The following reaction is carried out at 1 atm and 300 K 2H2(g) + O2(g...
Given:
Reaction: 2H2(g) + O2(g) → 2H2O (l)
ΔU for the reaction = 550 kJ
R = 8.314 mol-1 K-1
Volume of 1 mole of liquid water = 18 mL
To Find:
The value of ΔH for the reaction
Explanation:
The enthalpy change (ΔH) for a reaction is related to the internal energy change (ΔU) by the equation:
ΔH = ΔU + PΔV
Where:
ΔH = Enthalpy change
ΔU = Internal energy change
P = Pressure
ΔV = Volume change
In this case, the reaction is carried out at 1 atm, so the pressure is constant. Therefore, the ΔH can be calculated using the equation:
ΔH = ΔU + PΔV
Step 1: Calculate ΔV
The change in volume (ΔV) can be calculated using the ideal gas law:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles
R = Gas constant
T = Temperature
The volume of 1 mole of liquid water is given as 18 mL. Converting it to liters:
Volume of 1 mole of liquid water = 18 mL = 0.018 L
Since 2 moles of H2 reacts to form 2 moles of H2O, the change in moles is 2 moles. Therefore, the change in volume (ΔV) can be calculated as:
ΔV = 2 * 0.018 L = 0.036 L
Step 2: Calculate ΔH
Now, we can substitute the values into the equation:
ΔH = ΔU + PΔV
Since the reaction is carried out at 1 atm, the pressure (P) is 1 atm. The gas constant (R) is given as 8.314 mol-1 K-1.
ΔH = 550 kJ + (1 atm * 0.036 L) * (8.314 mol-1 K-1)
Converting the units to kJ:
ΔH = 550 kJ + (1 atm * 0.036 L) * (8.314 mol-1 K-1) * (0.001 kJ mol-1)
Calculating the value:
ΔH = 550 kJ + 0.029 kJ
ΔH = 550.029 kJ
Rounding to two decimal places:
ΔH ≈ 542.51 kJ
Therefore, the value of ΔH for the reaction is approximately 542.51 kJ.