calculate the volume of the hydrogen that will combine with 40 litres of oxygen to form steam at 150 C and atmospheric pressure
2H2 + O2 ==> 2H2O
If we work in gases we can omit the step of converting to mols and use L directly.
40 L O2 x (2 mols H2/1 mol O2) = ? L O2.
To calculate the volume of hydrogen that will combine with oxygen to form steam, we first need to determine the balanced chemical equation for the reaction. The formula for the reaction between hydrogen and oxygen to produce steam is:
2H₂ + O₂ → 2H₂O
From the equation, we can see that two molecules of hydrogen (H₂) combine with one molecule of oxygen (O₂) to produce two molecules of water (H₂O).
Given that we have 40 liters of oxygen, we need to convert this volume into the number of moles. To do this, we need to use the ideal gas law equation:
PV = nRT
Where:
P = Pressure (atm)
V = Volume (liters)
n = Number of moles
R = Ideal gas constant (0.0821 L.atm/mol.K)
T = Temperature (Kelvin)
We also need to convert the temperature from Celsius to Kelvin by adding 273.15:
T = 150°C + 273.15 = 423.15 K
Now, let's calculate the number of moles of oxygen using the ideal gas law equation:
n(O₂) = (P(V))/(RT)
Since the pressure is given as atmospheric pressure, which is typically around 1 atm, we can substitute the values:
n(O₂) = (1 atm * 40 L) / (0.0821 L.atm/mol.K * 423.15 K)
n(O₂) ≈ 1.10 moles of oxygen
To determine the volume of hydrogen needed, we can use the stoichiometry of the equation. From the balanced equation, we see that 2 moles of hydrogen react with 1 mole of oxygen. Therefore, the number of moles of hydrogen required is half the number of moles of oxygen:
n(H₂) = (1.10 moles O₂) / 2
n(H₂) ≈ 0.55 moles of hydrogen
Finally, to calculate the volume of hydrogen, we can use the ideal gas law equation again:
V(H₂) = (n(H₂) * (R * T)) / P
Substituting the values:
V(H₂) = (0.55 mol * (0.0821 L.atm/mol.K * 423.15 K)) / 1 atm
V(H₂) ≈ 18.9 L
Therefore, approximately 18.9 liters of hydrogen are required to combine with 40 liters of oxygen to form steam at 150°C and atmospheric pressure.