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Directions: The answer to following question is a single digit integer ranging from 0 to 9. Enter the correct digit in the box given below.
The ratio between the root mean square speed of H2 at -223oC and that of O2 at 527oC is
Correct answer is '1'. Can you explain this answer?
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Directions: The answer to following question is a single digit integer...
Understanding Root Mean Square Speed
The root mean square (RMS) speed of a gas is given by the formula:
RMS speed = sqrt(3RT/M)
Where:
- R = Ideal gas constant (8.314 J/(mol·K))
- T = Absolute temperature in Kelvin
- M = Molar mass of the gas in kg/mol
Step 1: Convert Temperatures to Kelvin
- For H2 at -223°C:
- T(H2) = -223 + 273.15 = 50.15 K
- For O2 at 527°C:
- T(O2) = 527 + 273.15 = 800.15 K
Step 2: Determine Molar Masses
- Molar mass of H2 = 2 g/mol = 0.002 kg/mol
- Molar mass of O2 = 32 g/mol = 0.032 kg/mol
Step 3: Calculate RMS Speeds
- RMS speed of H2:
- RMS(H2) = sqrt(3 * 8.314 * 50.15 / 0.002)
- RMS speed of O2:
- RMS(O2) = sqrt(3 * 8.314 * 800.15 / 0.032)
Step 4: Find the Ratio
- The ratio of the RMS speeds is:
- Ratio = RMS(H2) / RMS(O2)
This ratio simplifies to:
Ratio = (sqrt(50.15 / 0.002)) / (sqrt(800.15 / 0.032))
When calculated, it results in a ratio close to 1.
Conclusion
The final answer to the ratio of the RMS speed of H2 at -223°C to that of O2 at 527°C is indeed '1'. This means that the speeds are comparable when considering the effects of temperature and molar mass.
The root mean square (RMS) speed of a gas is given by the formula:
RMS speed = sqrt(3RT/M)
Where:
- R = Ideal gas constant (8.314 J/(mol·K))
- T = Absolute temperature in Kelvin
- M = Molar mass of the gas in kg/mol
Step 1: Convert Temperatures to Kelvin
- For H2 at -223°C:
- T(H2) = -223 + 273.15 = 50.15 K
- For O2 at 527°C:
- T(O2) = 527 + 273.15 = 800.15 K
Step 2: Determine Molar Masses
- Molar mass of H2 = 2 g/mol = 0.002 kg/mol
- Molar mass of O2 = 32 g/mol = 0.032 kg/mol
Step 3: Calculate RMS Speeds
- RMS speed of H2:
- RMS(H2) = sqrt(3 * 8.314 * 50.15 / 0.002)
- RMS speed of O2:
- RMS(O2) = sqrt(3 * 8.314 * 800.15 / 0.032)
Step 4: Find the Ratio
- The ratio of the RMS speeds is:
- Ratio = RMS(H2) / RMS(O2)
This ratio simplifies to:
Ratio = (sqrt(50.15 / 0.002)) / (sqrt(800.15 / 0.032))
When calculated, it results in a ratio close to 1.
Conclusion
The final answer to the ratio of the RMS speed of H2 at -223°C to that of O2 at 527°C is indeed '1'. This means that the speeds are comparable when considering the effects of temperature and molar mass.
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Directions: The answer to following question is a single digit integer...
Root mean square velocity (urms) = 
= 1
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Directions: The answer to following question is a single digit integer ranging from 0 to 9. Enter the correct digit in the box given below.The ratio between the root mean square speed of H2 at -223oC and that of O2 at 527oC isCorrect answer is '1'. Can you explain this answer?
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