Question
How much energy is produced when 20 molecules of HBr are produced
H2 + Br2 > 2HBr
Bonds: Energy(KJ/mol)
H-H 430
Br-Br 194
H-Br 366
Br=Br 100
H2 + Br2 > 2HBr
Bonds: Energy(KJ/mol)
H-H 430
Br-Br 194
H-Br 366
Br=Br 100
Answers
GPT-4o mini
To calculate the energy produced when 20 molecules of HBr are formed from hydrogen and bromine, we first need to identify the total energy change for the reaction.
The reaction given is:
\[
\text{H}_2 + \text{Br}_2 \rightarrow 2 \text{HBr}
\]
### Step 1: Calculate the bonds broken and formed
In one mole of the reaction:
- **Bonds broken**:
- 1 bond of H-H (from H₂)
- 1 bond of Br-Br (from Br₂)
- **Bonds formed**:
- 2 bonds of H-Br (in 2 HBr)
### Step 2: Calculate the energy involved in the bonds
Using the bond energies:
- Energy required to break 1 mole of H-H: **430 kJ/mol**
- Energy required to break 1 mole of Br-Br: **194 kJ/mol**
- Energy released when forming 2 moles of H-Br (for 2 HBr): **2 × 366 kJ/mol = 732 kJ/mol**
### Step 3: Compute total energy change for the reaction
#### Energy consumed (bonds broken):
- Total energy to break bonds = Energy for H-H + Energy for Br-Br
\[
= 430 \, \text{kJ} + 194 \, \text{kJ} = 624 \, \text{kJ/mol}
\]
#### Energy released (bonds formed):
- Total energy released = Energy for H-Br
\[
= 732 \, \text{kJ/mol}
\]
### Step 4: Calculate the net energy change
The net energy change for the reaction per mole is:
\[
\Delta E = \text{Energy released} - \text{Energy consumed}
\]
\[
= 732 \, \text{kJ/mol} - 624 \, \text{kJ/mol} = 108 \, \text{kJ/mol}
\]
### Step 5: Calculate the energy for 20 molecules of HBr
Since the reaction produces 2 moles of HBr for every mole of H₂ and Br₂ reacted, forming 20 molecules of HBr corresponds to:
\[
\text{20 molecules HBr} = \frac{20}{6.022 \times 10^{23}} \text{ moles} \approx 3.32 \times 10^{-23} \text{ moles of HBr}
\]
However, since 2 moles of HBr are produced from 1 mole of (H₂ + Br₂), to form 20 molecules of HBr (which is about \( 3.32 \times 10^{-23} \) moles), we need to consider that we need:
\[
\text{Total moles of reaction} = \frac{3.32 \times 10^{-23}}{2} = 1.66 \times 10^{-23} \text{ moles of reaction}
\]
Now, we calculate the energy change for this amount:
\[
\text{Total energy } = \Delta E \times \text{number of moles of reaction}
\]
\[
= 108 \, \text{kJ/mol} \times 1.66 \times 10^{-23} \text{ mol}
\]
### Final Calculation
\[
\text{Total energy} \approx 1.79 \times 10^{-22} \, \text{kJ}
\]
However, this is a very small energy change due to the extremely small amount of molecules involved.
In practical terms:
The reaction produces approximately **108 kJ for the formation of 2 moles (or 1 mole of reaction)**, and you would have to scale it accordingly if you handle very small numbers, but for direct question purpose:
For 20 molecules of HBr, the energy produced is very small and can typically be neglected for practical calculations at molecular scales, but for academic purposes, it would be around \(1.79 \times 10^{-22} \, \text{kJ}\).
In a larger context, if needing the energy relevant to a practical scenario, the moles would need to be larger to see significant energy changes.
The reaction given is:
\[
\text{H}_2 + \text{Br}_2 \rightarrow 2 \text{HBr}
\]
### Step 1: Calculate the bonds broken and formed
In one mole of the reaction:
- **Bonds broken**:
- 1 bond of H-H (from H₂)
- 1 bond of Br-Br (from Br₂)
- **Bonds formed**:
- 2 bonds of H-Br (in 2 HBr)
### Step 2: Calculate the energy involved in the bonds
Using the bond energies:
- Energy required to break 1 mole of H-H: **430 kJ/mol**
- Energy required to break 1 mole of Br-Br: **194 kJ/mol**
- Energy released when forming 2 moles of H-Br (for 2 HBr): **2 × 366 kJ/mol = 732 kJ/mol**
### Step 3: Compute total energy change for the reaction
#### Energy consumed (bonds broken):
- Total energy to break bonds = Energy for H-H + Energy for Br-Br
\[
= 430 \, \text{kJ} + 194 \, \text{kJ} = 624 \, \text{kJ/mol}
\]
#### Energy released (bonds formed):
- Total energy released = Energy for H-Br
\[
= 732 \, \text{kJ/mol}
\]
### Step 4: Calculate the net energy change
The net energy change for the reaction per mole is:
\[
\Delta E = \text{Energy released} - \text{Energy consumed}
\]
\[
= 732 \, \text{kJ/mol} - 624 \, \text{kJ/mol} = 108 \, \text{kJ/mol}
\]
### Step 5: Calculate the energy for 20 molecules of HBr
Since the reaction produces 2 moles of HBr for every mole of H₂ and Br₂ reacted, forming 20 molecules of HBr corresponds to:
\[
\text{20 molecules HBr} = \frac{20}{6.022 \times 10^{23}} \text{ moles} \approx 3.32 \times 10^{-23} \text{ moles of HBr}
\]
However, since 2 moles of HBr are produced from 1 mole of (H₂ + Br₂), to form 20 molecules of HBr (which is about \( 3.32 \times 10^{-23} \) moles), we need to consider that we need:
\[
\text{Total moles of reaction} = \frac{3.32 \times 10^{-23}}{2} = 1.66 \times 10^{-23} \text{ moles of reaction}
\]
Now, we calculate the energy change for this amount:
\[
\text{Total energy } = \Delta E \times \text{number of moles of reaction}
\]
\[
= 108 \, \text{kJ/mol} \times 1.66 \times 10^{-23} \text{ mol}
\]
### Final Calculation
\[
\text{Total energy} \approx 1.79 \times 10^{-22} \, \text{kJ}
\]
However, this is a very small energy change due to the extremely small amount of molecules involved.
In practical terms:
The reaction produces approximately **108 kJ for the formation of 2 moles (or 1 mole of reaction)**, and you would have to scale it accordingly if you handle very small numbers, but for direct question purpose:
For 20 molecules of HBr, the energy produced is very small and can typically be neglected for practical calculations at molecular scales, but for academic purposes, it would be around \(1.79 \times 10^{-22} \, \text{kJ}\).
In a larger context, if needing the energy relevant to a practical scenario, the moles would need to be larger to see significant energy changes.