Answer to Question #210965 in General Chemistry for Fiona Yvonne Balia

Question #210965

K= 1.44 at 1000 k for synthesis gas reaction:

CO(g)+H2O →←CO2(g)+H2(g)

if initially the gases are introduced into an empty vessel at a partial pressure at 1.0 ATM each, what will be the equilibrium partial pressure of each gas?


1
Expert's answer
2021-06-28T08:12:16-0400

CO(g) + H2O(l) "\\leftrightarrow" CO2 (g) + H2 (g)

t=0 .... 1........--...........--...........--

.......1-P.....................P...........P

total pressure at equilibrium = 1+P

partial pressure of PCO = "\\frac{1-P}{1+P}" at equilibrium


partial pressure of P"_{CO_2}" = "\\frac{P}{1+P}" at equilibrium


partial pressure of P"_{H_2}" = "\\frac{P}{1+P}" at equilibrium


k = "\\frac{(\\frac{P}{1+P})(\\frac{P}{1+P})}{(\\frac{1-P}{1+P})}" = "\\frac{P^2}{1-P^2}"


1.44 = "\\frac{P^2}{1-P^2}"


1.44 - 1.44P2 = P2

1.44 = 2.44P2

P2 = "\\frac{1.44}{2.44}"

P = 0.768

so partial pressure of CO (PCO) ="\\frac{1-0.768}{1+0.768}"


so partial pressure of CO2 (P"_{C0_2}" ) ="\\frac{0.768}{1.768}"


so partial pressure of H2 (P"_{H_2}" ) ="\\frac{0.768}{1.768}"


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