Calculate the root mean square of bromine molecule at 23°c and 1.00 atm
rms = (3RT/.M). Isn't this just plugging into the formula and running the numbers?
V(RMS) in meters/sec = 158[SqrRt(T/M)]; T is in Kelvin, M = Mole weight.
oops.Left out the sqrt.
V rms = sqrt(3RT/M)
To calculate the root mean square (RMS) velocity of a molecule, we can use the following equation:
RMS velocity = sqrt((3 * R * T) / M)
Where:
- RMS velocity is the root mean square velocity
- R is the ideal gas constant (8.314 J/(mol·K))
- T is the temperature in Kelvin
- M is the molar mass of the molecule in kg/mol
Step 1: Convert the given temperature from Celsius to Kelvin:
T = 23°C + 273.15 = 296.15 K
Step 2: Determine the molar mass of the bromine (Br2) molecule.
Looking up the molar mass of bromine (Br), we find it is approximately 79.9 g/mol. Since bromine (Br2) consists of 2 bromine atoms, the molar mass of the bromine molecule is 2 * 79.9 g/mol = 159.8 g/mol.
Step 3: Convert the molar mass of bromine from grams/mol to kilograms/mol:
M = 159.8 g/mol * (1 kg/1000 g) = 0.1598 kg/mol
Step 4: Plug the values into the RMS velocity equation and solve:
RMS velocity = sqrt((3 * R * T) / M)
RMS velocity = sqrt((3 * 8.314 J/(mol·K) * 296.15 K) / 0.1598 kg/mol)
Calculating this expression will give you the RMS velocity of the bromine molecule at 23°C and 1.00 atm.