If He(g) has an average kinetic energy of 7590 J/mol under certain conditions, what is the root mean square speed of F2(g) molecules under the same conditions?
To find the root mean square speed of F2(g) molecules under the same conditions, we can use the equation:
vrms = √(3RT / M)
Where:
- vrms is the root mean square speed
- R is the ideal gas constant (8.314 J/(mol·K))
- T is the temperature in Kelvin
- M is the molar mass of the gas in kilograms per mole
First, we need to determine the molar mass of F2(g). The molar mass of fluorine (F) is 19.00 g/mol, and since there are two fluorine atoms in F2, the molar mass of F2(g) is:
M = 2 * 19.00 g/mol = 38.00 g/mol
Next, we convert the molar mass from grams to kilograms:
M = 38.00 g/mol * (1 kg / 1000 g) = 0.038 kg/mol
Now, we can calculate the root mean square speed. However, we need the temperature in Kelvin. If you don't have the temperature in Kelvin, you'll need to convert it.
Assuming you have the temperature in Kelvin, you can substitute the values into the equation:
vrms = √(3 * R * T / M)
= √(3 * 8.314 J/(mol·K) * T / 0.038 kg/mol)
= √(249.42 J·K/mol * T)
Finally, to find the root mean square speed, you'll need the value of T in Kelvin. With that value, you can calculate the root mean square speed using the formula above.