h 54m

8. Gases, Liquids and Solids

The Ideal Gas Law Applications

GOB Chemistry

8. Gases, Liquids and Solids

The Ideal Gas Law Applications

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2:38 minutes

Problem 67d

Textbook Question

A balloon is filled with helium gas with a partial pressure of 1.00 atm and neon gas with a partial pressure of 0.50 atm. For each of the following changes (a to e) of the initial balloon, select the diagram (A, B, or C) that shows the final volume of the balloon:
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d. The Kelvin temperature doubles and half of the gas atoms leak out (P does not change).

Verified step by step guidance

Step 1: Begin by identifying the relationship between the variables in the problem. The problem involves changes in temperature and the number of gas atoms, while pressure remains constant. Use the combined gas law: \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles, \( R \) is the gas constant, and \( T \) is temperature.

Step 2: Analyze the changes described in the problem. The Kelvin temperature doubles, so \( T_{final} = 2T_{initial} \). Half of the gas atoms leak out, meaning \( n_{final} = \frac{1}{2}n_{initial} \). Since pressure \( P \) does not change, the relationship between \( V \), \( n \), and \( T \) can be expressed as \( V \propto \frac{nT}{P} \).

Step 3: Substitute the changes into the proportionality equation. Initially, \( V_{initial} \propto n_{initial}T_{initial} \). After the changes, \( V_{final} \propto \frac{1}{2}n_{initial} \cdot 2T_{initial} \). Simplify this expression to find \( V_{final} \propto n_{initial}T_{initial} \), which indicates that the final volume is equal to the initial volume.

Step 4: Interpret the diagram provided. The balloon's volume should remain unchanged because the doubling of temperature compensates for the halving of the number of gas atoms, keeping the product \( nT \) constant.

Step 5: Select the diagram that matches the unchanged volume of the balloon. Based on the analysis, the correct diagram is the one that shows the balloon with the same volume as the initial state.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Partial Pressure

Partial pressure refers to the pressure exerted by a single type of gas in a mixture of gases. In this scenario, the balloon contains helium and neon gases, each contributing to the total pressure. Understanding partial pressure is crucial for predicting how changes in gas composition or conditions affect the overall behavior of the gas mixture.

Ideal Gas Law

The Ideal Gas Law (PV=nRT) relates the pressure (P), volume (V), temperature (T), and number of moles (n) of a gas. In this question, the doubling of the Kelvin temperature while considering the number of gas atoms that leak out directly impacts the volume of the balloon. This law helps in understanding how gas behavior changes with temperature and quantity.

Gas Leakage and Volume Change

When gas leaks from a balloon, the number of gas particles decreases, which typically leads to a reduction in pressure and volume. However, in this case, the pressure remains constant while the temperature increases, which complicates the expected outcome. Analyzing how these factors interplay is essential for determining the final volume of the balloon after the specified changes.

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Related Practice

Textbook Question

Two flasks of equal volume and at the same temperature contain different gases. One flask contains 5.0 g of O₂ and the other flask contains 5.0 g of H₂. Is each of the following statements true or false? Explain.

b. The pressures in the flasks are the same.

Textbook Question

At 100 °C, which of the following diagrams (1, 2, or 3) represents a gas sample that exerts the:

b. highest pressure?

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Textbook Question

Indicate which diagram (1, 2, or 3) represents the volume of the gas sample in a flexible container when each of the following changes (a to d) takes place:

d. Doubling the atmospheric pressure and doubling the Kelvin temperature.

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Textbook Question

Indicate which diagram (1, 2, or 3) represents the volume of the gas sample in a flexible container when each of the following changes (a to d) takes place:

c. Atmospheric pressure decreases if temperature does not change.

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Textbook Question

At a restaurant, a customer chokes on a piece of food. You put your arms around the person's waist and use your fists to push up on the person's abdomen, an action called the Heimlich maneuver.

b. Why does it cause the person to expel the food item from the airway?

The relationship between the partial pressure of a gas (P) and the number of moles of that gas (n) is best represented by which of the following graphs?

b. The pressures in the flasks are the same.

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