Consider the following equilibrium,
$CO(g) + 2H_2(g) = CH_3OH(g)$
0.1 mol of CO along with a catalyst is present in a 2 $dm^3$ flask maintained at 500 K. Hydrogen is introduced into the flask until the pressure is 5 bar and 0.04 mol of $CH_3OH$ is formed. The $K_{p}^\theta$ is ________ $\times10^{-3}$ (nearest integer).
Given: R=0.08 $dm^3$ bar $K^{-1}$ $mol^{-1}$
Assume only methanol is formed as the product and the system follows ideal gas behaviour.
Equilibrium Kp Calculation for CO + 2H2 Reaction
This solution details the step-by-step calculation for the equilibrium constant, $K_p$, for the reaction between carbon monoxide ($CO$) and hydrogen ($H_2$) to form methanol ($CH_3OH$), based on the provided equilibrium conditions.
Reaction Stoichiometry
The balanced chemical equation for the reaction is:
$CO(g) + 2H_2(g) \rightleftharpoons CH_3OH(g)$
Given Parameters
- Volume, $V = 2 \, dm^3$
- Temperature, $T = 500 \, K$
- Gas constant, $R = 0.08 \, dm^3 \, bar \, K^{-1} \, mol^{-1}$
- Initial moles of CO, $n_{CO,i} = 0.1 \, mol$
- Equilibrium moles of Methanol, $n_{CH_3OH,eq} = 0.04 \, mol$
- Total equilibrium pressure, $P_{total,eq} = 5 \, bar$
Equilibrium Moles Calculation
Let $x$ represent the extent of reaction in moles. Based on the stoichiometry and the amount of $CH_3OH$ formed:
- Equilibrium moles of $CH_3OH$, $n_{CH_3OH,eq} = +x = 0.04 \, mol$
- Equilibrium moles of $CO$, $n_{CO,eq} = n_{CO,i} - x = 0.1 \, mol - 0.04 \, mol = 0.06 \, mol$
Calculate the total moles at equilibrium using the ideal gas law ($P V = n R T$):
$n_{total,eq} = \frac{P_{total,eq} V}{R T} = \frac{(5 \, bar) \times (2 \, dm^3)}{(0.08 \, dm^3 \, bar \, K^{-1} \, mol^{-1}) \times (500 \, K)} = \frac{10}{40} = 0.25 \, mol$
Determine the equilibrium moles of $H_2$ by subtracting the known equilibrium moles from the total equilibrium moles:
$n_{H_2,eq} = n_{total,eq} - n_{CO,eq} - n_{CH_3OH,eq}$
$n_{H_2,eq} = 0.25 \, mol - 0.06 \, mol - 0.04 \, mol = 0.15 \, mol$
Equilibrium Partial Pressures Calculation
Partial pressures ($p_i$) are calculated using the mole fraction ($\frac{n_i}{n_{total,eq}}$) and the total equilibrium pressure ($P_{total,eq}$):
- $p_{CO,eq} = \frac{n_{CO,eq}}{n_{total,eq}} \times P_{total,eq} = \frac{0.06 \, mol}{0.25 \, mol} \times 5 \, bar = 1.2 \, bar$
- $p_{H_2,eq} = \frac{n_{H_2,eq}}{n_{total,eq}} \times P_{total,eq} = \frac{0.15 \, mol}{0.25 \, mol} \times 5 \, bar = 3.0 \, bar$
- $p_{CH_3OH,eq} = \frac{n_{CH_3OH,eq}}{n_{total,eq}} \times P_{total,eq} = \frac{0.04 \, mol}{0.25 \, mol} \times 5 \, bar = 0.8 \, bar$
$K_p$ Calculation
The equilibrium constant in terms of partial pressures ($K_p$) is defined as:
$K_p = \frac{p_{CH_3OH,eq}}{(p_{CO,eq}) \cdot (p_{H_2,eq})^2}$
Substitute the calculated partial pressures into the $K_p$ expression:
$K_p = \frac{0.8 \, bar}{(1.2 \, bar) \cdot (3.0 \, bar)^2} = \frac{0.8}{1.2 \times 9.0} = \frac{0.8}{10.8} \approx 0.074074$
Final Result Formatting
The question requires the $K_p$ value to be expressed in the format ________ $\times 10^{-3}$.
Convert the calculated $K_p$ value:
$K_p \approx 0.074074 = 74.074 \times 10^{-3}$
Rounding $74.074$ to the nearest integer gives 74.
Similar Questions
$CaCO_3(s) + 2HCl(aq) \rightarrow CaCl_2(aq) + CO_2(g) + H_2O(l)$
Consider the above reaction, what mass of $CaCl_2$ will be formed if 250 mL of 0.76 M HCl reacts with 1000 g of $CaCO_3$ ?
(Given: Molar mass of Ca, C, O, H and Cl are 40, 12, 16, 1 and 35.5 g $mol^{-1}$, respectively)- According to Bohr's model of hydrogen atom, which of the following statement is incorrect?
Two vessels A and B are connected via stopcock. The vessel A is filled with a gas at a certain pressure. The entire assembly is immersed in water and is allowed to come to thermal equilibrium with water. After opening the stopcock the gas from vessel A expands into vessel B and no change in temperature is observed in the thermometer. Which of the following statement is true ?Which of the following graphs correctly represents the plot of $K_H$ at 1 bar for gases in water versus temperature?
If equal volumes of $AB_2$ and $XY$ (both are salts) aqueous solutions are mixed, which of the following combination will give a precipitate of $AY_2$ at 300 K ?
(Given $K_{sp}$ (at 300 K) for $AY_2=5.2 \times 10^{-7}$)On complete combustion 1.0 g of an organic compound (X) gave 1.46 g of $CO_2$ and 0.567 g of $H_2O$. The empirical formula mass of compound (X) is ________ g.
(Given molar mass in g $mol^{-1}$ C: 12, H: 1, O: 16)Consider the following electrochemical cell at standard condition.
$Au(s)$|$QH_2,Q$| $NH_4X(0.01 M)$ | | $Ag^+ (1M)$|$Ag(s)$ $E_{cell}$ = +0.4 V
The couple $QH_2/Q$ represents quinhydrone electrode, the half cell reaction is given below :
[Given: $E_{Ag^+/Ag}^ \circ$ = +0.8 V and $\frac{2.303RT}{F}$ = 0.06 V ]
The $pK_b$ value of the ammonium halide salt ($NH_4X$) used here is ________. (nearest integer)For the reaction A $\rightarrow$ products.
The concentration of A at 10 minutes is ________ $\times10^{-3}$ mol $L^{-1}$ (nearest integer).
The reaction was started with 2.5 mol $L^{-1}$ of A.0.1 mol of the following given antiviral compound (P) will weigh ________ $\times10^{-1}g$ (nearest integer).
(Given : molar mass in g $mol^{-1}$ H : 1, C: 12, N : 14, O: 16, F: 19, I : 127)Among $10^{-9}$ g (each) of the following elements, which one will have the highest number of atoms? Element: Pb, Po, Pr and Pt
Important Questions from Physical Chemistry
$CaCO_3(s) + 2HCl(aq) \rightarrow CaCl_2(aq) + CO_2(g) + H_2O(l)$
Consider the above reaction, what mass of $CaCl_2$ will be formed if 250 mL of 0.76 M HCl reacts with 1000 g of $CaCO_3$ ?
(Given: Molar mass of Ca, C, O, H and Cl are 40, 12, 16, 1 and 35.5 g $mol^{-1}$, respectively)- According to Bohr's model of hydrogen atom, which of the following statement is incorrect?
Two vessels A and B are connected via stopcock. The vessel A is filled with a gas at a certain pressure. The entire assembly is immersed in water and is allowed to come to thermal equilibrium with water. After opening the stopcock the gas from vessel A expands into vessel B and no change in temperature is observed in the thermometer. Which of the following statement is true ?Which of the following graphs correctly represents the plot of $K_H$ at 1 bar for gases in water versus temperature?
If equal volumes of $AB_2$ and $XY$ (both are salts) aqueous solutions are mixed, which of the following combination will give a precipitate of $AY_2$ at 300 K ?
(Given $K_{sp}$ (at 300 K) for $AY_2=5.2 \times 10^{-7}$)
