Solve Ideal Gas Problems: Volume, Translation Energy & More

[Kelju Ivan]

There are some problems which have me completely stumped.

1. A balloon has a volume of 10.5dm^3. Its mass is 8.5g and inside is helium at a pressure of 1.05atm. Atmospheric pressure is 1.00atm and both the helium and the outside air is 25.0C (degrees Celcius). Define the tension in the balloons string. Molar mass of helium is 4.00g/mol and air's is 29.1g/mol.

I guess the tension is caused by the buouancy of the ball and can be expressed as T=B-w.

Now... I could solve this the traditional way by using the density of air, but the value is not given so there must be a way to get through this by using those molar masses. I have no idea how. Please help.

2. In another problem a diver has a tank of pressurized air. I am given the initial temperature, pressure and mass of the air as well as the values after the dive, the molar mass of air and the atmospheric pressure. I need to find out the volume of the gas. The air is considered to be a diatomic ideal gas.

Now I have the equation pV = nRT = (m/M)RT so I could directly solve for V with it being the only unknown. Now I wouldn't need the other set of values at all so this can't be right. The fact that the air is diatomic must chance something. I understand that there could now be collisions between the gas' atoms, but what effect does it have on this?

3. How do I calculate the average translation energy of non-ideal gas? I have 5.00l of hydrogen at atmospheric pressure and at a temperature of 25C.

For ideal gas I found the equation ½mv^2 = (3/2)kT where k is the Boltzman constant. There was no mention of the gas being ideal in the problem so I'm assuming it isn't. Any advice?

 

[M98Ranger]

1. To solve this problem, we can use the ideal gas law equation, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature. We can rearrange this equation to solve for n, which is the number of moles of helium in the balloon. We know the molar mass of helium, so we can use this to find the mass of helium in the balloon (m = n x molar mass). Then, we can use the buoyancy equation, B = ρVg, where B is the buoyant force, ρ is the density of air, V is the volume of the balloon, and g is the acceleration due to gravity. We can solve for ρ by using the ideal gas law equation and substituting in the values for pressure, temperature, and the molar mass of air. Once we have the density of air, we can use the buoyancy equation to find the buoyant force, and then use this to find the tension in the balloon's string.

2. The fact that the air is diatomic does not change the ideal gas law equation, but it does affect the value of the gas constant, R. For diatomic gases, the value of R is 8.314 J/mol·K, while for monatomic gases, it is 8.314 J/mol·K. So, when solving for the volume of the gas, make sure to use the correct value of R.

3. To calculate the average translation energy of a non-ideal gas, we can use the kinetic energy equation, KE = ½mv^2, where m is the mass of the gas molecule and v is the average velocity of the gas molecules. The average velocity can be found using the root mean square velocity equation, vrms = √(3RT/M), where R is the gas constant, T is the temperature, and M is the molar mass of the gas. So, we can use this equation to find the average velocity and then use it in the kinetic energy equation to find the average translation energy.