A sealed 99 m3 tank is filled with 6000 moles of ideal oxygen gas (diatomic) at an initial temperature of 270 K. The gas is heated to a final temperature of 320 K. The atomic mass of oxygen is 16.0 g/mol. The mass density of the oxygen gas, in Sl units, is closest to:
A sealed 99 m3 tank is filled with 6000 moles of ideal oxygen gas (diatomic) at an initial temperature of 270 K. The gas is heated to a final temperature of 320 K. The atomic mass of oxygen is 16.0 g/mol. The mass density of the oxygen gas, in Sl units, is closest to:
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![### Question 7
A sealed 99 m³ tank is filled with 6000 moles of ideal oxygen gas (diatomic) at an initial temperature of 270 K. The gas is heated to a final temperature of 320 K. The atomic mass of oxygen is 16.0 g/mol. The mass density of the oxygen gas, in SI units, is closest to:
- 3.9
- 1.9
- 1.5
- 2.4
- 0.97
#### Explanation:
To determine the closest mass density of the oxygen gas, you can use the data provided from the problem.
For reference:
\[
\text{Density} (\rho) = \frac{\text{mass}}{\text{volume}}
\]
Mass can be calculated using the number of moles and the atomic mass:
\[
\text{Mass} = \text{moles} \times \text{molecular mass}
\]
Given:
- Volume \( V = 99 \, m^3 \)
- Moles \( n = 6000 \) moles
- Molecular mass of O\(_2\) (since it is diatomic) = \( 2 \times 16 = 32 \, g/mol = 0.032 \, kg/mol \)
So, the mass of the gas is:
\[
\text{Mass} = 6000 \, \text{moles} \times 0.032 \, \text{kg/mol} = 192 \, \text{kg}
\]
Finally, density is:
\[
\rho = \frac{192 \, \text{kg}}{99 \, m^3} \approx 1.939 \, kg/m^3
\]
The closest value to this result is 1.9, so the correct answer is:
- 1.9](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8689a897-6f19-4f8c-bce2-bc1e854b9491%2Ff4ac4eb1-f486-4cf2-b60f-b5775fb778ec%2Ftt2qsq.jpeg&w=3840&q=75)
Transcribed Image Text:### Question 7
A sealed 99 m³ tank is filled with 6000 moles of ideal oxygen gas (diatomic) at an initial temperature of 270 K. The gas is heated to a final temperature of 320 K. The atomic mass of oxygen is 16.0 g/mol. The mass density of the oxygen gas, in SI units, is closest to:
- 3.9
- 1.9
- 1.5
- 2.4
- 0.97
#### Explanation:
To determine the closest mass density of the oxygen gas, you can use the data provided from the problem.
For reference:
\[
\text{Density} (\rho) = \frac{\text{mass}}{\text{volume}}
\]
Mass can be calculated using the number of moles and the atomic mass:
\[
\text{Mass} = \text{moles} \times \text{molecular mass}
\]
Given:
- Volume \( V = 99 \, m^3 \)
- Moles \( n = 6000 \) moles
- Molecular mass of O\(_2\) (since it is diatomic) = \( 2 \times 16 = 32 \, g/mol = 0.032 \, kg/mol \)
So, the mass of the gas is:
\[
\text{Mass} = 6000 \, \text{moles} \times 0.032 \, \text{kg/mol} = 192 \, \text{kg}
\]
Finally, density is:
\[
\rho = \frac{192 \, \text{kg}}{99 \, m^3} \approx 1.939 \, kg/m^3
\]
The closest value to this result is 1.9, so the correct answer is:
- 1.9
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