A gas cylinder of volume 26 liters contains an ideal gas at temperature 27 degrees C and pressure 1920 kPa. Some of the gas leaks until the pressure falls to 1500 kPa. How many moles of gas leaked, assuming that the temperature remains constant during this process?
P V = n R T
Final state:
P = 1.5*10^6 N/m^2
V = 26 liters = 26*10^-3 m^3
T =273+27 = 300 K
so
n R = PV/T = 1.5*26*10^3/300
= .13 * 10^3
R =8.314
so
n = .13*10^3/8.314 = 15.6 moles
Do that again for 1.92*10^6 N/m^2
and get a bigger initial n
then subtract
I got 1, is that right?
You mean I have to do it?
I can figure it out. Thanks for your help
1.92 /1.5 = 1.28
1.28* 15.6 = 19.97
19.97 - 15.6 = 4.37
To find the number of moles of gas that leaked, we can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure of the gas,
V is the volume of the gas,
n is the number of moles of gas,
R is the ideal gas constant (8.314 J/(mol K)),
and T is the temperature of the gas in Kelvin.
First, we need to convert the temperature from Celsius to Kelvin:
T(K) = T(C) + 273.15
T(K) = 27°C + 273.15 = 300.15 K
Now, we can calculate the initial number of moles of gas in the cylinder using the initial pressure (P1), volume (V), and temperature (T):
n1 = (P1 * V) / (R * T)
Substituting the values:
P1 = 1920 kPa
V = 26 liters = 0.026 m³
R = 8.314 J/(mol K)
T = 300.15 K
Converting the pressure from kilopascals to pascals:
P1 = 1920 kPa = 1920000 Pa
Plugging in the values:
n1 = (1920000 Pa * 0.026 m³) / (8.314 J/(mol K) * 300.15 K)
Now, we can calculate the final number of moles of gas after the leak using the final pressure (P2), which is 1500 kPa, and the remaining volume (V):
n2 = (P2 * V) / (R * T)
Converting the pressure from kilopascals to pascals:
P2 = 1500 kPa = 1500000 Pa
Plugging in the values:
n2 = (1500000 Pa * 0.026 m³) / (8.314 J/(mol K) * 300.15 K)
The difference between the initial and final number of moles of gas will give us the number of moles that leaked:
n_leak = n1 - n2
Now, let's calculate the number of moles of gas leaked based on the given values:
First, calculate n1:
n1 = (1920000 Pa * 0.026 m³) / (8.314 J/(mol K) * 300.15 K) ≈ 2.262 moles
Next, calculate n2:
n2 = (1500000 Pa * 0.026 m³) / (8.314 J/(mol K) * 300.15 K) ≈ 1.770 moles
Finally, calculate the number of moles leaked:
n_leak = n1 - n2 ≈ 2.262 moles - 1.770 moles ≈ 0.492 moles
Therefore, approximately 0.492 moles of gas leaked from the cylinder.