NEET Equilibrium — Set 5

Question 1

For the reaction $ \ce{A(g) + 2B(g) <=> 3C(g)} $, $ K_c = 27 $ at 300 K. If 0.5 moles of $ \ce{A} $ and 2 moles of $ \ce{B} $ are placed in a 1 L vessel, what is $ [\ce{C}] $ at equilibrium?

Accepted Answer

Initial: $ [\ce{A}] = 0.5 \, \text{M} $, $ [\ce{B}] = 2 \, \text{M} $, $ [\ce{C}] = 0 $. Let $ 3x $ be moles of $ \ce{C} $ formed, so $ \ce{A} $ decreases by $ x $, $ \ce{B} $ by $ 2x $. At equilibrium: $ [\ce{A}] = 0.5 - x $, $ [\ce{B}] = 2 - 2x $, $ [\ce{C}] = 3x $. $ K_c = \frac{[\ce{C}]^3}{[\ce{A}][\ce{B}]^2} = \frac{(3x)^3}{(0.5 - x)(2 - 2x)^2} = 27 $, $ \frac{27x^3}{(0.5 - x)(4 - 4x + 4x^2)} = 27 $, $ x^3 = (0.5 - x)(1 - x)^2 $, $ x \approx 0.3 $, $ [\ce{C}] = 3 \times 0.3 = 0.9 \, \text{M} $.

Question 2

The $ K_{sp} $ of $ \ce{Fe(OH)2} $ is $ 4.9 \times 10^{-17} $. What is the pH at which $ [\ce{Fe^{2+}}] = 1.0 \times 10^{-6} \, \text{M} $ in a saturated solution?

Accepted Answer

For $ \ce{Fe(OH)2 <=> Fe^{2+} + 2OH-} $, $ K_{sp} = [\ce{Fe^{2+}}][\ce{OH-}]^2 = 4.9 \times 10^{-17} $, $ (1.0 \times 10^{-6})[\ce{OH-}]^2 = 4.9 \times 10^{-17} $, $ [\ce{OH-}]^2 = 4.9 \times 10^{-11} $, $ [\ce{OH-}] = 7.0 \times 10^{-6} $, $ \text{pOH} = 5.15 $, $ \text{pH} = 14 - 5.15 = 8.85 $.

Question 3

For $ \ce{PCl5(g) <=> PCl3(g) + Cl2(g)} $, $ K_c = 0.04 $ at 500 K. If 0.5 mol of $ \ce{PCl5} $ is placed in a 2 L vessel with 0.1 mol of $ \ce{Cl2} $, what is $ [\ce{PCl3}] $ at equilibrium?

Accepted Answer

Initial: $ [\ce{PCl5}] = \frac{0.5}{2} = 0.25 \, \text{M} $, $ [\ce{Cl2}] = \frac{0.1}{2} = 0.05 \, \text{M} $, $ [\ce{PCl3}] = 0 $. Let $ x $ be $ [\ce{PCl3}] $ at equilibrium, so $ [\ce{PCl5}] = 0.25 - x $, $ [\ce{Cl2}] = 0.05 + x $. $ K_c = \frac{[\ce{PCl3}][\ce{Cl2}]}{[\ce{PCl5}]} = \frac{x (0.05 + x)}{0.25 - x} = 0.04 $. Solving, $ x(0.05 + x) = 0.04(0.25 - x) $, $ 0.05x + x^2 = 0.01 - 0.04x $, $ x^2 + 0.09x - 0.01 = 0 $, $ x = \frac{-0.09 \pm \sqrt{0.0081 + 0.04}}{2} $, $ x \approx 0.1 \, \text{M} $.

NEET Chemistry: Equilibrium — Practice Set 5

Q1. For the reaction \( \ce{A(g) + 2B(g) <=> 3C(g)} \), \( K_c = 27 \) at 300 K. If 0.5 moles of \( \ce{A} \) and 2 moles of \( \ce{B} \) are placed in a 1 L vessel, what is \( [\ce{C}] \) at equilibrium?

Q2. The \( K_{sp} \) of \( \ce{Fe(OH)2} \) is \( 4.9 \times 10^{-17} \). What is the pH at which \( [\ce{Fe^{2+}}] = 1.0 \times 10^{-6} \, \text{M} \) in a saturated solution?

Q3. For \( \ce{PCl5(g) <=> PCl3(g) + Cl2(g)} \), \( K_c = 0.04 \) at 500 K. If 0.5 mol of \( \ce{PCl5} \) is placed in a 2 L vessel with 0.1 mol of \( \ce{Cl2} \), what is \( [\ce{PCl3}] \) at equilibrium?

Q4. For \( \ce{Ag2SO4} \), if the solubility is \( 2.0 \times 10^{-2} \, \text{M} \), what is \( K_{sp} \)?

Q5. What is the conjugate acid of \( \ce{CO3^{2-}} \)?

Q6. The \( K_{sp} \) of \( \ce{PbSO4} \) is \( 1.6 \times 10^{-8} \). In a 0.01 M \( \ce{Na2SO4} \) solution, what is \( [\ce{Pb^{2+}}] \) in a saturated solution?

Q7. The solubility of \( \ce{BaSO4} \) in water is \( 1.05 \times 10^{-5} \, \text{mol/L} \). What is its \( K_{sp} \)?

Q8. For \( \ce{2X(g) <=> Y(g) + Z(g)} \), if the volume is halved at constant temperature, the equilibrium shifts towards which direction?

Q9. In the equilibrium \( \ce{N2(g) + 3H2(g) <=> 2NH3(g)} \), increasing the pressure shifts the equilibrium towards which direction?

Q10. A weak acid \( \ce{HB} \) has \( K_a = 4.0 \times 10^{-6} \). If its 0.05 M solution is mixed with 0.025 M \( \ce{NaOH} \), what is the pH of the resulting solution?