The bond energy of the O2 molecule is 495.
a) calculate the minimum frequency and max wavelength of light required to break this bond.
b) how many photons of this wavelength would it take in order to break open the bonds of all the oxygen molecules in a 384 mL container filled with oxygen at a pressure of 183.5 KPa and a temp of 36 degrees C? Assume 1 photon is used to break 1 oxygen bond.
i don't even know how to begin to solve this problem?!?!?!
That is 495 what? J/mol? kJ/mol? kJ/molecule. J/atom? just what?
Use E = hc/lambda where E is Joules, h is Planck's constant = 6.626 x 10^-34, c = speed of light in m/s (3 x 10^8 m/s)
and lambda will be in meters. To determine frequency, use c = lamda x freq.
For #2.
Use PV = nRT. I would convert kPa to atmospheres, T remember is in Kelvin, R is 0.08205 L*atm/mol*K, V must be in liters. Calculate n and from that determine how many molecules of O2 you have. The way I read the problem 1 photon is required to break 1 bond; therefore, you simply need to know how many bonds there are to be broken.
Post your work if you get stuck.
To solve this problem, we can use the concept of energy and the equation E = hf, where E is the energy of a photon, h is Planck's constant (6.626 x 10^-34 Js), and f is the frequency of the light.
a) To calculate the minimum frequency required to break the bond, we need to convert the bond energy from joules to electron volts (eV). 1 eV = 1.602 x 10^-19 J.
Bond Energy = 495 J
Convert to eV:
495 J * (1 eV / 1.602 x 10^-19 J) = 3.086 x 10^3 eV
Now, we can calculate the minimum frequency using the equation:
E = hf
f = E / h
Minimum Frequency = (3.086 x 10^3 eV) / (6.626 x 10^-34 Js)
Remember, you need to convert eV to joules:
1 eV = 1.602 x 10^-19 J
b) The minimum frequency of light required to break the bond in one oxygen molecule is found in part (a).
To calculate the maximum wavelength, we can use the equation c = fλ, where c is the speed of light (3.00 x 10^8 m/s) and λ is the wavelength.
Maximum Wavelength = c / f
Now, let's calculate the maximum wavelength by substituting the values:
Maximum Wavelength = (3.00 x 10^8 m/s) / (minimum frequency)
Next, we need to calculate the number of oxygen molecules in the container. We can use the ideal gas law equation:
PV = nRT
P = pressure = 183.5 kPa
V = volume = 384 mL = 384 x 10^-6 m^3
n = number of moles
R = ideal gas constant = 8.314 J/(mol·K)
T = temperature = 36 °C = 36 + 273.15 K
First, convert pressure to Pascals (Pa):
183.5 kPa = 183.5 x 10^3 Pa
Next, convert temperature to Kelvin:
36 °C = 36 + 273.15 K
Now, we can solve for the number of moles (n) using the ideal gas law equation:
n = (P * V) / (R * T)
Finally, to calculate the number of photons required, divide the number of bonds by the Avogadro constant (6.022 x 10^23):
Number of Photons = (Total number of oxygen molecules) / (Avogadro constant)
No worries! Let's break down the problem step by step.
a) To calculate the minimum frequency and maximum wavelength of light required to break the bond of the O2 molecule, we can use the equation:
E = hν = hc/λ
where:
- E is the energy required to break the bond (495 kJ/mol in this case, according to your question)
- h is Planck's constant (6.626 x 10^-34 Js)
- ν is the frequency of light
- c is the speed of light (2.998 x 10^8 m/s)
- λ is the wavelength of light
To find the minimum frequency, we rearrange the equation:
ν = E / h
Substituting the values, we have:
ν = (495,000 J/mol) / (6.626 x 10^-34 Js)
Simplify the equation, and the units of mol cancel out, leaving you with units of 1/s (which is Hz, or hertz).
For the maximum wavelength, we rearrange the equation as follows:
λ = c / ν
Substituting the values, we have:
λ = (2.998 x 10^8 m/s) / ν
Now you can substitute the value of ν that you calculated previously to find the maximum wavelength.
b) To calculate the number of photons needed to break the bonds of all the oxygen molecules in a container, we need to determine the number of oxygen molecules (moles) present in the container.
First, we need to convert the pressure (183.5 KPa) to units of atm (atmospheres). Divide the pressure by 101.325 KPa/atm to get the pressure in atmospheres.
Next, we need to convert the volume (384 mL) to units of L (liters). Divide the volume by 1000 to get the volume in liters.
Now we can use the Ideal Gas Law equation:
PV = nRT
where:
- P is the pressure in atm
- V is the volume in L
- n is the number of moles
- R is the ideal gas constant (0.0821 L·atm/(mol·K))
- T is the temperature in Kelvin
Rearrange the equation to solve for n:
n = PV / RT
Plug in the values for P, V, R, and T (remember to convert the temperature from Celsius to Kelvin) to find the number of moles of oxygen molecules in the container.
Finally, you can multiply the number of moles of oxygen molecules by Avogadro's number (6.022 x 10^23 molecules/mol) to find the total number of oxygen molecules in the container. Since we assume 1 photon is used to break 1 oxygen bond, this will give you the number of photons needed to break all the oxygen bonds.
I hope this helps you in solving the problem! If you have any further questions, feel free to ask.