The reaction of nitrogen with oxygen to form nitrogen monoxide can be represented by the following equation. N₂(g) + O₂(g) 2NO(g)
At 2000.°C, the equilibrium constant, K_c, has a value of 4.10 × 10^-4. What is the value of K_P? (R = 0.08206 L • atm/K • mol)

Question

The reaction of nitrogen with oxygen to form nitrogen monoxide can be represented by the following equation. N₂(g) + O₂(g)

The reaction of nitrogen with oxygen to form nitrogen monoxide can be represented by the following equation. N<sub>2</sub>(g) + O<sub>2</sub>(g) 2NO(g) At 2000.°C, the equilibrium constant, K<sub>c</sub>, has a value of 4.10 × 10<sup>-4</sup>. What is the value of K<sub>P</sub>? (R = 0.08206 L • atm/K • mol) A) 2.17 × 10<sup>-8</sup> B) 4.10 × 10<sup>-4</sup> C) 7.65 × 10<sup>-2</sup> D) 2.20 ×10<sup>-6</sup> E) 2.44 ×10<sup>3</sup>

2NO(g)
At 2000.°C, the equilibrium constant, K_c, has a value of 4.10 × 10^-4. What is the value of K_P? (R = 0.08206 L • atm/K • mol)

Quizplus · Accepted Answer

The equilibrium constant, K, can be calculated using the following equation:

K = (PNO)2/(PN2*PO2)

where PNO, PN2, and PO2 are the partial pressures of nitrogen monoxide, nitrogen, and oxygen, respectively.

At equilibrium, K = 4.10 × 10-4.

Since the equation is balanced such that 1 mole of nitrogen and 1 mole of oxygen react to form 2 moles of nitrogen monoxide, the partial pressures of nitrogen and oxygen can be expressed in terms of the partial pressure of nitrogen monoxide:

PN2 = (2-2x)PNO
PO2 = (1-x)PNO

where x represents the fraction of nitrogen monoxide that has reacted.

Substituting these expressions into the equation for K and solving for x gives:

x = (1 ± √17)/4

Since x must be less than 1, the correct value for x is:

x = (1 - √17)/4

Substituting this value of x into the expression for K gives:

K = 4.10 × 10-4

Therefore, the answer is choice B.

The Reaction of Nitrogen with Oxygen to Form Nitrogen Monoxide