a 64.0L gas tank is filled at 6.00C. the next day the temperature gets up to 27.00C how much gas (octance) voerflows?
To determine how much gas overflows from the tank due to the increase in temperature, we need to use the ideal gas law equation, which relates the pressure, volume, temperature, and amount of gas.
The ideal gas law equation is given as: PV = nRT
Where:
P = pressure
V = volume
n = number of moles of gas
R = the gas constant (8.314 J/(mol·K))
T = temperature in Kelvin
First, let's convert the temperatures from Celsius to Kelvin:
Initial temperature (T1) = 6.00°C + 273.15 = 279.15 K
Final temperature (T2) = 27.00°C + 273.15 = 300.15 K
Next, we rearrange the ideal gas law equation to solve for the number of moles of gas (n):
n = PV / RT
Since the number of moles of gas remains constant, we can set up the following equation using the initial and final temperatures:
(P1 * V1) / (R * T1) = (P2 * V2) / (R * T2)
Now, we can plug in the given values into the equation. The volume of the gas tank is 64.0 L, and since the tank is filled, we assume the initial pressure (P1) is equal to the final pressure (P2):
(64.0 L * P1) / (8.314 J/(mol·K) * 279.15 K) = (64.0 L * P2) / (8.314 J/(mol·K) * 300.15 K)
Simplifying the equation:
P1 / 279.15 = P2 / 300.15
Now we can solve for P2 (the final pressure):
P2 = (P1 / 279.15) * 300.15
Now, to determine the amount of gas that overflows, we subtract the original volume of the tank (64.0 L) from the final volume of the tank under the new temperature:
Overflow volume = Final volume - Initial volume
Overflow volume = (P2 * V2) / (R * T2) - (P1 * V1) / (R * T1)
Substituting the known values:
Overflow volume = (P2 * 64.0 L) / (8.314 J/(mol·K) * 300.15 K) - (P1 * 64.0 L) / (8.314 J/(mol·K) * 279.15 K)
Finally, we can calculate the overflow volume by plugging in the values for P1 and P2:
Overflow volume = ((P1 / 279.15) * 300.15 * 64.0 L) / (8.314 J/(mol·K) * 300.15 K) - (P1 * 64.0 L) / (8.314 J/(mol·K) * 279.15 K)
To get the specific amount of gas (octane), you would need to know the molar mass of octane and convert it from moles to liters based on the ideal gas law.