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Mixture of equal masses of O2 and O3 gases are allowed to effuse through orifice then what will be the ratio of the rate of effusion of O3 and O2?
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Mixture of equal masses of O2 and O3 gases are allowed to effuse throu...
Effusion is the process by which a gas escapes through a small hole into a vacuum. According to Graham's law of effusion, the rate of effusion of a gas is inversely proportional to the square root of its molar mass.
In this case, we have a mixture of equal masses of O2 and O3 gases. To determine the ratio of their effusion rates, we need to compare their molar masses.
1. Molar Mass of O2:
The molar mass of O2 is calculated by adding the atomic masses of two oxygen atoms. The atomic mass of oxygen is approximately 16.00 g/mol. Therefore, the molar mass of O2 is:
Molar Mass of O2 = 2 * Atomic Mass of Oxygen = 2 * 16.00 g/mol = 32.00 g/mol
2. Molar Mass of O3:
The molar mass of O3 is calculated by adding the atomic masses of three oxygen atoms. Therefore, the molar mass of O3 is:
Molar Mass of O3 = 3 * Atomic Mass of Oxygen = 3 * 16.00 g/mol = 48.00 g/mol
3. Ratio of Effusion Rates:
According to Graham's law of effusion, the ratio of the rates of effusion of two gases is given by the square root of the ratio of their molar masses.
Rate of effusion of O3 / Rate of effusion of O2 = sqrt(Molar Mass of O2 / Molar Mass of O3)
Rate of effusion of O3 / Rate of effusion of O2 = sqrt(32.00 g/mol / 48.00 g/mol)
Rate of effusion of O3 / Rate of effusion of O2 = sqrt(2/3)
Therefore, the ratio of the rate of effusion of O3 to O2 is sqrt(2/3).
4. Simplifying the Ratio:
To simplify the ratio, we can multiply both the numerator and denominator by sqrt(3) to eliminate the square root:
Rate of effusion of O3 / Rate of effusion of O2 = (sqrt(2/3) * sqrt(3)) / (sqrt(3) * sqrt(1))
Rate of effusion of O3 / Rate of effusion of O2 = sqrt(6) / sqrt(3)
Rate of effusion of O3 / Rate of effusion of O2 = sqrt(2)
Therefore, the ratio of the rate of effusion of O3 to O2 is sqrt(2).
Conclusion:
The ratio of the rate of effusion of O3 to O2 is sqrt(2) or approximately 1.414. This means that O3 effuses approximately 1.414 times faster than O2 when both gases are present in equal masses.
In this case, we have a mixture of equal masses of O2 and O3 gases. To determine the ratio of their effusion rates, we need to compare their molar masses.
1. Molar Mass of O2:
The molar mass of O2 is calculated by adding the atomic masses of two oxygen atoms. The atomic mass of oxygen is approximately 16.00 g/mol. Therefore, the molar mass of O2 is:
Molar Mass of O2 = 2 * Atomic Mass of Oxygen = 2 * 16.00 g/mol = 32.00 g/mol
2. Molar Mass of O3:
The molar mass of O3 is calculated by adding the atomic masses of three oxygen atoms. Therefore, the molar mass of O3 is:
Molar Mass of O3 = 3 * Atomic Mass of Oxygen = 3 * 16.00 g/mol = 48.00 g/mol
3. Ratio of Effusion Rates:
According to Graham's law of effusion, the ratio of the rates of effusion of two gases is given by the square root of the ratio of their molar masses.
Rate of effusion of O3 / Rate of effusion of O2 = sqrt(Molar Mass of O2 / Molar Mass of O3)
Rate of effusion of O3 / Rate of effusion of O2 = sqrt(32.00 g/mol / 48.00 g/mol)
Rate of effusion of O3 / Rate of effusion of O2 = sqrt(2/3)
Therefore, the ratio of the rate of effusion of O3 to O2 is sqrt(2/3).
4. Simplifying the Ratio:
To simplify the ratio, we can multiply both the numerator and denominator by sqrt(3) to eliminate the square root:
Rate of effusion of O3 / Rate of effusion of O2 = (sqrt(2/3) * sqrt(3)) / (sqrt(3) * sqrt(1))
Rate of effusion of O3 / Rate of effusion of O2 = sqrt(6) / sqrt(3)
Rate of effusion of O3 / Rate of effusion of O2 = sqrt(2)
Therefore, the ratio of the rate of effusion of O3 to O2 is sqrt(2).
Conclusion:
The ratio of the rate of effusion of O3 to O2 is sqrt(2) or approximately 1.414. This means that O3 effuses approximately 1.414 times faster than O2 when both gases are present in equal masses.
Community Answer
Mixture of equal masses of O2 and O3 gases are allowed to effuse throu...
Rate(O3)/rate(O2)=(√molar mass of O2)/(√molar mass of O3) =√32/√48=√2/√3
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Mixture of equal masses of O2 and O3 gases are allowed to effuse through orifice then what will be the ratio of the rate of effusion of O3 and O2?
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Mixture of equal masses of O2 and O3 gases are allowed to effuse through orifice then what will be the ratio of the rate of effusion of O3 and O2? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Mixture of equal masses of O2 and O3 gases are allowed to effuse through orifice then what will be the ratio of the rate of effusion of O3 and O2? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Mixture of equal masses of O2 and O3 gases are allowed to effuse through orifice then what will be the ratio of the rate of effusion of O3 and O2?.
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