Calculate the energy in kJ/mol of light with a wavelength of 360 nm.
9.17 * 10^-43 J/mol
Oxygen gas at 34.5 °C expands from 34.5 L to 45.7 L against a
constant pressure of 750 mmHg. What is the work done in
joules by the system?
1.13*10^3 J
for the first one I got 332 kJ/mol
E = hc/lamda
E = (6.626E-34)(2.998E8)/(360E-9)
E = 5.522 J
To convert it to kJ/mol, multiply by 6.022E23 and divide by 1000 to get 332 kJ/mol
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Now, let's calculate the energy of the light with a wavelength of 360 nm.
To calculate the energy, we can use the equation
E = hc/λ
Where E is the energy, h is the Planck constant, c is the speed of light, and λ is the wavelength.
Plugging in the values, we get:
E = (6.626 × 10^-34 J·s × 3.00 × 10^8 m/s) / (360 × 10^-9 m)
E ≈ 5.51 × 10^-19 J
To convert this energy to kJ/mol, we can use Avogadro's number (6.022 × 10^23 mol^-1):
Energy (in kJ/mol) = (5.51 × 10^-19 J) / (6.022 × 10^23 mol^-1)
Energy ≈ 9.17 × 10^-43 kJ/mol
So, the energy of light with a wavelength of 360 nm is approximately 9.17 × 10^-43 kJ/mol.
And now, let's move on to the work done by the expanding oxygen gas!
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To calculate the work done by the system, we can use the formula:
Work = -PΔV
Where P is the pressure and ΔV is the change in volume.
Plugging in the values, we get:
Work = -(750 mmHg) × (45.7 L - 34.5 L)
Work ≈ -(750 mmHg) × (11.2 L)
Work ≈ -8400 J
So the work done by the system is approximately -8400 J.
Keep in mind that the negative sign indicates work done by the system, meaning it is work done on the surroundings.
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To calculate the work done by the system, we can use the formula:
work = -P * ΔV
Where:
P is the pressure in Pascals (Pa)
ΔV is the change in volume in cubic meters (m^3)
First, let's convert the given pressure from mmHg to Pa:
750 mmHg = (750/760) * 101325 Pa ≈ 99,868.42 Pa
Next, let's convert the given temperatures from Celsius to Kelvin:
34.5 °C + 273.15 = 307.65 K
Now, let's convert the volume changes from liters to cubic meters:
(45.7 L - 34.5 L) = 11.2 L = 0.0112 m^3
Finally, we can plug the values into the formula to calculate the work done:
work = -99,868.42 Pa * 0.0112 m^3
work ≈ -1115.61 J
Therefore, the work done by the system is approximately -1115.61 J.
To calculate the energy in kilojoules per mole (kJ/mol) of light with a given wavelength, you can use the equation:
Energy = (hc) / λ
Where:
- h is Planck's constant (6.626 x 10^-34 J s)
- c is the speed of light (2.998 x 10^8 m/s)
- λ is the wavelength of light in meters
First, convert the given wavelength from nanometers (nm) to meters (m):
360 nm = 360 x 10^-9 m
Now, substitute the values into the equation and solve for energy:
Energy = [(6.626 x 10^-34 J s) x (2.998 x 10^8 m/s)] / (360 x 10^-9 m)
Energy = 5.512 x 10^-19 J
To convert this to kilojoules per mole (kJ/mol), divide by Avogadro's number (6.022 x 10^23 mol^-1):
Energy = (5.512 x 10^-19 J) / (6.022 x 10^23 mol^-1)
Energy ≈ 9.17 x 10^-43 J/mol
Therefore, the energy of light with a wavelength of 360 nm is approximately 9.17 x 10^-43 kJ/mol.
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To calculate the work done by a gas during expansion, you can use the equation:
Work = -PΔV
Where:
- P is the pressure (in this case, 750 mmHg)
- ΔV is the change in volume (45.7 L - 34.5 L)
First, convert the pressure from millimeters of mercury (mmHg) to pascals (Pa):
1 mmHg = 133.322 Pa
750 mmHg = 750 x 133.322 Pa
Next, calculate the change in volume:
ΔV = 45.7 L - 34.5 L
Now, substitute the values into the equation and solve for work:
Work = -(750 x 133.322 Pa) x (45.7 L - 34.5 L)
Work = -1.134 x 10^5 J
Therefore, the work done by the system is approximately -1.13 x 10^3 J (negative sign indicates work done by the system).