Rank gases from highest average molecular speed to lowest Ne, HBr, CO
Highest molecular speed goes with the lowest molecular weight. Use the atomic weight for (monatomic) neon.
Neon is lighter tnan HBr or CO.
Hence...
To rank the gases from highest average molecular speed to lowest, we need to consider the concept of root-mean-square (RMS) speed. The RMS speed represents the average speed of gas molecules in a sample.
To calculate the RMS speed, we can use the following formula:
RMS speed = √(3RT/M)
Where:
- R is the ideal gas constant (8.314 J/(mol·K))
- T is the temperature in Kelvin (K)
- M is the molar mass of the gas in kilograms per mole (kg/mol)
Let's calculate the RMS speed for each gas and compare them.
1. Neon (Ne):
Neon has an atomic mass of approximately 20.18 grams per mole (g/mol). To convert this to kilograms per mole, we divide by 1000.
Molar mass of Ne = 20.18 g/mol / 1000 = 0.02018 kg/mol
2. Hydrogen Bromide (HBr):
Hydrogen Bromide has a molar mass of approximately 80.912 g/mol.
Molar mass of HBr = 80.912 g/mol / 1000 = 0.080912 kg/mol
3. Carbon Monoxide (CO):
Carbon Monoxide has a molar mass of approximately 28.01 g/mol.
Molar mass of CO = 28.01 g/mol / 1000 = 0.02801 kg/mol
Now let's assume a temperature, for example, 298 Kelvin (room temperature), and calculate the RMS speed using the formula mentioned earlier.
RMS speed of Ne = √(3 * 8.314 J/(mol·K) * 298 K / 0.02018 kg/mol)
RMS speed of HBr = √(3 * 8.314 J/(mol·K) * 298 K / 0.080912 kg/mol)
RMS speed of CO = √(3 * 8.314 J/(mol·K) * 298 K / 0.02801 kg/mol)
By calculating these values, we can determine the ranking of gases from highest to lowest average molecular speed.