NEET Equilibrium — Set 3

Question 1

For $ \ce{A(g) + 2B(g) <=> 2C(g)} $, $ K_p = 1 $ at 400 K. If $ P_{\ce{A}} = 0.5 \, \text{atm} $, $ P_{\ce{B}} = 1 \, \text{atm} $ initially, what is $ P_{\ce{C}} $ at equilibrium?

Accepted Answer

Let $ P_{\ce{C}} = 2x $, $ P_{\ce{A}} = 0.5 - x $, $ P_{\ce{B}} = 1 - 2x $. $ K_p = \frac{(P_{\ce{C}})^2}{P_{\ce{A}} P_{\ce{B}}^2} = \frac{(2x)^2}{(0.5 - x)(1 - 2x)^2} = 1 $, $ 4x^2 = (0.5 - x)(1 - 2x)^2 $, $ x \approx 0.25 $, $ P_{\ce{C}} = 0.5 \, \text{atm} $.

Question 2

For $ \ce{2SO2(g) + O2(g) <=> 2SO3(g)} $, $ K_p = 100 $ at 800 K. If initial pressures are $ P_{\ce{SO2}} = 1 \, \text{atm} $, $ P_{\ce{O2}} = 0.5 \, \text{atm} $, what is $ P_{\ce{SO3}} $ at equilibrium?

Accepted Answer

Let $ P_{\ce{SO3}} = 2x $, $ P_{\ce{SO2}} = 1 - 2x $, $ P_{\ce{O2}} = 0.5 - x $. $ K_p = \frac{(P_{\ce{SO3}})^2}{P_{\ce{SO2}}^2 P_{\ce{O2}}} = \frac{(2x)^2}{(1 - 2x)^2 (0.5 - x)} = 100 $, $ \frac{4x^2}{(1 - 2x)^2 (0.5 - x)} = 100 $, $ \frac{2x}{1 - 2x} \cdot \frac{1}{\sqrt{0.5 - x}} = 10 $, $ x \approx 0.45 $, $ P_{\ce{SO3}} = 0.9 \, \text{atm} $.

Question 3

For $ \ce{N2O4(g) <=> 2NO2(g)} $, $ K_p = 0.16 $ at 298 K. If the initial pressure of $ \ce{N2O4} $ is 2 atm in a closed vessel, what is the total pressure at equilibrium ($ R = 0.0831 \, \text{bar L/mol K} $)?

Accepted Answer

Let $ P_{\ce{NO2}} = 2x $, $ P_{\ce{N2O4}} = 2 - x $, total pressure = $ 2 - x + 2x = 2 + x $. $ K_p = \frac{(P_{\ce{NO2}})^2}{P_{\ce{N2O4}}} = \frac{(2x)^2}{2 - x} = 0.16 $, $ \frac{4x^2}{2 - x} = 0.16 $, $ 4x^2 = 0.32 - 0.16x $, $ 4x^2 + 0.16x - 0.32 = 0 $, $ x^2 + 0.04x - 0.08 = 0 $, $ x = \frac{-0.04 \pm \sqrt{0.0016 + 0.32}}{2} $, $ x \approx 0.27 $. Total pressure = $ 2 + 0.27 = 2.27 \, \text{atm} $.

NEET Chemistry: Equilibrium — Practice Set 3

Q1. For \( \ce{A(g) + 2B(g) <=> 2C(g)} \), \( K_p = 1 \) at 400 K. If \( P_{\ce{A}} = 0.5 \, \text{atm} \), \( P_{\ce{B}} = 1 \, \text{atm} \) initially, what is \( P_{\ce{C}} \) at equilibrium?

Q2. For \( \ce{2SO2(g) + O2(g) <=> 2SO3(g)} \), \( K_p = 100 \) at 800 K. If initial pressures are \( P_{\ce{SO2}} = 1 \, \text{atm} \), \( P_{\ce{O2}} = 0.5 \, \text{atm} \), what is \( P_{\ce{SO3}} \) at equilibrium?

Q3. For \( \ce{N2O4(g) <=> 2NO2(g)} \), \( K_p = 0.16 \) at 298 K. If the initial pressure of \( \ce{N2O4} \) is 2 atm in a closed vessel, what is the total pressure at equilibrium (\( R = 0.0831 \, \text{bar L/mol K} \))?

Q4. For \( \ce{BaF2(s) <=> Ba^{2+}(aq) + 2F-(aq)} \), \( K_{sp} = 1.7 \times 10^{-6} \). In a 0.01 M \( \ce{NaF} \) solution, what is \( [\ce{Ba^{2+}}] \) in a saturated solution?

Q5. The equilibrium constant \( K_p \) for \( \ce{N2O4(g) <=> 2NO2(g)} \) is 0.98 at 298 K. What is \( K_c \) at this temperature (\( R = 0.0831 \, \text{bar L/mol K} \))?

Q6. For \( \ce{H2(g) + I2(g) <=> 2HI(g)} \), \( K_c = 50 \) at 700 K. If 0.2 mol \( \ce{H2} \) and 0.3 mol \( \ce{I2} \) are in a 1 L vessel, what is \( [\ce{HI}] \) at equilibrium?

Q7. In \( \ce{2A(g) <=> B(g) + C(g)} \), \( K_c = 0.01 \) and \( [\ce{A}] = 0.2 \, \text{M} \), \( [\ce{B}] = 0.02 \, \text{M} \), \( [\ce{C}] = 0.02 \, \text{M} \) at equilibrium. What happens if \( \ce{B} \) is removed?

Q8. In the equilibrium \( \ce{2XY(g) <=> X2(g) + Y2(g)} \), decreasing the volume shifts the equilibrium in which direction?

Q9. The \( K_b \) of \( \ce{NH3} \) is \( 1.8 \times 10^{-5} \). What is the \( K_a \) of \( \ce{NH4+} \)?

Q10. For the reaction \( \ce{2SO2(g) + O2(g) <=> 2SO3(g)} \), if the initial moles of \( \ce{SO2} \) and \( \ce{O2} \) are 2 and 1 respectively in a 1 L vessel, and at equilibrium 1 mole of \( \ce{SO3} \) is formed, what is \( K_c \)?