Scientific Understanding

**What are Partial Pressures?**

The concept behind partial pressures is quite simple, but many books and example questions make the thinking behind them overly complicated. Partial pressures is all about adding up the pressures of each gas separately in a container to get the overall (total) gas pressure inside that container. For example, our atmosphere is a container. 99% of our atmosphere is made up for Nitrogen (N_{2}), Oxygen (O_{2}), and Carbon Dioxide (CO_{2}). At sea level the pressure of the N_{2} is about 0.7 atm, the pressure of the O_{2} is about 0.2 atm, and the pressure of CO_{2} is about 0.1 atm. If you add all those up you get 1 atm which is the total pressure of our atmosphere at sea level. So all the gas pressures together equals the total.

N_{2} + O_{2} + CO_{2} = Total Pressure

We use an example like this above to extrapolate a more complex equation like the one below.

P_{1} + P_{2} + P_{3}…… = P_{T}

P_{1} is the pressure of gas 1, P_{2} is the pressure of gas 2, P_{3} is the pressure of gas 3, the dot dot dot (…) just means we could keep adding more pressures if more gasses were in the container. P_{T} is pressure total. In theory, this equation could have just a P_{1} through P_{2} or it could have P_{1} through P_{1000000}. It all depends on how many gasses that you have in that particular container.

**Examples**: Solve for the following partial pressure problems.

If a container has 4 atm of He and 7atm of Ar what is the total pressure?

Answer: 11 atm

If a container has 6 atm of F_{2}, 2 atm of N_{2} and a total pressure of 12 atm, how much pressure is the Ne exerting?

Answer: 4 atm

Cl_{2} is bubbled through water and collected in an inverted test tube that is immersed in the same water. If the pressure of the Cl_{2} bubbled into the test tube is 1.5 atm and the total pressure in the test tube is 1.8 atm then what is the pressure of the H_{2}O gas in the tube.

Answer: 0.3 atm

**VIDEO Partial Pressure Demonstrated Example 1**: If a container has 9 atm of Ne, 1 atm of He and a total pressure of 18 atm. What is the partial pressure of the Ar in the containter?

**Step 1:**

What information are we given?

Answer:

Ne pressure = 9 atm

He pressure = 1 atm

Total pressure = 18 atm

**Step 2:**

What does the question ask for?

Answer : Ar pressure = ?

**Step 3:**

How do we set up the problem?

Answer: Start with the equation

P_{Ne} + P_{He} + P_{Ar} = |
P_{T} |

**Step 4:**

What can we fill in for the equation?

Answer: The information we are given (red).

9 + 1 + P_{Ar} = |
18 |

**Step 5:**

How do we rearrange the equation?

Answer: Minus 9 and 1 from the left side and right side (red).

9 + 1 + P_{Ar} – 9 – 1 = |
18 – 9 – 1 |

**Step 6:**

Simplify

P_{Ar} = |
18 – 9 – 1 |

**Step 7:**

How do I do the calculations?

Answer: 18 – 9 – 1 = 8

**Step 8:**

What is the complete answer?

COMPLETE ANSWER: 8 atm

**VIDEO Partial Pressure Demonstrated Example 2**: N_{2} is bubbled through water and collected in an inverted test tube that is immersed in the same water. If the pressure of the N_{2} bubbled into the test tube is 2.3 atm and the total pressure in the test tube is 2.7 atm then what is the pressure of the H_{2}O gas in the tube.

**Step 1:**

What information are we given?

Answer:

N_{2} pressure = 2.3 atm

Total pressure = 2.7 atm

**Step 2:**

What does the question ask for?

Answer : H_{2}O pressure = ?

**Step 3:**

How do we set up the problem?

Answer: Start with the equation

P_{N2} + P_{H2O} = |
P_{T} |

**Step 4:**

What can we fill in for the equation?

Answer: The information we are given (red).

2.3 + P_{H2O} = |
2.7 |

**Step 5:**

How do we rearrange the equation?

Answer: Minus 2.3 from the left side and right side (red).

2.3 + P_{H2O} – 2.3 = |
2.7 – 2.3 |

**Step 6:**

Simplify

P_{H2O} = |
2.7 – 2.3 |

**Step 7:**

How do I do the calculations?

Answer: 2.7 – 2.3 = 0.4

**Step 8:**

What is the complete answer?

COMPLETE ANSWER: 0.4 atm

**PRACTICE PROBLEMS**: Solve these partial pressure problems below.

If a container has 3.5 atm of O_{2} and 1.2 atm of N_{2} what is the total pressure?

Answer: 4.7 atm

If a container has 5 atm of Cl_{2}, 6 atm of BH_{3} and a total pressure of 13 atm, how much pressure is the Ar exerting?

Answer: 2 atm

CH_{4} is bubbled through water and collected in an inverted test tube that is immersed in the same water. If the pressure of the CH_{4} bubbled into the test tube is 2.8 atm and the total pressure in the test tube is 3.2 atm then what is the pressure of the H_{2}O gas in the tube.

Answer: 0.4 atm