Question

Iron fillings and water are placed in a $5$ litre vessel and sealed. The tank was heated to ${1000}^{o}C$. Upon analysis the tank was found to contain $1.1g$ of hydrogen and $42.5g$ of water vapour. If the reaction in the tank is represented by,
$3Fe\left(s\right)+4H_{2}O\left(g\right)\rightleftharpoons {Fe}_3{O}_4\left(s\right)+4H_2\left(g\right)$
the value of equilibrium constant, $K_c$, is

• A. $30$
• B. $0.03$
• C. $3$
• D. $0.003$

Answer 1

Answer: (D)

$0.003$

Iron fillings and water are placed in a $5$ litre vessel and sealed. The tank was heated to ${1000}^{o}C$. Upon analysis the tank was found to contain $1.1g$ of hydrogen and $42.5g$ of water vapour.
The reaction in the tank is represented by,
$3Fe\left(s\right)+4H_{2}O\left(g\right)\rightleftharpoons {Fe}_3{O}_4\left(s\right)+4H_2\left(g\right)$
The molar masses of $H_2$ and $H_{2}O$ are 2 g/mol and 18 g/mol respectively.
The number of moles of $H_2=\frac{1.1g}{2g/mol}=0.55mol$
The number of moles of $H_{2}O=\frac{42.5g}{18g/mol}=2.36mol$
$\left[H_2\right]=\frac{0.55mol}{5L}=0.11M$
$\left[H_{2}O\right]=\frac{2.36mol}{5L}=0.472M$
The value of equilibrium constant is
$K_c=(\frac{\left[H_2\right]}{\left[H_{2}O\right]}{)}^4$
$K_c=(\frac{0.11M}{0.472M}{)}^4$
$K_c=0.003$