According to Le Chatelier's principle, increasing the pressure on a gaseous system will favor the side with fewer moles of gas. In the given equilibrium reaction, the left-hand side has 4 moles of gas (1 mole of CO and 3 moles of H\(_2\)) and the right-hand side has 2 moles of gas (1 mole of CH\(_4\) and 1 mole of H\(_2\)O). Therefore, increasing the pressure will shift the equilibrium towards the right (in the forward direction), increasing the concentration of products and decreasing the concentration of reactants.
- (A) The concentration of reactants and products increases because the equilibrium shifts toward the products side.
- (B) The equilibrium will shift in the forward direction to produce more CH\(_4\) and H\(_2\)O.
- (C) The equilibrium constant remains unchanged, as pressure does not affect the value of the equilibrium constant at constant temperature.
Therefore, the correct answer is (1) (A) and (B) only.
For the reaction A(g) $\rightleftharpoons$ 2B(g), the backward reaction rate constant is higher than the forward reaction rate constant by a factor of 2500, at 1000 K.
[Given: R = 0.0831 atm $mol^{–1} K^{–1}$]
$K_p$ for the reaction at 1000 K is:
Let \( y^2 = 12x \) be the parabola and \( S \) its focus. Let \( PQ \) be a focal chord of the parabola such that \( (SP)(SQ) = \frac{147}{4} \). Let \( C \) be the circle described by taking \( PQ \) as a diameter. If the equation of the circle \( C \) is: \[ 64x^2 + 64y^2 - \alpha x - 64\sqrt{3}y = \beta, \] then \( \beta - \alpha \) is equal to:
Let one focus of the hyperbola $ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 $ be at $ (\sqrt{10}, 0) $, and the corresponding directrix be $ x = \frac{\sqrt{10}}{2} $. If $ e $ and $ l $ are the eccentricity and the latus rectum respectively, then $ 9(e^2 + l) $ is equal to:
Let $ A \in \mathbb{R} $ be a matrix of order 3x3 such that $$ \det(A) = -4 \quad \text{and} \quad A + I = \left[ \begin{array}{ccc} 1 & 1 & 1 \\2 & 0 & 1 \\4 & 1 & 2 \end{array} \right] $$ where $ I $ is the identity matrix of order 3. If $ \det( (A + I) \cdot \text{adj}(A + I)) $ is $ 2^m $, then $ m $ is equal to: