Answer:
The molar concentration of radon is 4.38 x 10⁻⁶ mol.L⁻¹
Explanation:
Molar fraction = number of moles of a certain component / total number of moles
Partial pressure = Total pressure x molar fraction
Partial pressure = 34 atm x 3.2 x 10⁻⁶
Partial pressure = 1.09 x 10⁻⁴ atm
Considering radon as an ideal gas, PV = nRT
molar concentration = n/V
n/V = P/RT
n/V = 1.09 x 10⁻⁴ atm / 0.082 L.atm.mol⁻¹K⁻¹ x 303.15K
n/V = 4.38 x 10⁻⁶ mol.L⁻¹
Considering the Dalton's partial pressure and ideal gas law, the molar concentration of radon in the water is [tex]4.38x10^{-6} \frac{mol}{L}[/tex].
The pressure exerted by a particular gas in a mixture is known as its partial pressure.
So, Dalton's law states that the total pressure of a gas mixture is equal to the sum of the pressures that each gas would exert if it were alone:
[tex]P_{T} =P_{A} +P_{B} +...+P_{n}[/tex]
where n is the amount of gases in the mixture.
Dalton's partial pressure law can also be expressed in terms of the mole fraction of the gas in the mixture. So in a mixture of two or more gases, the partial pressure of gas A can be expressed as:
[tex]P_{A} =x_{A} P_{T}[/tex]
An ideal gas is characterized by three state variables: absolute pressure (P), volume (V), and absolute temperature (T). The relationship between them constitutes the ideal gas law, an equation that relates the three variables if the amount of substance, number of moles n, remains constant and where R is the molar constant of gases:
P×V = n×R×T
In this case, you know:
[tex]x_{A} =[/tex] 3.2×10⁻⁶
[tex]P_{T}=[/tex] 34 atm
Replacing in the Dalton's law:
[tex]P_{A} =[/tex] 3.2×10⁻⁶ ×34 atm
[tex]P_{A} =[/tex] 1.088×10⁻⁴ atm
Considering radon as an ideal gas, it is satisfied: P×V = n×R×T
The molar concentration of radon is [tex]\frac{n}{V}[/tex]
From ideal gas law:
[tex]\frac{n}{V} =\frac{P}{RxT}[/tex]
You know:
Replacing:
[tex]\frac{n}{V} =\frac{1.088x10^{-4} atm}{0.082\frac{atm L}{mol K}x303 K}[/tex]
[tex]\frac{n}{V} =4.38x10^{-6} \frac{mol}{L}[/tex]
Finally, the molar concentration of radon in the water is [tex]4.38x10^{-6} \frac{mol}{L}[/tex].
Learn more about
Ideal gas law:
https://brainly.com/question/4147359
Dalton's partial pressure:
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Molar fraction = number of moles of a certain component / total number of moles
Partial pressure = Total pressure x molar fraction
Partial pressure = 34 atm x 3.2 x 10⁻⁶
Partial pressure = 1.09 x 10⁻⁴ atm
Considering radon as an ideal gas, PV = nRT
molar concentration = n/V
n/V = P/RT
n/V = 1.09 x 10⁻⁴ atm / 0.082 L.atm.mol⁻¹K⁻¹ x 303.15K
n/V = 4.38 x 10⁻⁶ mol.L⁻¹
