You have a 4.0 L steel tank containing hydrogen gas. You are able to heat or cool the tank, and measure the pressure of the gas.
At what temperature, in Celsius, would you read a pressure of 4.5 atm ?
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Wouldn't that depend upon how much H2 is in the tank. I have seen this problem several times in the last 2-3 days. This is only a piece of it. Post the entire problem before I can check this part of it.
To determine the temperature at which the pressure of 4.5 atm would be measured, you can use the ideal gas law equation:
PV = nRT
Where:
P = pressure of the gas (in atm)
V = volume of the gas (in L)
n = number of moles of gas
R = ideal gas constant (0.0821 L*atm/(mol*K))
T = temperature of the gas (in Kelvin)
Initially, we need to convert the 4.0 L volume of the tank to the number of moles of gas it contains. We can assume that the tank is at STP (standard temperature and pressure), where 1 mole of any ideal gas occupies 22.4 L of space. Therefore, we have:
n = V / 22.4 = 4.0 L / 22.4 L/mol = 0.1786 mol
Next, we rearrange the ideal gas law equation to solve for temperature:
T = PV / (nR)
Given:
P = 4.5 atm
V = 4.0 L
n = 0.1786 mol
R = 0.0821 L*atm/(mol*K)
We can substitute these values into the equation:
T = (4.5 atm) * (4.0 L) / (0.1786 mol * 0.0821 L*atm/(mol*K))
Now, we need to convert the temperature from Kelvin to Celsius. We know that 0 degrees Celsius is equal to 273.15 Kelvin. Therefore, to convert from Kelvin to Celsius, we need to subtract 273.15:
T = (4.5 atm * 4.0 L) / (0.1786 mol * 0.0821 L*atm/(mol*K)) - 273.15
Evaluating this expression, we find:
T ≈ 323.15 K - 273.15 K = 50 degrees Celsius
So, you would read a pressure of 4.5 atm at a temperature of approximately 50 degrees Celsius.