If H for the reaction I2 (s) 2I (g) is 153 kJ/mol. What is the longest wavelength of light that can break an I – I bond? In other words, what is the minimum energy, expressed in terms of wavelength, required to break one I – I bond?
A. 246 nm
B. 465 nm
C. 349 nm
D. 699 nm
E. 783 nm
Well, breaking an I-I bond sounds pretty intense. I mean, those iodine atoms must really be holding on tight, right? Let's see if we can find the right wavelength to break this bond.
We know that the energy required to break one I-I bond is 153 kJ/mol. Now, to find the minimum energy required in terms of wavelength, we can use the equation:
E = hc/λ
Where E is the energy, h is Planck's constant, c is the speed of light, and λ is the wavelength.
By rearranging the equation, we can solve for λ:
λ = hc/E
Now we just need to plug in the values. Planck's constant (h) is about 6.626 x 10^-34 J·s, and the speed of light (c) is approximately 3.00 x 10^8 m/s.
Let's do the math:
λ = (6.626 x 10^-34 J·s) x (3.00 x 10^8 m/s) / (153,000 J/mol)
After crunching the numbers, we find that the longest wavelength of light that can break an I-I bond is approximately 465 nm. So, the answer is B. 465 nm.
Remember, though, this is just an approximation. Breaking bonds can be a bit complicated, so it's best not to take it too lightly. Ba-dum-tss!
To answer this question, we need to know the relationship between energy and wavelength of light. This can be calculated using the equation:
E = hc/λ
Where:
E is the energy of the light,
h is Planck's constant (6.626 × 10^-34 J·s),
c is the speed of light (3.00 × 10^8 m/s),
and λ is the wavelength of light.
To find the minimum energy required to break one I-I bond, we need to calculate the energy change (∆H) for the reaction I2 (s) → 2I (g).
Given that ∆H = 153 kJ/mol, we can convert it to joules per molecule by dividing by Avogadro's number, which is 6.022 × 10^23 molecules/mol.
Next, we use the equation:
∆H = nE
Where:
∆H is the energy change for the reaction (in joules/molecule),
n is the number of I-I bonds broken per molecule,
and E is the energy required to break one I-I bond.
Since we have 2I formed from breaking 1 I-I bond, we can say that n = 1/2.
Now we can calculate the energy required to break one I-I bond:
E = ∆H / n = (153 kJ/mol) / (1/2) = 306 kJ/mol
To convert this energy into joules, we multiply by 1000:
E = 306 kJ/mol × (1000 J/kJ) = 306,000 J/mol
Finally, we can calculate the wavelength of light with this energy using the equation:
E = hc/λ
Solving for λ:
λ = hc/E = (6.626 × 10^-34 J·s × 3.00 × 10^8 m/s) / 306,000 J/mol
Calculating this expression gives us:
λ = 6.85 × 10^-7 m
To convert this into nanometers, we multiply by 10^9:
λ = 6.85 × 10^-7 m × 10^9 nm/m = 685 nm
Therefore, the longest wavelength of light that can break an I-I bond is 685 nm.
None of the options provided match this answer exactly, so you may want to double-check your available answer choices or consider that there may be a mistake in the question itself.