A 75.0 L stainless steel container was charged with 3.00 atm of hydrogen gas and 4.00 atm of oxygen gas. A spark ignited the mixture, producing water.
What is the pressure in the tank at 25°C?
in atm
What is the pressure in the tank at 125°C?
in atm
40 atm
To find the pressure in the tank at different temperatures, you would need to apply the ideal gas law equation, which states:
PV = nRT
Where:
P is the pressure in atm,
V is the volume in liters,
n is the number of moles of gas,
R is the ideal gas constant (0.0821 L.atm/(K.mol)),
T is the temperature in Kelvin.
To solve for the pressure (P), you can rearrange the equation as follows:
P = (nRT) / V
However, before we can calculate the pressures, we need to find the number of moles of each gas present in the tank.
Given:
Volume of the tank (V) = 75.0 L
Partial pressure of hydrogen gas (PH₂) = 3.00 atm
Partial pressure of oxygen gas (PO₂) = 4.00 atm
To find the number of moles (n) for each gas, we can use the equation:
n = PV / RT
Let's start by calculating the number of moles of hydrogen gas:
nH₂ = (PH₂ * V) / (RT)
nH₂ = (3.00 atm * 75.0 L) / (0.0821 L.atm/(K.mol) * 298 K)
Next, let's calculate the number of moles of oxygen gas:
nO₂ = (PO₂ * V) / (RT)
nO₂ = (4.00 atm * 75.0 L) / (0.0821 L.atm/(K.mol) * 298 K)
Now that we have the number of moles for each gas, we can substitute these values into the ideal gas law equation to find the pressure at each temperature.
To calculate the pressure at 25°C (which is 298 K), substitute the values into the equation:
P25 = ((nH₂ + nO₂) * RT) / V
P125 = ((nH₂ + nO₂) * R * T) / V
For the pressure at 125°C (which is 398 K), substitute the values into the equation:
P125 = ((nH₂ + nO₂) * RT) / V
I will now calculate the values for you.
Write the equation and balance it.
Calculate n for H2 and n for O2 and change these to concentration in mols/L.
Determine the limiting reagent.
Determine how much of the other reagent remains after the reaction.
Convert molarities remaining and formed into mols (mol/L x 75 L = mols.
Convert mols H2O to grams. The number I have seems to be small enough to ignore it (that is, it won't take up much volume) but you need to verify that. I have also ignored the vapor pressure of water for the first part.
Then PV = nRT and use mols of the remaining reagent, V = 75 L, R and 298 K to calculate pressure. You probably need to confirm that the vapor pressure of the water can be ignored.
For the second part, notice that 125 C is enough to change ALL of the water to vapor so you have two contributors to the pressure. You should be able to do this on your own.
Check my thinking. It's late at night.