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A 25 x 10-3 m3 volume cylinder is filled with 1 mol of O2 gas at room temperature (300 K). The molecular diameter of O2 and its root mean square speed, are found to be 0.3 nm and 200 m/s, respectively. What is the average collision rate (per second) for an O2 molecule?
- a)~102
- b)~1010
- c)~1013
- d)~1011
Correct answer is option 'B'. Can you explain this answer?
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A 25 x 10-3 m3 volume cylinder is filled with 1 mol of O2 gas at room ...
Putting values,
Frequency 0.2 x 1010/sec
or Frequency ≌ 1010/sec
Frequency 0.2 x 1010/sec
or Frequency ≌ 1010/sec
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A 25 x 10-3 m3 volume cylinder is filled with 1 mol of O2 gas at room ...
To determine the average collision rate per second for an O2 molecule in the given scenario, we need to consider the volume of the cylinder, the molecular diameter of O2, and its root mean square speed.
1. Calculate the number of O2 molecules:
Given that 1 mole of O2 gas is present, we can use Avogadro's number (6.022 × 10^23 mol^-1) to calculate the number of O2 molecules. Therefore, the number of O2 molecules is:
Number of O2 molecules = 1 mol × 6.022 × 10^23 mol^-1 = 6.022 × 10^23 molecules
2. Determine the volume occupied by a single O2 molecule:
The volume occupied by a single O2 molecule can be approximated as a sphere with a diameter equal to the molecular diameter of O2 (0.3 nm). Using the formula for the volume of a sphere, we can calculate the volume occupied by a single O2 molecule as:
Volume of a single O2 molecule = (4/3)π(r^3) = (4/3)π(0.3/2)^3 = 0.014137 nm^3
3. Calculate the total volume occupied by all O2 molecules:
The total volume occupied by all O2 molecules can be calculated by multiplying the volume of a single molecule by the number of molecules:
Total volume occupied by O2 molecules = Volume of a single O2 molecule × Number of O2 molecules
Total volume occupied by O2 molecules = 0.014137 nm^3 × 6.022 × 10^23 molecules = 8.507 × 10^21 nm^3
4. Convert the total volume to cubic meters:
To calculate the average collision rate per second, we need to convert the total volume occupied by O2 molecules to cubic meters:
Total volume occupied by O2 molecules = 8.507 × 10^21 nm^3
Converting nm^3 to m^3: 1 nm^3 = (10^-9 m)^3 = 10^-27 m^3
Total volume occupied by O2 molecules = 8.507 × 10^21 nm^3 × 10^-27 m^3/nm^3 = 8.507 × 10^-6 m^3
5. Determine the average collision rate per second:
The average collision rate per second can be calculated using the formula:
Collision rate = (Total volume occupied by O2 molecules) / (Volume of the cylinder × Root mean square speed of O2)
Collision rate = 8.507 × 10^-6 m^3 / (25 × 10^-3 m^3 × 200 m/s)
Collision rate ≈ 1.7014 × 10^-2 s^-1
Since the collision rate is approximately 1.7014 × 10^-2 s^-1, which is of the order of 10^0, the correct answer is approximately 10^0, or option (b) ~10^10.
1. Calculate the number of O2 molecules:
Given that 1 mole of O2 gas is present, we can use Avogadro's number (6.022 × 10^23 mol^-1) to calculate the number of O2 molecules. Therefore, the number of O2 molecules is:
Number of O2 molecules = 1 mol × 6.022 × 10^23 mol^-1 = 6.022 × 10^23 molecules
2. Determine the volume occupied by a single O2 molecule:
The volume occupied by a single O2 molecule can be approximated as a sphere with a diameter equal to the molecular diameter of O2 (0.3 nm). Using the formula for the volume of a sphere, we can calculate the volume occupied by a single O2 molecule as:
Volume of a single O2 molecule = (4/3)π(r^3) = (4/3)π(0.3/2)^3 = 0.014137 nm^3
3. Calculate the total volume occupied by all O2 molecules:
The total volume occupied by all O2 molecules can be calculated by multiplying the volume of a single molecule by the number of molecules:
Total volume occupied by O2 molecules = Volume of a single O2 molecule × Number of O2 molecules
Total volume occupied by O2 molecules = 0.014137 nm^3 × 6.022 × 10^23 molecules = 8.507 × 10^21 nm^3
4. Convert the total volume to cubic meters:
To calculate the average collision rate per second, we need to convert the total volume occupied by O2 molecules to cubic meters:
Total volume occupied by O2 molecules = 8.507 × 10^21 nm^3
Converting nm^3 to m^3: 1 nm^3 = (10^-9 m)^3 = 10^-27 m^3
Total volume occupied by O2 molecules = 8.507 × 10^21 nm^3 × 10^-27 m^3/nm^3 = 8.507 × 10^-6 m^3
5. Determine the average collision rate per second:
The average collision rate per second can be calculated using the formula:
Collision rate = (Total volume occupied by O2 molecules) / (Volume of the cylinder × Root mean square speed of O2)
Collision rate = 8.507 × 10^-6 m^3 / (25 × 10^-3 m^3 × 200 m/s)
Collision rate ≈ 1.7014 × 10^-2 s^-1
Since the collision rate is approximately 1.7014 × 10^-2 s^-1, which is of the order of 10^0, the correct answer is approximately 10^0, or option (b) ~10^10.
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A 25 x 10-3 m3 volume cylinder is filled with 1 mol of O2 gas at room temperature (300 K). The molecular diameter of O2 and its root mean square speed, are found to be 0.3 nm and 200 m/s, respectively. What is the average collision rate (per second) for an O2 molecule?a)~102b)~1010c)~1013d)~1011Correct answer is option 'B'. Can you explain this answer?
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A 25 x 10-3 m3 volume cylinder is filled with 1 mol of O2 gas at room temperature (300 K). The molecular diameter of O2 and its root mean square speed, are found to be 0.3 nm and 200 m/s, respectively. What is the average collision rate (per second) for an O2 molecule?a)~102b)~1010c)~1013d)~1011Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A 25 x 10-3 m3 volume cylinder is filled with 1 mol of O2 gas at room temperature (300 K). The molecular diameter of O2 and its root mean square speed, are found to be 0.3 nm and 200 m/s, respectively. What is the average collision rate (per second) for an O2 molecule?a)~102b)~1010c)~1013d)~1011Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 25 x 10-3 m3 volume cylinder is filled with 1 mol of O2 gas at room temperature (300 K). The molecular diameter of O2 and its root mean square speed, are found to be 0.3 nm and 200 m/s, respectively. What is the average collision rate (per second) for an O2 molecule?a)~102b)~1010c)~1013d)~1011Correct answer is option 'B'. Can you explain this answer?.
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