Calculate the root mean square speed (rms) for gaseous NH3 at 315 K
rms speed sqrt(3RT/M)
R is 8.314 T is in Kelvin and M is molar mass NH3.
To calculate the root mean square speed (rms) of a gas, you can use the equation:
rms = √(3RT/M)
Where:
- rms: root mean square speed
- R: gas constant (8.314 J/(mol·K))
- T: temperature (in Kelvin)
- M: molar mass of the gas (in kg/mol)
In this case, gaseous NH3 (ammonia) is the gas, and the temperature is given as 315 K.
The molar mass of NH3 is:
M(NH3) = atomic mass of N + 3 * atomic mass of H
= 14.01 g/mol + 3 * 1.01 g/mol
= 17.03 g/mol
To use the equation to calculate the rms, we need to convert the molar mass to kg/mol:
M(NH3) = 17.03 g/mol * (1 kg / 1000 g)
= 0.01703 kg/mol
Now we can substitute the values into the equation and solve for the rms:
rms = √(3 * R * T / M)
= √(3 * 8.314 J/(mol·K) * 315 K / 0.01703 kg/mol)
Calculating this using a calculator:
rms ≈ √(7429.61 J/(mol·K) * 315 K / 0.01703 kg/mol)
≈ √(2211635.15 J/(mol·K) / 0.01703 kg/mol)
≈ √129785949.12 J/(kg·mol)
≈ 360.25 m/s
Therefore, the root mean square speed (rms) of gaseous NH3 at 315 K is approximately 360.25 m/s.