The enthalpy change for the reaction below at 25oC is -2,051 kJ (per mole of C10H22). What is the internal energy change for the reaction at 25oC?
10 CO(g) + 21 H2(g) --> C10H22(l) + 10 H2O(l)
Enter your answer in kJ (per mole of C10H22), rounded to the nearest kilojoule.
dE = q + w
q is -2.05 kJ/mol C10H22
w you must obtain from volume on the left - volume on the right, then w = -p*delta V.
How do you calculate the volume on the left and on the right?
To find the internal energy change for the reaction, we can use the equation:
ΔH = ΔU + ΔnRT
Where:
ΔH is the enthalpy change
ΔU is the internal energy change
Δn is the change in the number of moles of gas molecules
R is the ideal gas constant
T is the temperature in Kelvin
First, we need to determine the change in the number of moles of gas molecules. Looking at the balanced equation, we see that 10 moles of CO and 21 moles of H2 react to produce 1 mole of C10H22 and 10 moles of H2O. Hence, the change in moles is:
Δn = (10 + 21) - (1 + 10) = 20 moles
Next, we need to convert the temperature to Kelvin. Since the given temperature is 25 oC, we add 273 to it:
T = 25 + 273 = 298 K
Now we rearrange the equation to solve for ΔU:
ΔU = ΔH - ΔnRT
ΔU = -2,051 kJ - (20 mol)(8.314 J/mol·K)(298 K)
Note: We convert kJ to J by multiplying by 1000.
ΔU = -2,051,000 J - (20 mol)(8.314 J/mol·K)(298 K)
Finally, we convert J to kJ by dividing by 1000 and round to the nearest kilojoule:
ΔU = -2,051,000 J - (20 mol)(8.314 J/mol·K)(298 K)
ΔU ≈ -2,051 kJ
Therefore, the internal energy change for the reaction at 25°C is approximately -2,051 kJ (per mole of C10H22).