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Given that the most probable speed of oxygen gas is 1000 ms–1, the mean/average speed (ms–1) under the same conditions is:
- a)1224
- b)1128
- c)886
- d)816
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Given that the most probable speed of oxygen gas is 1000 ms–1, t...
⁻¹, calculate its root mean square speed.
The root mean square (rms) speed of a gas can be calculated using the formula:
v_rms = √(3kT/m)
where k is the Boltzmann constant (1.38 × 10⁻²³ J/K), T is the temperature in Kelvin, and m is the mass of one molecule of the gas.
To calculate the rms speed of oxygen gas, we need to know its temperature and mass.
The temperature is not given in the question, so we will assume a standard temperature of 273 K (0°C).
The mass of one molecule of oxygen gas (O₂) is 32 g/mol (since oxygen gas is composed of two oxygen atoms, each with a mass of 16 g/mol).
Converting the mass to kilograms:
m = 32 g/mol × (1 kg/1000 g) = 0.032 kg/mol
To find the mass of one molecule, we divide by Avogadro's number (6.02 × 10²³ molecules/mol):
m = 0.032 kg/mol ÷ (6.02 × 10²³ molecules/mol) = 5.32 × 10⁻²⁶ kg/molecule
Now we can substitute these values into the rms speed formula:
v_rms = √(3kT/m)
v_rms = √[(3 × 1.38 × 10⁻²³ J/K × 273 K) / (5.32 × 10⁻²⁶ kg/molecule)]
v_rms = 484 m/s
Therefore, the root mean square speed of oxygen gas is approximately 484 m/s.
The root mean square (rms) speed of a gas can be calculated using the formula:
v_rms = √(3kT/m)
where k is the Boltzmann constant (1.38 × 10⁻²³ J/K), T is the temperature in Kelvin, and m is the mass of one molecule of the gas.
To calculate the rms speed of oxygen gas, we need to know its temperature and mass.
The temperature is not given in the question, so we will assume a standard temperature of 273 K (0°C).
The mass of one molecule of oxygen gas (O₂) is 32 g/mol (since oxygen gas is composed of two oxygen atoms, each with a mass of 16 g/mol).
Converting the mass to kilograms:
m = 32 g/mol × (1 kg/1000 g) = 0.032 kg/mol
To find the mass of one molecule, we divide by Avogadro's number (6.02 × 10²³ molecules/mol):
m = 0.032 kg/mol ÷ (6.02 × 10²³ molecules/mol) = 5.32 × 10⁻²⁶ kg/molecule
Now we can substitute these values into the rms speed formula:
v_rms = √(3kT/m)
v_rms = √[(3 × 1.38 × 10⁻²³ J/K × 273 K) / (5.32 × 10⁻²⁶ kg/molecule)]
v_rms = 484 m/s
Therefore, the root mean square speed of oxygen gas is approximately 484 m/s.
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