Respuesta :
Explanation:
The given data is as follows.
V = 732.0 L, m = 212.0 g, T = 293 K
It is known that molar mass of nitrogen is 28.02 g/mol and molar mass of neon is 20.18 g/mol.
(a) As it is given that mass of both the gases is same. Therefore, higher is the molar mass of the gas, slower will be its average speed.
Therefore, average speed of nitrogen is less that the average speed of neon.
(b) According to the ideal gas equation, PV = nRT.
So, first calculate the number of moles of nitrogen are as follows.
n = [tex]\frac{mass}{\text{molar mass}}[/tex]
= [tex]\frac{212 g}{28.02 g/mol}[/tex]
= 7.56 mol
Now, pressure of nitrogen will be as follows.
PV = nRT
[tex]P \times 732.0 L = 7.56 mol \times 0.0821 L atm/mol K \times 293 K[/tex]
P = 0.248 atm
Whereas moles of neon will be as follows.
n = [tex]\frac{mass}{\text{molar mass}}[/tex]
= [tex]\frac{212 g}{20.18 g/mol}[/tex]
= 10.5 mol
Now, pressure of neon will be as follows.
PV = nRT
[tex]P \times 732.0 L = 10.5 mol \times 0.0821 L atm/mol K \times 293 K[/tex]
P = 0.345 atm
Therefore, pressure of neon is more than the pressure of nitrogen gas.
(c) Formula for collision frequency is as follows.
f = [tex]\frac{\nu}{\lambda}[/tex]
As [tex]\nu_{rms} = \sqrt{\frac{3RT}{M}}[/tex]
where, M = molar mass of gas
Therefore, collision frequency is inversely proportional to molar mass of a gas. And, as nitrogen has high molar mass than neon.
Therefore, collision frequency of nitrogen is less than that of neon.
(d) As density is mass divided by volume.
Mathematically, Density = [tex]\frac{mass}{volume}[/tex]
Also, in the given situation mass and volume for both the gases is same. Hence, density of both nitrogen and neon will be the same at given temperature.
(a) The neon gas will have the greatest average speed.
(b) The pressure of the nitrogen gas will be the greatest because it has greater number of moles.
(c) The neon gas will have the greatest collision frequency.
(d) The density of both gases is the same since their masses and volume is the same.
The given parameters;
- volume of the tank, = 732 L
- mass of the gas, = 212 g
- temperature, T = 293 K
- molar mass of nitrogen gas, = 28 g
- molar mass of neon gas, = 20 g
(a) The average speed of the gases decreases with increase in weight of the gas. Thus, the neon gas will have the greatest average speed.
(b) Apply ideal gas law to determine the gas that will have the greatest pressure;
PV = nRT
where;
- n is the number of moles of the gases
[tex]n_{neon } = \frac{20}{212} = 0.094 \ mole[/tex]
[tex]n_{nitrogen} = \frac{28}{212} = 0.132 \ mole[/tex]
Thus, the pressure of the nitrogen gas will be the greatest because it has greater number of moles.
(c) The collision frequency of the gases is determined by their average speed.
Thus, the neon gas will have the greatest collision frequency.
(d) The density of the of the gases is determined by mass and volume.
[tex]\rho = \frac{mass}{volume}[/tex]
Thus, the density of both gases is the same since their masses and volume is the same.
Learn more here:https://brainly.com/question/21912477
