If a gas has a urms of 425m/s at 25 degrees C, what is the molar mass of the gas?
Vrms= sqrt (3kT/mass)= sqrt(3RT/M)
solve for M
R uiversal gas constant, T temp in kelvins
urms = sqrt(3RT/M)
To find the molar mass of the gas, we can make use of the root mean square velocity equation:
urms = √((3RT) / M)
Where:
urms = root mean square velocity
R = ideal gas constant (8.314 J/(mol·K))
T = temperature in Kelvin
M = molar mass of the gas
First, we need to convert the given temperature of 25 degrees Celsius to Kelvin.
T (Kelvin) = T (Celsius) + 273.15
T (Kelvin) = 25 + 273.15
T (Kelvin) ≈ 298.15 K
Now, we can substitute the given values into the urms equation and solve for M.
425 m/s = √((3 * 8.314 J/(mol·K) * 298.15 K) / M)
Let's square both sides of the equation to eliminate the square root:
(425 m/s)^2 = (3 * 8.314 J/(mol·K) * 298.15 K) / M
M = (3 * 8.314 J/(mol·K) * 298.15 K) / (425 m/s)^2
By plugging in the values and solving the equation, we can find the molar mass of the gas.