Scientific Understanding

**What is the equilibrium constant Kp and how does it relate to pressure?
**

You can also talk about a chemical equation and its equilibrium in the form of pressure. Most books and teachers will call this equilibrium constant Kp. It works the same as any other equilibrium constant. All the same rules apply as in the equilibrium equations we have been solving for so far. The only difference is you can use the values of pressure (usually in atm, torr, mmHg, or Pa). For the examples I give I will use the units of atm. Because Kp does not directly involve concentration the Kp equation for the equilibrium constant is slightly different. You don’t use brackets in the equation so the equation looks like the one below.

For the chemical equation: N_{2(g)} + 3 H_{2(g)} <—-> 2 NH_{3(g)}

Kp = | ( NH_{3} )^{2} |

( N_{2} ) ( H_{2} )^{3} |

**VIDEO Solving the Equilibrium Equation (Kp) Demonstrated Example 1**: What is the equilibrium constant of the equation below when the pressure at equilibrium of C_{4} is 1atm, O_{2} is 4atm, and CO_{2} is 5atm?

C_{4(s)} + 4 O_{2(g)} <—-> 4 CO_{2(g)}

What is the equilibrium equation look like with chemicals?

Kp = | ( CO_{2 } )^{4} |

( O_{2} )^{4} |

C_{4} is not shown above because it is a solid. Replace the chemicals with their corresponding pressure (numbers).

Kp = | ( 5atm )^{4} |

( 4atm )^{4} |

Calculate in steps. First the exponents.

Kp = | ( 625atm^{4} ) |

( 256atm^{4} ) |

Then divide top and bottom

Kp = | 2.44 |

1 |

COMPLETE ANSWER: Kp = 2.44

**PRACTICE PROBLEMS**: Solve the problems below for the Kp or different pressures.

What is the Kp of the equation below when the pressure at equilibrium of N_{2}O_{3} is 20atm, N_{2} is 5atm, and O_{2} is 9atm?

2 N_{2}O_{3(g)} <——> 2 N_{2(g)} + 3 O_{2(g)}

Answer: Kp = 45 atm^{3}

What is the equilibrium constant of the equation below when the pressure at equilibrium of Ba(OH)_{2} is 0.1atm, HCl is 0.2 atm, and BaCl_{2} is 0.4atm?

Ba(OH)_{2}_{(aq)} + 2 HCl_{(aq)} <—-> 2 H_{2}O_{(l)} + BaCl_{2}_{(aq)}

Answer: Kp = 100 atm^{-2}

What is the pressure of O_{2} in the equation below when the pressure at equilibrium of H_{2}O is 0.7atm, H_{2} is 40atm, and Kp is 65atm?

2 H_{2}O_{(g)} <—-> 2 H_{2(g)} + O_{2(g)}

Answer: pressure of O_{2} = 0.02 atm

What is the pressure of NH_{3} in the equation below when the pressure at equilibrium of OF_{2} is 0.5 atm, N_{2}F_{4} is 1.3atm, O_{2} is 2.5atm, H_{2} is 0.8atm, and the Kp is 2.7 * 10^{2}atm?

2 OF_{2(g)} + 2 NH_{3(g)} <—> N_{2}F_{4(g)} + O_{2(g)} + 3 H_{2(g)}

Answer: pressure of NH_{3} = 0.157 atm