Thermal decomposition of gaseous `X_(2)` to gaseous `X` at `298K` takes place according to the following equation:
`X(g)hArr2X(g)`
The standard reaction Gibbs energy `Delta_(r)G^(@)`, of this reaction is positive. At the start of the reaction, there is one mole of `X_(2)` and no `X`. As the reaction proceeds, the number of moles of `X` formed is given by `beta`. Thus `beta_("equilibrium")` is the number of moles of `X` formed at equilibrium. The reaction is carried out at a constant total pressure of 2 bar. Consider the gases to behave ideally.
[Given, `R=0.083L` bar `K^(-1) mol^(-1)`)
The equilibrium constant `K_(p)` for this reaction at `298K`, in terms of `beta_("equilibrium")` is
Thermal decomposition of gaseous `X_(2)` to gaseous `X` at `298K` takes place according to the following equation:
`X(g)hArr2X(g)`
The standard reaction Gibbs energy `Delta_(r)G^(@)`, of this reaction is positive. At the start of the reaction, there is one mole of `X_(2)` and no `X`. As the reaction proceeds, the number of moles of `X` formed is given by `beta`. Thus `beta_("equilibrium")` is the number of moles of `X` formed at equilibrium. The reaction is carried out at a constant total pressure of 2 bar. Consider the gases to behave ideally.
[Given, `R=0.083L` bar `K^(-1) mol^(-1)`)
The equilibrium constant `K_(p)` for this reaction at `298K`, in terms of `beta_("equilibrium")` is
`X(g)hArr2X(g)`
The standard reaction Gibbs energy `Delta_(r)G^(@)`, of this reaction is positive. At the start of the reaction, there is one mole of `X_(2)` and no `X`. As the reaction proceeds, the number of moles of `X` formed is given by `beta`. Thus `beta_("equilibrium")` is the number of moles of `X` formed at equilibrium. The reaction is carried out at a constant total pressure of 2 bar. Consider the gases to behave ideally.
[Given, `R=0.083L` bar `K^(-1) mol^(-1)`)
The equilibrium constant `K_(p)` for this reaction at `298K`, in terms of `beta_("equilibrium")` is
A
`(8beta_("equilibrium")^(2))/(2-beta_("equilibrium"))`
B
`(8beta_("equilibrium")^(2))/(4-beta_("equilibrium")^(2))`
C
`(4beta_("equilibrium")^(2))/(2-beta_("equilibrium"))`
D
`(4beta_("equilibrium")^(2))/(4-beta_("equilibrium")^(2))`
Text Solution
Verified by Experts
The correct Answer is:
B
`{:(,X_(2) (g) ,hArr,2X(g)),("At t=0,",1,,0):}`
At eqm. `(1-(beta_(eq))/(2)) " "beta_(eq)`
`K_(p) =((pX)^(2))/((pX_(2)))`
`P_(X) =((beta_(eq))/(1-(beta_(eq))/(2)+beta_(eq))) P_("total") =((beta_(eq))/((1-beta_(eq))/(2)))P_("total")`
`PX_(2)=((1-(beta_(eq))/(2))/(1+(beta_(eq))/(2)))P_("total")`
`K_(p) =[((beta_(eq))/(1+(beta_(eq))/(2))) P_("total") ]^(2)/(((1-(beta_(eq))/(2))/(1+(beta_(eq))/(1))) P_("total"))=((beta_(eq)^(2))/(1-(beta_(eq)^(2))/(4)))p_("total")`
`=((4beta_(eq)^(2))/(4-beta_(eq)^(2))) P_("total") =((4beta_(eq)^(2))/(4-beta_(eq)^(2))) xx2 =(8beta_(eq)^(2))/(4-beta_(eq)^(2))`
At eqm. `(1-(beta_(eq))/(2)) " "beta_(eq)`
`K_(p) =((pX)^(2))/((pX_(2)))`
`P_(X) =((beta_(eq))/(1-(beta_(eq))/(2)+beta_(eq))) P_("total") =((beta_(eq))/((1-beta_(eq))/(2)))P_("total")`
`PX_(2)=((1-(beta_(eq))/(2))/(1+(beta_(eq))/(2)))P_("total")`
`K_(p) =[((beta_(eq))/(1+(beta_(eq))/(2))) P_("total") ]^(2)/(((1-(beta_(eq))/(2))/(1+(beta_(eq))/(1))) P_("total"))=((beta_(eq)^(2))/(1-(beta_(eq)^(2))/(4)))p_("total")`
`=((4beta_(eq)^(2))/(4-beta_(eq)^(2))) P_("total") =((4beta_(eq)^(2))/(4-beta_(eq)^(2))) xx2 =(8beta_(eq)^(2))/(4-beta_(eq)^(2))`
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Thermal decomposition of gaseous X_(2) to gaseous X at 298 K takes place according to the following equation : X_(2) (g) 2X(g) The standard reaction Gibbs energy, Delta_(r)G° , of this reaction is positive. At the start of the reaction, there is one moe of X_(2) and no X. As the reaction proceeds, the number of moles of X formed is given by beta . Thus, beta_("equilibrium") is the number of moles of X formed at equilibrium. The reaction is carried out at a constant total pressure of 2 bar. Consider the gases to behave ideally. (Given : R = 0.083 L bar K^(-1) mol^(-1) ) The Incorrect statement among the following, for this reaction is
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Thermal decomposition of gaseous X_(2) to gaseous X at 298 K takes place according to the following equation : X_(2) (g) 2X(g) The standard reaction Gibbs energy, Delta_(r)G° , of this reaction is positive. At the start of the reaction, there is one moe of X_(2) and no X. As the reaction proceeds, the number of moles of X formed is given by beta . Thus, beta_("equilibrium") is the number of moles of X formed at equilibrium. The reaction is carried out at a constant total pressure of 2 bar. Consider the gases to behave ideally. (Given : R = 0.083 L bar K^(-1) mol^(-1) ) The equilibrium constant K_(p) for this reaction at 298 K, in terms of beta_("equilibrium") , is
Thermal decomposition of gaseous X_(2) to gaseous X at 298 K takes place according to the following equation : X_(2) (g) 2X(g) The standard reaction Gibbs energy, Delta_(r)G° , of this reaction is positive. At the start of the reaction, there is one moe of X_(2) and no X. As the reaction proceeds, the number of moles of X formed is given by beta . Thus, beta_("equilibrium") is the number of moles of X formed at equilibrium. The reaction is carried out at a constant total pressure of 2 bar. Consider the gases to behave ideally. (Given : R = 0.083 L bar K^(-1) mol^(-1) ) The equilibrium constant K_(p) for this reaction at 298 K, in terms of beta_("equilibrium") , is
A
`(8beta_("equilibrium")^(2))/(2-beta_("equilibrium"))`
B
`(8beta_("equilibrium")^(2))/(4-beta_("equilibrium")^(2))`
C
`(4beta_("equilibrium")^(2))/(2-beta_("equilibrium"))`
D
`(4beta_("equilibrium")^(2))/(4-beta_("equilibrium")^(2))`
Thermal decomposition of gaseous X_(2) to gaseous X at 298K takes place according to the following equation: X(g)hArr2X(g) The standard reaction Gibbs energy Delta_(r)G^(@) , of this reaction is positive. At the start of the reaction, there is one mole of X_(2) and no X . As the reaction proceeds, the number of moles of X formed is given by beta . Thus beta_("equilibrium") is the number of moles of X formed at equilibrium. The reaction is carried out at a constant total pressure of 2 bar. Consider the gases to behave ideally. [Given, R=0.083L bar K^(-1) mol^(-1) ) The incorrect statement among the following for this reaction, is
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A
Decrease in the total pressure will result in the formation of more moles of gaseous `X`
B
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C
`beta_("equilibrium")=0.7`
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Thermal decomposition of gaseous X_(2) to gaseous X at 298 K takes place according to following equation X_(2) (g) hArr 2X(g) The standard reaction Gibbs energy Delta_(r)G^(@) of this reaction is positive . At the start of the reaction there is one mole of X_(2) " and no. " X . As the reaction proceeds the number of moles of X formed is given by beta . Thus beta_("equilibrium") is the the number of moles of X formed at equilibrium . The reaction is carried out a constant total pressure of 2 bar. Consider the gases to behave ideally. ("Given" : R =0.083 L " bar " K^(-1) " mol"^(-1)) The incorrect statement among the following for this reaction is
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A
Decrease in the total pressure will result in formation of more moles of gaseous X
B
At the start of the reaction , dissocition of gaseous `X_(2)` takes place spontaneously
C
`beta_("equilibrium") =0.7`
D
`K_(c)lt 7`
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