91Ó°ÊÓ

Chemical equilibrium is the state in which concentration of both thereactants andproducts have no further tendency to change with time.

Nitrogen is thechemical element with thesymbol N andatomic number 7. Nitrogen is anonmetal and the lightest member ofgroup 15 of the periodic table, often called the pnictogens.

Hydrogen is thechemical element with thesymbol H andatomic number 1. Hydrogen is the lightest element. Atstandard conditions hydrogen is agas ofdiatomic molecules having theformula H₂.

Given information

The volume of the vessel is 1.00L

At equilibrium constants

\(\begin{array}{*{20}{c}}{\left( {{{\rm{N}}_2}} \right) = 1.00{\rm{M}}}\\{\left( {{{\rm{H}}_2}} \right) = 0.50{\rm{M}}}\\{\left( {{\rm{N}}{{\rm{H}}_3}} \right) = 0.25{\rm{M}}}\end{array}\)

The Equillibrium constant is

\({K_c} = \frac{{{{\left| {{\rm{N}}{{\rm{H}}_3}} \right|}^2}}}{{\left| {{N_2}} \right| \times {{\left| {{H_2}} \right|}^3}}}\)

\(\frac{{{{(0.25)}^2}}}{{1.00 \times {{(0.5)}^3}}} = 0.5\)

We have to calculate the number of moles of hydrogen to be removed from the vessel to increase the concentration of nitrogen to 1.1M

The new equilibrium concentration of the\(\left| {{{\rm{N}}_2}} \right|{\rm{\;is\;}}1.1{\rm{M}}\)

And new initial concentrations are

\(\begin{array}{*{20}{c}}{ - \left( {{{\rm{N}}_2}} \right) = 1.00{\rm{M}}}\\{ - \left( {{{\rm{H}}_2}} \right) = 0.50{\rm{M}} - {\rm{x}}}\\{ - \left( {{\rm{N}}{{\rm{H}}_3}} \right) = 0.25{\rm{M}}}\end{array}\)

\({{\rm{N}}_2}({\rm{g}}) + 3{{\rm{H}}_2}({\rm{g}}) \to 2{\rm{N}}{{\rm{H}}_3}({\rm{g}})\)

\(\begin{array}{*{20}{c}}{{K_c} = \frac{{{{\left( {N{H_3}} \right)}^2}}}{{\left( {{N_2}} \right) \times {{\left( {{H_2}} \right)}^3}}}}\\{0.5 = \frac{{{{(0.05)}^2}}}{{1.1 \times {{(0.80 - x)}^3}}}}\end{array}\)

\(\begin{array}{*{20}{c}}{{{(0.80 - x)}^3} = 0.0045}\\{0.80 - x = 0.16565}\\{x = 0.634{\rm{M}}}\end{array}\)

Since initial concentration of hydrogen is \(0.50{\rm{\;mol,\;}}\)and we have to remove \(0.634{\rm{mol}}\) the equilibrium concentration cannot be \(1.1{\rm{M}}\)