Respuesta :
Answer: Partial pressure of helium gas is 162.24 atm.
Explanation:
Total pressure in Heloix [tex]p_o=208 atm[/tex]
Mole fraction of oxygen =[tex]\chi_{o}=0.22[/tex]
Mole fraction of helium =[tex]\chi_{He}=1-\chi_{o}=1-0.22=0.78[/tex]
According Dalton's law of partial pressure.
partial pressure of oxygen gas in Heloix:
[tex]p_{o}=p_o\times \chi_{o}=208 atm\times 0.22=45.76 atm[/tex]
partial pressure of helium gas in Heloix:
[tex]p_{He}=p_o\times \chi_{He}=208 atm\times 0.78=162.24 atm[/tex]
Partial pressure of helium gas is 162.24 atm.
The partial pressure of He gas in tank is [tex]\boxed{{\mathbf{162}}{\mathbf{.24 atm}}}[/tex].
Further explanation:
Mole fraction is defined as the number of moles of one component divided by the total number of moles of the solution. The mole fraction of all components present in the solution is equal to 1. It is denoted by X.
The formula to calculate mole fraction of substance is as follows:
[tex]X = \frac{{{\text{Number of moles of substance}}}}{{{\text{Total number of moles}}}}[/tex]
For a mixture of two substances, A and B, the mole fractions of each would be written as follows:
Mole fraction of A:
[tex]{X_A} = \frac{{{\text{mol of A}}}}{{{\text{mol of A}} + {\text{mol of B}}}}[/tex]
Mole fraction of B:
[tex]{X_B} = \frac{{{\text{mol of B}}}}{{{\text{mol of A}} + {\text{mol of B}}}}[/tex]
Also, mole fraction of A and B is equal to 1. It is expressed as follows:
[tex]{X_A}+{X_B}={\text{1}}[/tex] …… (1)
According to Dalton’s law of partial pressure, the total pressure is the sum of the partial pressure of each gas. The formula to calculate total pressure is as follows:
[tex]{P_{{\text{total}}}}={P_{\text{a}}}+{P_{\text{b}}}+....[/tex] …… (2)
Here,
[tex]{P_{{\text{total}}}}[/tex]is the total pressure of all gas in a mixture.
[tex]{P_{\text{a}}}[/tex], [tex]{P_{\text{b}}}[/tex] are the partial pressures of gas [tex]a[/tex]and [tex]b[/tex].
The formula to calculate the partial pressure of a particular gas is:
[tex]{P_{{\text{gas}}}}={X_{{\text{gas}}}}\cdot {P_{{\text{total}}}}[/tex] …... (3)
Here,
[tex]{P_{{\text{gas}}}}[/tex]is the partial pressure of the gas.
[tex]{P_{{\text{total}}}}[/tex]is the total pressure of the mixture.
[tex]{X_{{\text{gas}}}}[/tex]is the mole fraction of gas.
Heliox is a mixture of two gases and that is helium and oxygen gas.
Mole fraction of oxygen gas[tex]\left({{X_{\text{O}}}}\right)[/tex] is 0.22.
The reation between mole fraction of helium and oxygen gas is as follows:
[tex]{X_{{\text{He}}}}+{X_{\text{O}}}=1[/tex] …… (4)
Rearrange equation (4) to calculate mole fraction of helium [tex]\left({{X_{{\text{He}}}}}\right)[/tex].
[tex]\begin{aligned}{X_{{\text{He}}}}&=1 - {X_{\text{O}}}\\&=1 - 0.22\\&=0.78\\\end{aligned}[/tex]
The formula to calculate the partial pressure of a particular gas is:
[tex]{P_{{\text{He}}}}={X_{^{{\text{He}}}}}\times{P_{{\text{Heliox}}}}[/tex] …... (5)
Mole fraction of helium gas [tex]\left({{X_{{\text{He}}}}}\right)[/tex]is 0.78.
Also, the total pressure of heliox[tex]({P_{{\text{Heliox}}}})[/tex] is 208 atm.
Substitute these values in equation (5) to calculate the partial pressure of helium gas[tex]\left({{P_{{\text{He}}}}}\right)[/tex].
[tex]\begin{aligned}{P_{{\text{He}}}}&={\text{0}}{\text{.78}}\times{\text{208 atm}}\\&={\text{162}}{\text{.24}}\;{\text{atm}}\\\end{aligned}[/tex]
Hence, the partial pressure of He gas in tank is 162.24 atm.
Learn more:
1. Calculate the moles of chlorine in 8 moles of carbon tetrachloride: https://brainly.com/question/3064603
2. Which law states the direct relationship between volume and absolute temperature at constant pressure? https://brainly.com/question/1403211
Answer details:
Grade: High School
Subject: Chemistry
Chapter: Gases and the kinetic-molecular theory
Keywords: partial pressure, dalton’s law, mole fraction, mole, He gas, 162.24 atm, 078, 0.22, 208 atm.
