Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Get the answers you need quickly and accurately from a dedicated community of experts on our Q&A platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
To solve this problem, we will systematically explore the properties of each flask to determine which statement is true:
### Data Given:
- Flask Volume (both flasks): 2.0 L
- Temperature (both flasks): 298 K
- Mass of O2 in Flask A: 16.00 grams
- Mass of N2 in Flask B: 28.0 grams
### Molecular Weights:
- Molar Mass of O2: 32.00 g/mol
- Molar Mass of N2: 28.02 g/mol
### Calculations:
1. Number of Moles:
For Flask A (O2):
[tex]\[ \text{Moles of O2} = \frac{\text{mass}}{\text{molar mass}} = \frac{16.00 \text{ g}}{32.00 \text{ g/mol}} = 0.5 \text{ mol} \][/tex]
For Flask B (N2):
[tex]\[ \text{Moles of N2} = \frac{\text{mass}}{\text{molar mass}} = \frac{28.0 \text{ g}}{28.02 \text{ g/mol}} \approx 1.0 \text{ mol} \][/tex]
2. Using the Ideal Gas Law (PV = nRT):
Where R (gas constant) = 0.0821 L·atm/(mol·K)
For Flask A:
[tex]\[ P_A = \frac{n \cdot R \cdot T}{V} = \frac{0.5 \cdot 0.0821 \cdot 298}{2.0} \approx 6.12 \text{ atm} \][/tex]
For Flask B:
[tex]\[ P_B = \frac{n \cdot R \cdot T}{V} = \frac{1.0 \cdot 0.0821 \cdot 298}{2.0} \approx 12.22 \text{ atm} \][/tex]
3. Density:
Density is calculated as:
[tex]\[ \text{Density} = \frac{\text{mass}}{\text{volume}} \][/tex]
For Flask A:
[tex]\[ \text{Density}_A = \frac{16.00 \text{ g}}{2.0 \text{ L}} = 8.0 \text{ g/L} \][/tex]
For Flask B:
[tex]\[ \text{Density}_B = \frac{28.0 \text{ g}}{2.0 \text{ L}} = 14.0 \text{ g/L} \][/tex]
4. Number of Molecules:
Using Avogadro's number ([tex]\(6.022 \times 10^{23}\)[/tex] molecules/mol):
For Flask A:
[tex]\[ \text{Number of molecules in Flask A} = 0.5 \text{ mol} \times 6.022 \times 10^{23} \approx 3.011 \times 10^{23} \text{ molecules} \][/tex]
For Flask B:
[tex]\[ \text{Number of molecules in Flask B} = 1.0 \text{ mol} \times 6.022 \times 10^{23} \approx 6.0177 \times 10^{23} \text{ molecules} \][/tex]
### Comparison of Statements:
- Statement a: Flask A contains molecules with higher average kinetic energy than Flask B.
- This is false because the average kinetic energy of gas molecules depends on temperature, which is the same for both flasks.
- Statement b: Flask A has a higher density than Flask B.
- This is false because the density of Flask A (8.0 g/L) is less than the density of Flask B (14.0 g/L).
- Statement c: Flask A contains fewer molecules than Flask B.
- This is true because Flask A contains approximately [tex]\(3.011 \times 10^{23}\)[/tex] molecules, which is less than the approximately [tex]\(6.0177 \times 10^{23}\)[/tex] molecules in Flask B.
- Statement d: Flask A has a higher pressure than Flask B.
- This is false because the pressure in Flask A (6.12 atm) is less than the pressure in Flask B (12.22 atm).
### Conclusion:
The correct statement is:
c. Flask A contains fewer molecules than Flask B.
### Data Given:
- Flask Volume (both flasks): 2.0 L
- Temperature (both flasks): 298 K
- Mass of O2 in Flask A: 16.00 grams
- Mass of N2 in Flask B: 28.0 grams
### Molecular Weights:
- Molar Mass of O2: 32.00 g/mol
- Molar Mass of N2: 28.02 g/mol
### Calculations:
1. Number of Moles:
For Flask A (O2):
[tex]\[ \text{Moles of O2} = \frac{\text{mass}}{\text{molar mass}} = \frac{16.00 \text{ g}}{32.00 \text{ g/mol}} = 0.5 \text{ mol} \][/tex]
For Flask B (N2):
[tex]\[ \text{Moles of N2} = \frac{\text{mass}}{\text{molar mass}} = \frac{28.0 \text{ g}}{28.02 \text{ g/mol}} \approx 1.0 \text{ mol} \][/tex]
2. Using the Ideal Gas Law (PV = nRT):
Where R (gas constant) = 0.0821 L·atm/(mol·K)
For Flask A:
[tex]\[ P_A = \frac{n \cdot R \cdot T}{V} = \frac{0.5 \cdot 0.0821 \cdot 298}{2.0} \approx 6.12 \text{ atm} \][/tex]
For Flask B:
[tex]\[ P_B = \frac{n \cdot R \cdot T}{V} = \frac{1.0 \cdot 0.0821 \cdot 298}{2.0} \approx 12.22 \text{ atm} \][/tex]
3. Density:
Density is calculated as:
[tex]\[ \text{Density} = \frac{\text{mass}}{\text{volume}} \][/tex]
For Flask A:
[tex]\[ \text{Density}_A = \frac{16.00 \text{ g}}{2.0 \text{ L}} = 8.0 \text{ g/L} \][/tex]
For Flask B:
[tex]\[ \text{Density}_B = \frac{28.0 \text{ g}}{2.0 \text{ L}} = 14.0 \text{ g/L} \][/tex]
4. Number of Molecules:
Using Avogadro's number ([tex]\(6.022 \times 10^{23}\)[/tex] molecules/mol):
For Flask A:
[tex]\[ \text{Number of molecules in Flask A} = 0.5 \text{ mol} \times 6.022 \times 10^{23} \approx 3.011 \times 10^{23} \text{ molecules} \][/tex]
For Flask B:
[tex]\[ \text{Number of molecules in Flask B} = 1.0 \text{ mol} \times 6.022 \times 10^{23} \approx 6.0177 \times 10^{23} \text{ molecules} \][/tex]
### Comparison of Statements:
- Statement a: Flask A contains molecules with higher average kinetic energy than Flask B.
- This is false because the average kinetic energy of gas molecules depends on temperature, which is the same for both flasks.
- Statement b: Flask A has a higher density than Flask B.
- This is false because the density of Flask A (8.0 g/L) is less than the density of Flask B (14.0 g/L).
- Statement c: Flask A contains fewer molecules than Flask B.
- This is true because Flask A contains approximately [tex]\(3.011 \times 10^{23}\)[/tex] molecules, which is less than the approximately [tex]\(6.0177 \times 10^{23}\)[/tex] molecules in Flask B.
- Statement d: Flask A has a higher pressure than Flask B.
- This is false because the pressure in Flask A (6.12 atm) is less than the pressure in Flask B (12.22 atm).
### Conclusion:
The correct statement is:
c. Flask A contains fewer molecules than Flask B.
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.
