Respuesta :
Explanation:
Henry's law states that the amount of gas dissolved or molar solubility of gas is directly proportional to the partial pressure of the liquid.
To calculate the molar solubility, we use the equation given by Henry's law, which is:
[tex]C_{g}=K_H\times p_{g}[/tex]
where,
[tex]K_H[/tex] = Henry's constant
[tex]p_{g}[/tex] = partial pressure of gas
A.
Henry constant = [tex]K_H= 3.1\times 10^{-2}mol/L.atm[/tex]
Pressure of the carbon dioxide gas in an unopened bottle:
=[tex]p_{CO_2}=4.0 atm[/tex]
Putting values in above equation, we get:
[tex]C_{CO_2}=3.1\times 10^{-2}mol/L.atm\times 4.0 atm\\\\C_{CO_2}=0.124 mol/L[/tex]
0.124 mol/L is the solubility of [tex]CO_2[/tex] gas-in-an-unopened soft drink bottle.
B.
Molarity of [tex]CO_2[/tex] gas = 0.124 mol/L
Moles of [tex]CO_2[/tex] gas in 2 Liter of soft drink:
= 0.124 mol/L × 2 L = 0.248 mol
0.248 moles of [tex]CO_2[/tex] gas are dissolved in an unopened 2 liter soft drink bottle.
C.
Pressure at sea level = P = 1 atm
Mole fraction carbon dioxide gas at sea level:
= [tex]\chi_{CO_2}=3.3\times 10^{-4}[/tex]
So, partial pressure of the [tex]CO_2[/tex] gas :
[tex]p_{CO_2}=P\times \chi_{CO_2}=1atm\times 3.3\times 10^{-4}[/tex]
[tex]p_{CO_2}=3.3\times 10^{-4} atm[/tex]
Henry constant = [tex]K_H= 3.1\times 10^{-2}mol/L.atm[/tex]
The solubility of [tex]CO_2[/tex] gas in the opened soft drink at sea level:
[tex]C_{CO_2} =3.1\times 10^{-2}mol/L.atm\times 3.3\times 10^{-4} atm[/tex]
[tex]=1.023\times 10^{-5} mol/L[/tex]
[tex]1.023\times 10^{-5} mol/L[/tex] is the solubility of [tex]CO_2[/tex] gas in opened soft drink bottle at sea level.
D.
Molarity of [tex]CO_2[/tex] gas in opened soft drink bottle at sea level = [tex]1.023\times 10^{-5} mol/L[/tex]
Moles of [tex]CO_2[/tex] gas in 2 Liter of soft drink left open at sea level?:
= [tex]1.023\times 10^{-5} mol/L\times 2L=2.046\times 10^{-5} mol[/tex]
[tex]2.046\times 10^{-5} [/tex]moles of [tex]CO_2[tex] gas are dissolved in 2 liter soft drink left open at sea level?
