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...
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![**Chemistry Practice Problem: Gas Density Calculation**
**Problem:**
The density of NO₂ in a 4.50 L tank at 760.0 torr and 25.0 ℃ is _______ g/L.
**Options:**
- A. 1.68
- B. 1.88
- C. 3.27
- D. 1.64
- E. 9.30
**Explanation:**
The problem requires calculating the density of nitrogen dioxide (NO₂) under specified conditions using the Ideal Gas Law in conjunction with density formulas. Recall:
1. Convert the given conditions to appropriate units (if necessary). Here, pressure is already given in torr which is equivalent to 1 atm.
2. Use the Ideal Gas Law:
\[ PV = nRT \]
where \( P \) = pressure, \( V \) = volume, \( n \) = number of moles, \( R \) = ideal gas constant (0.0821 L·atm/(mol·K)), and \( T \) = temperature in Kelvin.
3. Calculate the molar mass of NO₂:
\[ \text{Molar mass of NO}_2 = 14 \, (\text{N}) + 2 \times 16 \, (\text{O}) = 46 \, \text{g/mol} \]
4. Convert temperature to Kelvin:
\[ T = 25.0 + 273.15 = 298.15 \, \text{K} \]
5. Using the Ideal Gas Law to find \( n \):
\[ P = 1 \, \text{atm} \]
\[ V = 4.50 \, \text{L} \]
\[ n = \frac{PV}{RT} = \frac{(1)(4.50)}{(0.0821)(298.15)} = 0.184 \, \text{moles} \]
6. Calculate the mass from moles:
\[ \text{Mass} = n \times \text{Molar mass} = 0.184 \, \text{moles} \times 46 \, \text{g/mol} = 8.464 \, \text{g} \]
7. Finally, calculate the density:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0ec4e4dd-380a-451c-aeb3-9cf66efaad71%2F6bbf1e02-1349-49dc-bc8f-53e904c712ae%2F0k9tasw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Chemistry Practice Problem: Gas Density Calculation**
**Problem:**
The density of NO₂ in a 4.50 L tank at 760.0 torr and 25.0 ℃ is _______ g/L.
**Options:**
- A. 1.68
- B. 1.88
- C. 3.27
- D. 1.64
- E. 9.30
**Explanation:**
The problem requires calculating the density of nitrogen dioxide (NO₂) under specified conditions using the Ideal Gas Law in conjunction with density formulas. Recall:
1. Convert the given conditions to appropriate units (if necessary). Here, pressure is already given in torr which is equivalent to 1 atm.
2. Use the Ideal Gas Law:
\[ PV = nRT \]
where \( P \) = pressure, \( V \) = volume, \( n \) = number of moles, \( R \) = ideal gas constant (0.0821 L·atm/(mol·K)), and \( T \) = temperature in Kelvin.
3. Calculate the molar mass of NO₂:
\[ \text{Molar mass of NO}_2 = 14 \, (\text{N}) + 2 \times 16 \, (\text{O}) = 46 \, \text{g/mol} \]
4. Convert temperature to Kelvin:
\[ T = 25.0 + 273.15 = 298.15 \, \text{K} \]
5. Using the Ideal Gas Law to find \( n \):
\[ P = 1 \, \text{atm} \]
\[ V = 4.50 \, \text{L} \]
\[ n = \frac{PV}{RT} = \frac{(1)(4.50)}{(0.0821)(298.15)} = 0.184 \, \text{moles} \]
6. Calculate the mass from moles:
\[ \text{Mass} = n \times \text{Molar mass} = 0.184 \, \text{moles} \times 46 \, \text{g/mol} = 8.464 \, \text{g} \]
7. Finally, calculate the density:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} =
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