### Ideal Gas Law Calculation for Neon GasGiven:- Volume of neon gas (Ne): \( 42 \, \text{L} \)- Pressure: \( 0.41 \, \text{atm} \)- Temperature: \( 460 \, \text{K} \)- Atomic mass of neon: \( 20.2 \, \text{g/mol} \)- Ideal gas constant, \( R \): \( 8.314 \, \text{J/(mol·K)} \)The mass of the neon gas is closest to:#### Options:A. \( 0.001717 \, \text{kg} \) B. \( 0.009644 \, \text{kg} \) C. \( 0.001636 \, \text{kg} \) D. \( 0.001566 \, \text{kg} \) E. \( 0.009214 \, \text{kg} \) F. \( 0.001595 \, \text{kg} \)### Steps to Solve:1. **Convert given values to SI units where necessary:** - Pressure: \( 0.41 \, \text{atm} = 0.41 \times 101325 \, \text{Pa} = 41543.25 \, \text{Pa} \) - Volume: \( 42 \, \text{L} = 42 \times 10^{-3} \, \text{m}^3 = 0.042 \, \text{m}^3 \) 2. **Use the ideal gas law \( PV = nRT \) to find the number of moles \( n \):** \[ n = \frac{PV}{RT} \] \[ n = \frac{ (41543.25 \, \text{Pa}) (0.042 \, \text{m}^3)}{ (8.314 \, \text{J/(mol·K)}) (460 \, \text{K})} \] \[ n \approx \frac{1744.812}{3812.44} \approx 0.457 \, \text{mol} \]3. **Convert moles of neon

Given data: Volume , V=4.2 L Pressure, P=4.1 atm Temperature, T=460 K Atomic mass of neon, M=20.2…

MXJWA A 4.2 L volume of neon gas (Ne) is at a pressure of 4.1 atm and a temperature of 460 K. The atomic mass of neon is 20.2_g/mol, and the ideal gas constant is R = 8.314.J/mol K. The mass of the neon gas is closest to 8. D. 0.01717 kg 0.00964 kg 0.01566 kg 0.009214 kg E. 0.01636 kg F. 0.01595 kg ARC 1--1

MXJWA A 4.2 L volume of neon gas (Ne) is at a pressure of 4.1 atm and a temperature of 460 K. The atomic mass of neon is 20.2_g/mol, and the ideal gas constant is R = 8.314.J/mol K. The mass of the neon gas is closest to 8. D. 0.01717 kg 0.00964 kg 0.01566 kg 0.009214 kg E. 0.01636 kg F. 0.01595 kg ARC 1--1

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ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

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Concept explainers

First law of Thermodynamics

The word thermodynamics consists of two words: thermo- and dynamics. Dynamics means the study of motion. The field of thermodynamics is all about the study of the movement of heat. In a more meaningful way, it is stated as the study of the transfer of energy. Energy transfer is something that we encounter in day-to-day life. Automobiles, chemical reactions, refrigerators, and power generators work on the basis of thermodynamic principles.

Question

### Ideal Gas Law Calculation for Neon Gas

Given:
- Volume of neon gas (Ne): \( 42 \, \text{L} \)
- Pressure: \( 0.41 \, \text{atm} \)
- Temperature: \( 460 \, \text{K} \)
- Atomic mass of neon: \( 20.2 \, \text{g/mol} \)
- Ideal gas constant, \( R \): \( 8.314 \, \text{J/(mol·K)} \)

The mass of the neon gas is closest to:

#### Options:
A. \( 0.001717 \, \text{kg} \)
B. \( 0.009644 \, \text{kg} \)
C. \( 0.001636 \, \text{kg} \)
D. \( 0.001566 \, \text{kg} \)
E. \( 0.009214 \, \text{kg} \)
F. \( 0.001595 \, \text{kg} \)

### Steps to Solve:
1. **Convert given values to SI units where necessary:**
- Pressure: \( 0.41 \, \text{atm} = 0.41 \times 101325 \, \text{Pa} = 41543.25 \, \text{Pa} \)
- Volume: \( 42 \, \text{L} = 42 \times 10^{-3} \, \text{m}^3 = 0.042 \, \text{m}^3 \)

2. **Use the ideal gas law \( PV = nRT \) to find the number of moles \( n \):**
\[
n = \frac{PV}{RT}
\]
\[
n = \frac{ (41543.25 \, \text{Pa}) (0.042 \, \text{m}^3)}{ (8.314 \, \text{J/(mol·K)}) (460 \, \text{K})}
\]
\[
n \approx \frac{1744.812}{3812.44} \approx 0.457 \, \text{mol}
\]

3. **Convert moles of neon

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