Ethyl chloride 1C2H5Cl2, a substance used as a topical anes-thetic, is prepared by reaction of ethylene with hydrogen chloride: C2H41g2 + HCl1g2 ¡ C2H5Cl1g2 ΔH° = - 72.3 kJ How much PV work is done in kilojoules, and what is the value of ΔE in kilojoules if 89.5 g of ethylene and 125 g of HCl are allowed to react at atmospheric pressure and the volume change is - 71.5 L?

Verified step by step guidance

1. Step 1: Determine the moles of reactants.
2. Calculate the moles of ethylene (C_2H_4) using its molar mass: \( \text{moles of } C_2H_4 = \frac{89.5 \text{ g}}{28.05 \text{ g/mol}} \).
3. Calculate the moles of HCl using its molar mass: \( \text{moles of HCl} = \frac{125 \text{ g}}{36.46 \text{ g/mol}} \).
4. Step 2: Identify the limiting reactant.
5. Compare the mole ratio of C_2H_4 to HCl from the balanced equation to determine the limiting reactant.>
6. Step 3: Calculate the enthalpy change (ΔH) for the reaction.
7. Use the limiting reactant to find the moles of product formed and calculate \( \Delta H = \text{moles of product} \times (-72.3 \text{ kJ/mol}) \).
8. Step 4: Calculate the PV work done.
9. Use the formula \( w = -P\Delta V \) where \( P = 1 \text{ atm} \) and \( \Delta V = -71.5 \text{ L} \). Convert the work from L·atm to kJ using the conversion factor \( 1 \text{ L·atm} = 0.1013 \text{ kJ} \).
10. Step 5: Calculate the change in internal energy (ΔE).
11. Use the formula \( \Delta E = \Delta H + w \) to find the change in internal energy in kJ.>

Key Concepts

Enthalpy Change (ΔH)

Enthalpy change (ΔH) is the heat absorbed or released during a chemical reaction at constant pressure. In this case, the reaction of ethylene with hydrogen chloride releases energy, indicated by a negative ΔH value of -72.3 kJ. This value helps determine the energy dynamics of the reaction and is crucial for calculating the total energy change when combined with other energy considerations.

Work Done (PV Work)

PV work refers to the work done by or on a system due to volume changes at constant pressure. It is calculated using the formula W = -PΔV, where P is the pressure and ΔV is the change in volume. In this scenario, with a volume change of -71.5 L at atmospheric pressure, understanding how to calculate this work is essential for determining the overall energy balance of the reaction.

Internal Energy Change (ΔE)

The internal energy change (ΔE) of a system accounts for both the heat exchanged and the work done during a process. It can be calculated using the equation ΔE = ΔH - W, where W is the work done. In this question, knowing how to relate ΔH and PV work to find ΔE is vital for understanding the energy transformations occurring during the reaction.