KVPY Sample Paper KVPY Stream-SX Model Paper-10

For the reaction \[\operatorname{C}\left( s \right)+C{{O}_{2}}(g)\to 2CO\left( g \right),\] \[{{K}_{P}}=63\] atm at 1000 K. If at equilibrium: \[{{P}_{C{{O}_{2}}}}\text{ }=\text{ }10\]then the total pressure of the gases at equilibrium is

A) 6.3 atm

B) 6.93 atm

C) 0.63 atm

D) 0.693 atm

Correct Answer: B

Solution :

\[C\left( s \right)+C{{O}_{2}}\left( g \right)\xrightarrow[{}]{}2CO\left( g \right)\]

Apply law of mass action,

\[{{K}_{P}}=\frac{{{\left( {{P}_{C{{O}_{2}}}} \right)}^{2}}}{{{P}_{C{{O}_{2}}}}}\]

Given: \[{{\operatorname{K}}_{P}}=65\operatorname{and}\,{{P}_{CO}}=10{{P}_{C{{O}_{2}}}}\]

\[63=\frac{{{\left( 10{{P}_{C{{O}_{2}}}} \right)}^{2}}}{{{P}_{C{{O}_{2}}}}}\]

Or \[63=\frac{100{{\left( {{P}_{C{{O}_{2}}}} \right)}^{2}}}{{{P}_{C{{O}_{2}}}}}\operatorname{or}\,63=100{{P}_{C{{O}_{2}}}}\]

\[{{\operatorname{P}}_{C{{O}_{2}}}}=\frac{63}{100}=0.63atm\]

\[{{\operatorname{P}}_{C{{O}_{2}}}}=102{{P}_{C{{O}_{2}}}}=10\times 0.63=6.3atm\]

\[{{\operatorname{P}}_{total}}={{P}_{C{{O}_{2}}}}+{{P}_{CO}}=0.63+6.3=6.93atm\]