Answer :
The temperature of the gas is, 301.7 K
The root mean square speed is,
Explanation :
To calculate the volume of argon gas we are using ideal gas equation:
where,
P = pressure of nitrogen gas = 1.15 atm
V = volume of nitrogen gas
T = temperature of nitrogen gas
R = gas constant = 0.0821 L.atm/mole.K
w = mass of nitrogen gas
M = molar mass of nitrogen gas = 28 g/mole
= density of nitrogen gas =
Now put all the given values in the ideal gas equation, we get:
Therefore, the temperature of the gas is, 301.7 K
Now we have to determine the root mean square speed of the molecule.
The formula used for root mean square speed is:
where,
= root mean square speed
k = Boltzmann’s constant =
T = temperature = 301.7 K
M = atomic mass of nitrogen gas = 0.028 kg/mole
= Avogadro’s number =
Now put all the given values in the above root mean square speed formula, we get:
The root mean square speed is,