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Calculate the root mean square velocity of ozone kept in a closed vessel at 20°C and 82 cm mercury pressure.
Correct answer is '390.2'. Can you explain this answer?
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Calculate the root mean square velocity of ozone kept in a closed vess...
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Calculate the root mean square velocity of ozone kept in a closed vess...
To calculate the root mean square velocity (vrms) of a gas, we can use the following formula:
vrms = √(3 * k * T / m)
Where:
- vrms is the root mean square velocity
- k is the Boltzmann constant (1.38 × 10^-23 J/K)
- T is the temperature in Kelvin
- m is the molar mass of the gas in kg
First, we need to convert the temperature from Celsius to Kelvin:
T = 20 + 273.15 = 293.15 K
The molar mass of ozone (O3) is approximately 48 g/mol or 0.048 kg/mol.
Now we can substitute the values into the formula:
vrms = √(3 * 1.38 × 10^-23 J/K * 293.15 K / 0.048 kg/mol)
vrms = √(3 * 1.38 × 10^-23 J * 293.15 / 0.048 kg)
vrms = √(1.6134 × 10^-20 J * 293.15 / 0.048 kg)
vrms = √(4.72929 × 10^-18 J / 0.048 kg)
vrms = √9.85394 × 10^-17 m²/s²)
Converting the units to cm/s:
vrms = √(9.85394 × 10^-17 m²/s²) * (100 cm/1 m) * (1 s/1 s)
vrms = √(9.85394 × 10^-15 cm²/s²)
vrms = 9.926 × 10^-8 cm/s
Therefore, the root mean square velocity of ozone at 20°C in a closed vessel is approximately 9.926 × 10^-8 cm/s.
vrms = √(3 * k * T / m)
Where:
- vrms is the root mean square velocity
- k is the Boltzmann constant (1.38 × 10^-23 J/K)
- T is the temperature in Kelvin
- m is the molar mass of the gas in kg
First, we need to convert the temperature from Celsius to Kelvin:
T = 20 + 273.15 = 293.15 K
The molar mass of ozone (O3) is approximately 48 g/mol or 0.048 kg/mol.
Now we can substitute the values into the formula:
vrms = √(3 * 1.38 × 10^-23 J/K * 293.15 K / 0.048 kg/mol)
vrms = √(3 * 1.38 × 10^-23 J * 293.15 / 0.048 kg)
vrms = √(1.6134 × 10^-20 J * 293.15 / 0.048 kg)
vrms = √(4.72929 × 10^-18 J / 0.048 kg)
vrms = √9.85394 × 10^-17 m²/s²)
Converting the units to cm/s:
vrms = √(9.85394 × 10^-17 m²/s²) * (100 cm/1 m) * (1 s/1 s)
vrms = √(9.85394 × 10^-15 cm²/s²)
vrms = 9.926 × 10^-8 cm/s
Therefore, the root mean square velocity of ozone at 20°C in a closed vessel is approximately 9.926 × 10^-8 cm/s.
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Calculate the root mean square velocity of ozone kept in a closed vess...
To calculate the root mean square (RMS) velocity of ozone at 20°C, we can use the equation:
RMS velocity = sqrt(3 * k * T / m)
Where:
- k is the Boltzmann constant (1.38 x 10^-23 J/K)
- T is the temperature in Kelvin (20°C = 293.15 K)
- m is the molar mass of ozone (48 g/mol)
First, let's convert the molar mass of ozone to kg/mol:
molar mass of ozone = 48 g/mol = 0.048 kg/mol
Now, let's calculate the RMS velocity:
RMS velocity = sqrt(3 * (1.38 x 10^-23 J/K) * (293.15 K) / (0.048 kg/mol))
RMS velocity ≈ sqrt(6.422 x 10^-21 J / (kg/mol))
To convert the units from m^2/s^2 to cm/s, we need to multiply by the conversion factor of 100 cm/m:
RMS velocity ≈ sqrt(6.422 x 10^-19 cm^2 / (kg/mol))
Now, we need to convert the units from kg/mol to g/mol by multiplying by 1000 g/kg:
RMS velocity ≈ sqrt(6.422 x 10^-16 cm^2 / (g/mol))
Finally, we can simplify the equation and calculate the RMS velocity:
RMS velocity ≈ 8.02 x 10^6 cm/s
Therefore, the root mean square velocity of ozone kept in a closed vessel at 20°C is approximately 8.02 x 10^6 cm/s.
RMS velocity = sqrt(3 * k * T / m)
Where:
- k is the Boltzmann constant (1.38 x 10^-23 J/K)
- T is the temperature in Kelvin (20°C = 293.15 K)
- m is the molar mass of ozone (48 g/mol)
First, let's convert the molar mass of ozone to kg/mol:
molar mass of ozone = 48 g/mol = 0.048 kg/mol
Now, let's calculate the RMS velocity:
RMS velocity = sqrt(3 * (1.38 x 10^-23 J/K) * (293.15 K) / (0.048 kg/mol))
RMS velocity ≈ sqrt(6.422 x 10^-21 J / (kg/mol))
To convert the units from m^2/s^2 to cm/s, we need to multiply by the conversion factor of 100 cm/m:
RMS velocity ≈ sqrt(6.422 x 10^-19 cm^2 / (kg/mol))
Now, we need to convert the units from kg/mol to g/mol by multiplying by 1000 g/kg:
RMS velocity ≈ sqrt(6.422 x 10^-16 cm^2 / (g/mol))
Finally, we can simplify the equation and calculate the RMS velocity:
RMS velocity ≈ 8.02 x 10^6 cm/s
Therefore, the root mean square velocity of ozone kept in a closed vessel at 20°C is approximately 8.02 x 10^6 cm/s.
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Calculate the root mean square velocity of ozone kept in a closed vessel at 20°C and 82 cm mercury pressure.Correct answer is '390.2'. Can you explain this answer?
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Calculate the root mean square velocity of ozone kept in a closed vessel at 20°C and 82 cm mercury pressure.Correct answer is '390.2'. Can you explain this answer? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about Calculate the root mean square velocity of ozone kept in a closed vessel at 20°C and 82 cm mercury pressure.Correct answer is '390.2'. Can you explain this answer? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Calculate the root mean square velocity of ozone kept in a closed vessel at 20°C and 82 cm mercury pressure.Correct answer is '390.2'. Can you explain this answer?.
Calculate the root mean square velocity of ozone kept in a closed vessel at 20°C and 82 cm mercury pressure.Correct answer is '390.2'. Can you explain this answer? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about Calculate the root mean square velocity of ozone kept in a closed vessel at 20°C and 82 cm mercury pressure.Correct answer is '390.2'. Can you explain this answer? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Calculate the root mean square velocity of ozone kept in a closed vessel at 20°C and 82 cm mercury pressure.Correct answer is '390.2'. Can you explain this answer?.
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