Question

current attempt in progress
estimate δu for the following reaction using bond energies: (see table 3-2.)
c₂h₄(g) + br₂ (g) → c₂h₄br₂ (g)

-275 kj/mol
-360 kj/mol
-90 kj/mol
275 kj/mol
90 kj/mol

Explanation:

Step1: Identify bonds broken and formed

- Bonds broken: 1 \( C = C \) (bond energy of \( C = C \) is about \( 614 \, \text{kJ/mol} \)) and 1 \( Br - Br \) (bond energy of \( Br - Br \) is about \( 193 \, \text{kJ/mol} \)).
- Bonds formed: 2 \( C - Br \) (bond energy of \( C - Br \) is about \( 285 \, \text{kJ/mol} \)) and 1 \( C - C \) (bond energy of \( C - C \) is about \( 348 \, \text{kJ/mol} \)).

Step2: Calculate energy for bonds broken

Energy required to break bonds: \( E_{\text{broken}} = E_{C = C} + E_{Br - Br} = 614 + 193 = 807 \, \text{kJ/mol} \)

Step3: Calculate energy for bonds formed

Energy released when bonds form: \( E_{\text{formed}} = 2 \times E_{C - Br} + E_{C - C} = 2\times285 + 348 = 570 + 348 = 918 \, \text{kJ/mol} \)

Step4: Calculate \( \Delta U \)

\( \Delta U = E_{\text{broken}} - E_{\text{formed}} = 807 - 918 = -111 \, \text{kJ/mol} \). Wait, maybe using more accurate bond energies. Let's check standard bond energies:
- \( C = C \): \( 614 \, \text{kJ/mol} \)
- \( Br - Br \): \( 193 \, \text{kJ/mol} \)
- \( C - Br \): \( 285 \, \text{kJ/mol} \)
- \( C - C \): \( 348 \, \text{kJ/mol} \)

Wait, maybe the reaction is \( C_2H_4(g) + Br_2(g) ightarrow C_2H_4Br_2(s) \), but maybe in gas phase? Wait, maybe the correct approach is:

The formula for \( \Delta H \) (and \( \Delta U \) is close for reactions with small volume change) using bond energies is \( \Delta H = \sum E_{\text{bonds broken}} - \sum E_{\text{bonds formed}} \)

For \( C_2H_4 \) (ethylene): structure is \( H_2C = CH_2 \), so 1 \( C = C \), 4 \( C - H \)

\( Br_2 \): 1 \( Br - Br \)

\( C_2H_4Br_2 \) (1,2 - dibromoethane): structure is \( BrCH_2 - CH_2Br \), so 1 \( C - C \), 4 \( C - H \), 2 \( C - Br \)

So bonds broken: 1 \( C = C \), 1 \( Br - Br \)

Bonds formed: 1 \( C - C \), 2 \( C - Br \)

So \( E_{\text{broken}} = 614 + 193 = 807 \, \text{kJ/mol} \)

\( E_{\text{formed}} = 348 + 2\times285 = 348 + 570 = 918 \, \text{kJ/mol} \)

\( \Delta H = 807 - 918 = -111 \, \text{kJ/mol} \). But the options are -275, -360, -90, 275, 90. Wait, maybe I used wrong bond energies. Let's check another source:

Bond energy of \( C = C \): 614 kJ/mol, \( Br - Br \): 193 kJ/mol, \( C - Br \): 285 kJ/mol, \( C - C \): 348 kJ/mol. Wait, maybe the reaction is \( C_2H_4 + Br_2 ightarrow C_2H_4Br_2 \), and maybe the bond energies are different. Wait, maybe the correct calculation is:

Wait, maybe the problem is using approximate values. Let's recalculate:

Bonds broken: \( C = C \) (614) + \( Br - Br \) (193) = 807

Bonds formed: 2 \( C - Br \) (285 each) + \( C - C \) (348) = 285*2 + 348 = 570 + 348 = 918

\( \Delta U = 807 - 918 = -111 \), but the closest option is -90? Wait, maybe the bond energy of \( C = C \) is 602, \( Br - Br \) 193, \( C - Br \) 285, \( C - C \) 346.

Then \( E_{\text{broken}} = 602 + 193 = 795 \)

\( E_{\text{formed}} = 2*285 + 346 = 570 + 346 = 916 \)

\( \Delta U = 795 - 916 = -121 \). Still not. Wait, maybe the reaction is in liquid phase? No, the reactants are gases, product is solid. But maybe the bond energy values are different. Wait, the options include -90. Maybe the correct calculation is:

Wait, another approach: The reaction is an addition reaction. The \( C = C \) bond (614) is broken, \( Br - Br \) (193) is broken. Then two \( C - Br \) (285 each) and one \( C - C \) (348) are formed.

So \( \Delta U = (614 + 193) - (2*285 + 348) = 807 - (570 + 348) = 807 - 918 = -111 \). But the options have -90. Maybe the bond energy of \( C = C \) is 600, \( Br - Br \) 200, \( C - Br \) 290, \( C - C \) 350.

Then \( E_{\text{broken}} = 600 + 200 = 800 \)

\( E_{\text{formed}} = 2*290 + 350 = 580 + 350 = 930 \)

\( \Delta U = 800 - 930 = -130 \). Still not. Wait, maybe the answer is -90 kJ/mol. Maybe the bond energies used are:

\( C = C \): 610, \( Br - Br \): 190, \( C - Br \): 280, \( C - C \): 350.

Then \( E_{\text{broken}} = 610 + 190 = 800 \)

\( E_{\text{formed}} = 2*280 + 350 = 560 + 350 = 910 \)

\( \Delta U = 800 - 910 = -110 \). Close to -90? Maybe the problem has approximate values. Alternatively, maybe I made a mistake in bond identification.

Wait, \( C_2H_4 \) has 4 \( C - H \) bonds, \( C_2H_4Br_2 \) has 4 \( C - H \) bonds, so those don't change. So only \( C = C \), \( Br - Br \) broken, and \( C - C \), 2 \( C - Br \) formed. So the calculation is correct. The closest option is -90 kJ/mol.

Answer:

-90 kJ/mol