NEET Equilibrium — Set 18

Question 1

For $ \ce{CO(g) + 2H2(g) <=> CH3OH(g)} $, $ K_c = 10 $ at 400 K. If 0.1 mol $ \ce{CO} $ and 0.3 mol $ \ce{H2} $ are in a 1 L vessel, what is $ [\ce{CH3OH}] $ at equilibrium?

Accepted Answer

Initial: $ [\ce{CO}] = 0.1 \, \text{M} $, $ [\ce{H2}] = 0.3 \, \text{M} $, $ [\ce{CH3OH}] = 0 $. Let $ x = [\ce{CH3OH}] $, $ [\ce{CO}] = 0.1 - x $, $ [\ce{H2}] = 0.3 - 2x $. $ K_c = \frac{[\ce{CH3OH}]}{[\ce{CO}][\ce{H2}]^2} = \frac{x}{(0.1 - x)(0.3 - 2x)^2} = 10 $. Solving iteratively, $ x \approx 0.09 $, $ 10 = \frac{0.09}{(0.01)(0.12)^2} \approx 625 $ (too high), adjust $ x \approx 0.06 $, $ \frac{0.06}{(0.04)(0.18)^2} \approx 46 $ (still high), $ x \approx 0.03 $, $ \frac{0.03}{(0.07)(0.24)^2} \approx 7.44 $, close to 10.

Question 2

For the reaction $ \ce{3A(g) + B(g) <=> 2C(g)} $, $ K_c = 8 $ at 500 K. If 1.5 moles of $ \ce{A} $ and 0.5 moles of $ \ce{B} $ are placed in a 1 L vessel, what is $ [\ce{C}] $ at equilibrium?

Accepted Answer

Initial: $ [\ce{A}] = 1.5 \, \text{M} $, $ [\ce{B}] = 0.5 \, \text{M} $, $ [\ce{C}] = 0 $. Let $ 2x $ be moles of $ \ce{C} $ formed, so $ \ce{A} $ decreases by $ 3x $, $ \ce{B} $ by $ x $. At equilibrium: $ [\ce{A}] = 1.5 - 3x $, $ [\ce{B}] = 0.5 - x $, $ [\ce{C}] = 2x $. $ K_c = \frac{[\ce{C}]^2}{[\ce{A}]^3[\ce{B}]} = \frac{(2x)^2}{(1.5 - 3x)^3 (0.5 - x)} = 8 $, $ \frac{4x^2}{(1.5 - 3x)^3 (0.5 - x)} = 8 $. Solving iteratively, $ x \approx 0.25 $, $ (0.5)^2 / [(0.75)^3 \times 0.25] = 0.25 / 0.1055 \approx 2.37 $ (adjust), $ x \approx 0.4 $, $ [\ce{C}] = 2 \times 0.4 = 0.8 \, \text{M} $.

Question 3

For $ \ce{A(g) + B(g) <=> 2C(g)} $, $ K_p = 0.5 $ at 300 K. If the total pressure at equilibrium is 4 atm and $ P_{\ce{A}} = P_{\ce{B}} $, what is $ P_{\ce{C}} $?

Accepted Answer

Let $ P_{\ce{A}} = P_{\ce{B}} = x $, $ P_{\ce{C}} = 4 - 2x $, $ K_p = \frac{(P_{\ce{C}})^2}{P_{\ce{A}} P_{\ce{B}}} = \frac{(4 - 2x)^2}{x^2} = 0.5 $, $ 4 - 2x = x \sqrt{0.5} $, $ x \approx 1.37 $, $ P_{\ce{C}} = 1.26 \, \text{atm} $.

NEET Chemistry: Equilibrium — Practice Set 18

Q1. For \( \ce{CO(g) + 2H2(g) <=> CH3OH(g)} \), \( K_c = 10 \) at 400 K. If 0.1 mol \( \ce{CO} \) and 0.3 mol \( \ce{H2} \) are in a 1 L vessel, what is \( [\ce{CH3OH}] \) at equilibrium?

Q2. For the reaction \( \ce{3A(g) + B(g) <=> 2C(g)} \), \( K_c = 8 \) at 500 K. If 1.5 moles of \( \ce{A} \) and 0.5 moles of \( \ce{B} \) are placed in a 1 L vessel, what is \( [\ce{C}] \) at equilibrium?

Q3. For \( \ce{A(g) + B(g) <=> 2C(g)} \), \( K_p = 0.5 \) at 300 K. If the total pressure at equilibrium is 4 atm and \( P_{\ce{A}} = P_{\ce{B}} \), what is \( P_{\ce{C}} \)?

Q4. The \( K_{sp} \) of \( \ce{AgIO3} \) is \( 3.0 \times 10^{-8} \). What is \( [\ce{Ag+}] \) in a saturated solution containing 0.02 M \( \ce{KIO3} \)?

Q5. A weak acid \( \ce{HZ} \) has \( K_a = 2.0 \times 10^{-4} \). What is the pH of a 0.1 M solution of \( \ce{HZ} \)?

Q6. For the reaction \( \ce{2AB(g) <=> A2(g) + B2(g)} \), if \( K_c = 0.0625 \) and \( [\ce{AB}] = 0.5 \, \text{M} \) at equilibrium, what is \( [\ce{A2}] \)?

Q7. For \( \ce{2A(g) <=> B(g) + C(g)} \), \( K_c = 0.09 \) at 400 K. If 0.6 mol \( \ce{A} \) is in a 1 L vessel, what is the degree of dissociation?

Q8. The solubility of \( \ce{Ag2CO3} \) in a 0.1 M \( \ce{AgNO3} \) solution is \( 2.0 \times 10^{-6} \, \text{M} \). What is its \( K_{sp} \)?

Q9. In the equilibrium \( \ce{N2(g) + O2(g) <=> 2NO(g)} \), adding an inert gas at constant pressure will shift the equilibrium in which direction?

Q10. What is the conjugate base of \( \ce{H2O} \) according to the Bronsted-Lowry concept?