The pressure of gas is 1.05 atm when a 1.25 g sample of CO₂ is contained in a 750ml flask at 22.5°C.
Molecular weight of CO₂ is 1.25g ,Volume of CO₂ is 750ml,Temperature of CO₂ is 22.5°C and the gas constant is 0.08206 L atm/mol K.
Using the ideal gas law equation the pressure is found to be 1.05 atm.
To calculate the pressure of the gas, we can use the ideal gas law equation: [tex]PV=nRT[/tex]
Where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.
First, we need to convert the volume to liters by dividing by 1000: 750 ml = 0.75 L.
Next, we need to calculate the number of moles of CO₂ present in the flask. We can use the molecular weight of CO₂ to convert from grams to moles:
[tex]1.25 * (1 /44.01 ) = 0.0284 mol[/tex]
Now we can plug in the values into the ideal gas law equation:
[tex]PV=nRT[/tex]
[tex]P * 0.75 L = 0.0284 mol * 0.08206 L*atm/mol*K * (22.5 + 273.15) K[/tex]
Simplifying and solving for P, we get:
[tex]P = (0.0284 * 0.08206 * 295.65) / 0.75 = 1.05 atm[/tex]
Therefore, the pressure of the gas in the flask is 1.05 atm.
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calculate the engery of a photon needed to cause an electron in the 3s orbital to be excited to tthe 3p orbital
The energy of the photon needed to cause an electron in the 3s orbital to be excited to the 3p orbital is approximately 3.04 × [tex]10^{-18}[/tex] J (or about 1.90 eV).
To calculate the energy of a photon needed to cause an electron in the 3s orbital to be excited to the 3p orbital, we need to know the energy difference between these two orbitals.
The energy of an electron in a hydrogenic atom (an atom with one electron) can be calculated using the following formula:
[tex]E = - (Z^2 * Ry) / n^2[/tex]
where Z is the atomic number, Ry is the Rydberg constant (2.18 × [tex]10^{-18}[/tex]J), and n is the principal quantum number.
The energy difference between the 3s and 3p orbitals can be calculated by subtracting the energy of the 3s orbital from the energy of the 3p orbital.
For hydrogen, the energy of the 3s orbital is:
E(3s) = - ([tex]1^2[/tex]* 2.18 × [tex]10^{18}[/tex] J) / [tex]3^2[/tex]
E(3s) = - 0.242 ×[tex]10^{18}[/tex] J
And the energy of the 3p orbital is:
E(3p) = - ([tex]1^2[/tex] * 2.18 × [tex]10^{-18}[/tex] J) / 2^2
E(3p) = - 0.546 × [tex]10^{-18}[/tex] J
The energy difference between the two orbitals is:
ΔE = E(3p) - E(3s)
ΔE = (- 0.546 ×[tex]10^{18}[/tex] J) - (- 0.242 ×[tex]10^{-18}[/tex] J)
ΔE = - 0.304 × [tex]10^{-18}[/tex]J
This energy difference represents the energy required to excite an electron from the 3s orbital to the 3p orbital.
To calculate the energy of the photon needed to provide this energy, we use the formula:
E = hν
where E is the energy of the photon, h is Planck's constant (6.626 × [tex]10^{-34}[/tex]J·s), and ν is the frequency of the photon.
Rearranging this formula to solve for the frequency of the photon, we get:
ν = E / h
Substituting the energy difference we calculated, we get:
ν = (- 0.304 × [tex]10^{18}[/tex] J) / (6.626 × [tex]10^{-34}[/tex] J·s)
ν = - 4.59 × [tex]10^{15}[/tex]Hz
Finally, to calculate the energy of the photon, we use the formula:
E = hν
Substituting the frequency we calculated, we get:
E = (6.626 ×[tex]10^{-34}[/tex] J·s) x (- 4.59 × [tex]10^{15}[/tex] Hz)
E = - 3.04 × [tex]10^{-18}[/tex]J
Therefore, the energy of the photon needed to cause an electron in the 3s orbital to be excited to the 3p orbital is approximately 3.04 × 10^-18 J (or about 1.90 eV).
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