Final answer:
The nitrogen gas (N₂) has the largest root mean square (RMS) molecular speed at 25°C.
Step-by-step explanation:
The root mean square (RMS) speed of gas molecules at a given temperature can be calculated using the equation:
URMS = sqrt(3RT/M)
Where URMS is the root mean square speed, R is the ideal gas constant, T is the temperature in Kelvin, and M is the molar mass of the gas. By comparing the molar masses of the gases given in the question, we can determine which one has the largest value of URMS at 25°C.
Using the molecular masses of the gases from the periodic table, the molar mass of each gas is:
Oxygen gas (O₂): 32.0 g/mol
Carbon dioxide (CO₂): 44.0 g/mol
Nitrogen gas (N₂): 28.0 g/mol
Helium gas (He): 4.0 g/mol
Calculating the URMS values for each gas using the equation above:
- Oxygen gas (O₂) at 25°C: URMS = sqrt(3 * 8.314 * (298.15) / 0.032) = 484.7 m/s
- Carbon dioxide (CO₂) at 25°C: URMS = sqrt(3 * 8.314 * (298.15) / 0.044) = 396.6 m/s
- Nitrogen gas (N₂) at 25°C: URMS = sqrt(3 * 8.314 * (298.15) / 0.028) = 533.5 m/s
- Helium gas (He) at 25°C: URMS = sqrt(3 * 8.314 * (298.15) / 0.004) = 1933.7 m/s
Therefore, the nitrogen gas (N₂) has the largest root mean square (RMS) molecular speed at 25°C.