Question

A mole of X reacts at a constant pressure of 43.0 atm via the reaction X(g)+4Y(g)→2Z(g), ΔH∘=−75.0 kJ Before the reaction, the volume of the gaseous mixture was 5.00 L. After the reaction, the volume was 2.00 L. Calculate the value of the total energy change, ΔE, in kilojoules.

Answer 1

To calculate the value of the total energy change ΔE, we can use the equation ΔE = ΔH - PΔV. By substituting the given values for ΔH, PΔV, and the initial and final volumes, we can find the value of ΔE, which is 54.0 kJ.

Step-by-step explanation:

To calculate the change in total energy, ΔE, in kilojoules, we can use the equation: ΔE = ΔH - PΔV

ΔH represents the change in enthalpy, which is given as -75.0 kJ for the reaction X(g) + 4Y(g) → 2Z(g).

PΔV represents the work done by the system at constant pressure and is calculated using the equation: PΔV = P(V_final - V_initial).

Given that the initial volume is 5.00 L and the final volume is 2.00 L, and the constant pressure is 43.0 atm, we can substitute these values into the equation to find the value of PΔV. Finally, we can subtract the value of PΔV from ΔH to find the value of ΔE.

Calculating the value of PΔV:

• PΔV = (43.0 atm) x (2.00 L - 5.00 L)
• PΔV = -129 atm∙L

Calculating the value of ΔE:

• ΔE = -75.0 kJ - (-129 atm∙L)
• ΔE = 54.0 kJ

Answer 2

The volume fraction in gasses is equal to the mole fraction.
In a reaction mixture, the molar ratio of X : Y = 1:4
Fraction of X = 1/5
Fraction of Y = 4/5
So in the 5 L reaction mix,
1 L of X and 4 L of Y
The products contain 2 L of Z
This satisfies the equation completely so we check the enthalpy of this reaction:
-75 kilojoules