Consider the reaction
2H2O(g) --> 2H2(g) + O2(g)
deltaH = +483.6 kJ/mol
at a certain temperature. If the increase in volume is 32.7 L against an external pressure of 1.00 atm, calculate deltaU for the reaction. (1 L * atm = 101.3 J)
To calculate the change in internal energy (ΔU) for the reaction, you need to use the formula:
ΔU = ΔH - ΔnRT
where ΔH is the change in enthalpy, Δn is the change in moles, R is the ideal gas constant, and T is the temperature in Kelvin.
In this case, we are given ΔH as +483.6 kJ/mol. To convert it to J/mol, we multiply it by 1000 because there are 1000 J in 1 kJ:
ΔH = +483.6 kJ/mol * 1000 J/kJ = +483,600 J/mol
We are also given the volume change (ΔV) as 32.7 L and the external pressure (P) as 1.00 atm. Since the volume of gas increases, Δn would be +2 (moles of product - moles of reactant) because two moles of H2 gas are produced for every mole of H2O consumed.
Now, we can calculate ΔU using the formula:
ΔU = ΔH - ΔnRT
First, convert the volume change from liters to cubic meters because the unit of the ideal gas constant (R) is in J/(mol*K):
ΔV = 32.7 L * (1 m³ / 1000 L) = 0.0327 m³
Next, convert the temperature from Celsius to Kelvin:
T = temperature in Celsius + 273.15 = given temperature in Kelvin
Finally, plug in the values into the formula to calculate ΔU:
ΔU = +483,600 J/mol - (+2) * (0.0327 m³) * (1 atm * 101.3 J) / (1 mol * K * given temperature)
Simplify the equation:
ΔU = +483,600 J/mol - 2 * 0.0327 m³ * 1 atm * 101.3 J / (1 mol * given temperature)
Solving this equation will give you the value of ΔU for the reaction at the given temperature.