a gas tank holds 2685 L of propane, C3H8 at 830 mm Hg. What is the volume of the propane at standard pressure
PV=kT
That is V varies inversely with P.
So, if P at STP is 760mm, V at 830mm will be (760/830) * 2685
To find the volume of the propane at standard pressure, we need to use the Combined Gas Law equation. The equation is as follows:
(P1 * V1) / T1 = (P2 * V2) / T2
Where:
P1 = initial pressure (in this case, 830 mm Hg)
V1 = initial volume (in this case, 2685 L)
T1 = initial temperature (not given)
P2 = final pressure (standard pressure, which is 760 mm Hg)
V2 = final volume (what we're trying to find)
T2 = final temperature (not given)
Since we don't have any temperature values, we can assume that the temperature remains constant throughout the process, meaning that T1 = T2. Therefore, we can rewrite the equation as:
(P1 * V1) / T1 = (P2 * V2) / T2
or
(P1 * V1) = (P2 * V2)
Now, let's solve for V2:
V2 = (P1 * V1) / P2
Substituting the values we have:
V2 = (830 mm Hg * 2685 L) / 760 mm Hg
V2 ≈ 2922.24 L
Therefore, the volume of the propane at standard pressure is approximately 2922.24 L.
To find the volume of the propane at standard pressure, we need to use the ideal gas law equation, which is
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles
R = Ideal gas constant
T = Temperature
In this case, we know the initial pressure (830 mm Hg) and volume (2685 L) of the propane. We also need to know the number of moles of propane and the temperature.
Since we don't have the number of moles, we need to calculate it. To do that, we can use the equation:
PV = nRT
Rearranging the equation, we get:
n = PV / RT
Given that the gas constant R = 0.0821 L·atm/(mol·K), we can convert the pressure from mm Hg to atm by dividing it by 760 (since 1 atm = 760 mm Hg).
So, the equation becomes:
n = (830 mm Hg / 760) * (2685 L) / (0.0821 L·atm/(mol·K) * T)
Now, we can rearrange the equation to isolate V:
V = nRT / P
Knowing that we want to find the volume at standard pressure (which is 1 atm), we can substitute the values:
V = (n * 0.0821 L·atm/(mol·K) * T) / (1 atm)
Simplifying the equation, we get:
V = n * 0.0821 L·atm/(mol·K) * T
From this equation, we can see that the volume is directly proportional to the number of moles, so the volume at standard pressure will be the same as the initial volume.
Therefore, the volume of the propane at standard pressure is 2685 L.