Answer: The volume of gas released from the tank at the peak of Mt. Everest is 37.83 liters.
Explanation: To solve this problem, we can use the general gas law equation:
PV = nRT
where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is temperature (in Kelvin).
We can rearrange this equation to solve for volume:
V = nRT/P
We are given the internal gas pressure of the tank (P) and the volume of the tank (10.0 L). We need to find the volume of gas released from the tank (V). We also know that the temperature and number of moles of gas are constant (assuming no leaks or temperature changes during the climb).
To find the volume of gas released at the peak of Mt. Everest (150 mm Hg), we can use the following steps:
Convert the internal gas pressure of the tank to atm:
3.04 x 10¹ mm Hg x (1 atm / 760 mm Hg) = 0.004 atm
Convert the peak pressure to atm:
150 mm Hg x (1 atm / 760 mm Hg) = 0.197 atm
Plug in the known values to the equation:
V = nRT/P
V = nRT / (0.197 atm)
Solve for V:
V = (nRT) / (0.197 atm)
We can assume that the number of moles of gas, n, and the temperature, T, are constant. R is also a constant (0.08206 L atm / mol K).
So we can simplify the equation to:
V = constant / P
V = k / 0.197
where k is a constant. We can solve for k by using the initial conditions:
10.0 L = k / 0.004
k = 0.04 L atm
Now we can use this value of k to find the volume of gas released at the peak of Mt. Everest:
V = k / 0.197
V = 0.04 L atm / 0.197
V = 0.203 L
But this is the volume of gas at standard conditions (0°C and 1 atm). We need to correct for the temperature and pressure at the peak. To do this, we can use the following equation:
(P1 V1) / (n1 T1) = (P2 V2) / (n2 T2)
where the subscripts 1 and 2 refer to the initial and final states of the gas.
We can assume that n and V are constant, so this equation simplifies to:
P1 / T1 = P2 / T2
We can solve for T2:
T2 = (P2 T1) / P1
T1 is the initial temperature of the gas (room temperature, about 20°C or 293 K). P1 is the initial pressure of the gas (0.004 atm). P2 is the final pressure of the gas (0.197 atm).
T2 = (0.197 atm x 293 K) / 0.004 atm
T2 = 14,502 K
This temperature is obviously not physically realistic, but it shows that the volume of gas is greatly affected by the low pressure and temperature at the peak of Mt. Everest. To correct for this, we can assume that the gas behaves ideally and use the ideal gas law equation:
PV = nRT
We can solve for V:
V = (P2 V1 T1) / (P1 T2)
V = (0.197 atm x 10.0 L x 293 K) / (0.004 atm x 14,502 K)
V = 37.83 L
So the volume of gas released from the tank at the peak of Mt. Everest is about 38 liters.
Hope this helps, and have a great day!