If the rocket engine contains 1500.0 grams of H2O2 and an excess of N2H4, what volume of water vapor will be produced when the rocket fires up to a temperature of 540°C and a pressure of 1.2atm?
Write the equation and balance it.
Convert 1500g H2O2 to mols. mols = grams/molar mass
Convert mols H2O2 to mols H2O using the coefficients in the balanced equation.
Substitute mols H2O into PV = nRT and solve for volume at the conditions listed.
To determine the volume of water vapor produced when the rocket fires, we need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
First, we need to find the number of moles of H2O2. To do this, we'll use the molar mass of H2O2 (34.0147 g/mol):
n(H2O2) = mass (g) / molar mass (g/mol)
n(H2O2) = 1500.0 g / 34.0147 g/mol
n(H2O2) ≈ 44.13 mol
Since H2O2 has a 1:1 stoichiometric ratio with water vapor (H2O), the number of moles of water vapor produced will also be 44.13 mol.
Next, we need to convert the temperature to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 540°C + 273.15
T(K) ≈ 813.15 K
Now we can substitute the values into the ideal gas law equation to find the volume of water vapor:
PV = nRT
V = (nRT) / P
V = (44.13 mol * 0.0821 L·atm/(mol·K) * 813.15 K) / 1.2 atm
V ≈ 2889.39 L
Therefore, when the rocket fires, approximately 2889.39 liters of water vapor will be produced.
To find the volume of water vapor produced, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L atm/(mol·K))
T = temperature (in Kelvin)
First, let's calculate the number of moles of H2O2 using its molar mass. The molar mass of H2O2 is 34.02 g/mol.
Number of moles of H2O2 = mass of H2O2 / molar mass of H2O2
Number of moles of H2O2 = 1500.0 g / 34.02 g/mol
Next, since the reaction produces water vapor (H2O), we need to find the stoichiometric ratio between H2O2 and H2O. From the balanced chemical equation, we know that:
2 H2O2 → 2 H2O + O2
The stoichiometric ratio of H2O2 to H2O is 2:2, or 1:1.
Therefore, the number of moles of H2O produced will be equal to the number of moles of H2O2.
Number of moles of H2O = Number of moles of H2O2
Now we can use the ideal gas law to find the volume of water vapor:
V = nRT / P
But before we can calculate the volume, we need to convert the temperature to Kelvin:
Temperature in Kelvin = Temperature in Celsius + 273.15
Temperature in Kelvin = 540°C + 273.15 = 813.15 K
Now, substitute the values into the equation:
V = (Number of moles of H2O) * (ideal gas constant) * (temperature in Kelvin) / (pressure)
V = (Number of moles of H2O) * (0.0821 L atm/(mol·K)) * (813.15 K) / (1.2 atm)
Calculating this expression will give us the volume of water vapor produced in liters when the rocket engine fires up.