A tank of 0.35m^3 capacity contains H2 S gas at 300K. When 2.5 kg of gas is withdrawn, the temperature in the tank becomes 288K and the pressure 10.5 bar. Calculate the mass of gas initially kept in the tank and also the initial pressure.
At the end. P = 10.5 bar = 10.36 atm: V = 0.35 m^3 = 350 L: T = 288 K:
PV = nRT.
n = PV/RT = 10.36*350/0.08205*288
n = approx 150 but you need a better number than that.
grams H2S = 150 moles x molar mass H2S = 150*34 = approx 5,000 g. That's the mass of H2S in the tank AFTER 2.5 kg has been released. Therefore, the amount H2S initially is about 2,500 g + 5,000 = approx 7,500 g H2S.
What's the initial pressure? The conditions are as follows:
P = ?: V = 350 L: n = approx 7500/34 = approx 220 moles: T = 300 K
Plug into PV = nRT and solve for P (in atm). Convert to bar if needed knowing 1 bar = 0.987 atm. Remember that the calculations I've done are approximate and you should go through each one.Post your work if you run into trouble. BTW, this is not a thermodynamics problem (or if it is I've missed it badly). I think it is a idea gas problem. I spent quite some time trying to make it a Joule-Thomson (Lord Kelvin) problem.
To calculate the initial mass of gas in the tank, you can use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
First, we need to calculate the number of moles of hydrogen sulfide (H2S) gas initially present in the tank. We can use the mass and molar mass of H2S to find the number of moles.
The molar mass of H2S is:
Molar mass H2S = (2*1.008) + (1*32.06) = 34.076 g/mol
Given that 2.5 kg (or 2500 grams) of H2S gas is withdrawn, we can calculate the number of moles:
Number of moles = Mass / Molar mass
Number of moles = 2500 g / 34.076 g/mol
Now, we can calculate the initial number of moles of gas in the tank by subtracting the withdrawn moles from the total moles:
Initial number of moles = Total moles - Withdrawn moles
Next, we need to find the initial pressure of the gas in the tank. Since the temperature remains the same, we can use the equation:
P1V1 = n1RT
Where:
P1 = initial pressure
V1 = initial volume
n1 = initial number of moles
R = ideal gas constant
T = temperature
Rearranging the equation, we can solve for P1:
P1 = (n1RT) / V1
Now, let's plug in the given values:
V1 = 0.35 m^3 (capacity of the tank)
T = 300 K (initial temperature)
R = 8.314 J/(mol·K) (ideal gas constant)
Solve for n1:
n1 = (2500 g / 34.076 g/mol) - (2.5 kg / 34.076 g/mol)
Solve for P1:
P1 = (n1RT) / V1
Substituting the values, solve for P1.
Therefore, the initial mass of gas kept in the tank is calculated to be n1 grams, and the initial pressure is calculated to be P1 bar.
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 of gas
R is the ideal gas constant
T is the temperature
We have two different states of the gas in the tank: initial state (before withdrawing gas) and final state (after withdrawing gas).
Given:
Initial state:
V1 = 0.35 m^3 (volume)
T1 = 300 K (temperature)
P1 (initial pressure)
m1 (initial mass of gas)
Final state:
V2 = V1 (since the volume of the tank remains the same after withdrawing gas)
T2 = 288 K (temperature)
P2 = 10.5 bar (pressure after withdrawing gas)
m2 = 2.5 kg (mass of withdrawn gas)
First, let's find the number of moles of gas in the final state. We need to convert the pressure from bar to Pascal since the ideal gas constant is in SI units (8.314 J/(mol*K)):
P2_final = P2 * 100,000 (convert bar to Pascal)
Now, we can find the final number of moles:
n2 = (P2_final * V2) / (R * T2)
Next, let's find the initial number of moles of gas using the same equation but with the initial state values:
n1 = (P1 * V1) / (R * T1)
Since the mass of the withdrawn gas is given as m2, we can find the number of moles (n2) using the molar mass of the gas (which is H2S):
molar_mass = 34.08 g/mol (H2S molar mass)
n2 = m2 / molar_mass
Now, we can rearrange the equation to solve for P1 (initial pressure):
P1 = (n2 * R * T1) / V1
Finally, once we have P1, we can find the initial mass of gas (m1) using the equation:
m1 = n1 * molar_mass
Now we can substitute the given values into the equations and calculate the answers.