Scientific Understanding

**How do you do conversions between pressure units?**

Fundamentally, the pressure of a gas is how many times and with how much force are the molecules of air striking the container. It is like a massage. The person giving you a massage can strike your skin in many different ways. They can strike hard and often which would be high pressure or they can strike soft and infrequent which would be low pressure. The same is true with the molecules of air in a container like a balloon. The molecules can create a high pressure by striking hard and often or a low pressure by striking soft and infrequent. How we influence the molecules to create a high pressure or a low pressure? We can change several factors like the number of molecules we have, the volume of the container, and the temperature. All of the factors that influence pressure I will discuss later.

If you want additional explanation and descriptions of pressure then go to the pressure section the states of matter lesson.

What we need to know right now is how pressure is measured. Specifically, the units of pressure. The units of pressure include Pascal (Pa), atmospheres (atm), torr, and mm Hg. Torr and mm Hg are really the same thing where as Pascals and atmospheres are different from all others. A Pascal is the standard unit of measurement for the metric scale (the SI unit), however, atmospheres tend to be the most popular unit to use for pressure in a chemistry class. What are the conversions between the units of pressure?

1 atm = 1.013 * 10^{5} Pa = 760 torr = 760 mm Hg

Each of these can be written as ratios or proportions like below:

Atm:

1.013 * 10^{5} Pa |
760 torr | 760 mm Hg | ||

1 atm | 1 atm | 1 atm |

Pa:

1 atm | 760 torr | 760 mm Hg | ||

1.013 * 10^{5} Pa |
1.013 * 10^{5} Pa |
1.013 * 10^{5} Pa |

Torr:

1.013 * 10^{5} Pa |
1 atm | 760 mm Hg | ||

760 torr | 760 torr | 760 torr |

mm Hg:

1.013 * 10^{5} Pa |
1 atm | 760 torr | ||

760 mm Hg | 760 mm Hg | 760 mm Hg |

The ratios above are much like the ones we have used in other sections like unit conversions. If you have a hard time with the examples go back to the lesson just mentioned.

**Examples**: Convert the following pressure units.

How many mm Hg is a pressure of 2.3 atm?

Answer: 1748 mm Hg

If the pressure is 89 torr. How many pascals is that?

Answer: 11862 Pa

**VIDEO Pressure Conversions Demonstrated Example 1****:** How many atmospheres is 450 torr?

**Step 1:**

What information are we given?

Answer: 450 torr

**Step 2:**

What units does the question ask for?

Answer: atm

**Step 3:**

How do we set up the problem?

Answer:

450 torr | atm | |

1 |

**Step 4:**

What is the first conversion?

Answer: 1 atm = 760 torr

**Step 5:**

How do we set it up?

Answer: units first, set up the units that need to cancel out (in red)

450 torr | atm = | atm |

torr |

**Step 6:**

What comes next?

Answer: fill in the numbers and cross out units

450 torr | 1 atm = | atm |

760 torr |

**Step 7:**

Simplify by removing all crossed out units. The units in red are the ones that are left and match the answer units also in red.

450 | 1 atm = | atm |

760 |

**Step 8:**

How do I do the calculations?

Answer: 450 / 760 = 0.59

450 | 1 atm = | 0.59 atm |

760 |

**Step 9:**

What is the complete answer?

COMPLETE ANSWER: 0.59 atm

**VIDEO Pressure Conversions Demonstrated Example 2****:** If the pressure is 2.4 * 10^{4} Pa, how many mm Hg is that?

**Step 1:**

What information are we given?

Answer: 2.4 * 10^{4} Pa

**Step 2:**

What units does the question ask for?

Answer: mm Hg

**Step 3:**

How do we set up the problem?

Answer:

2.4 * 10^{4} Pa |
mm Hg | |

1 |

**Step 4:**

What is the first conversion?

Answer: 1.013 * 10^{5} Pa = 760 mm Hg

**Step 5:**

How do we set it up?

Answer: units first, set up the units that need to cancel out (in red)

2.4 * 10^{4} Pa |
mm Hg = | mm Hg |

Pa |

**Step 6:**

What comes next?

Answer: fill in the numbers and cross out units

2.4 * 10^{4} Pa |
760 mm Hg = | mm Hg |

1.013 * 10^{5} Pa |

**Step 7:**

Simplify by removing all crossed out units. The units in red are the ones that are left and match the answer units also in red.

2.4 * 10^{4} |
760 mm Hg = | mm Hg |

1.013 * 10^{5} |

**Step 8:**

How do I do the calculations?

Answer: (2.4 * 10^{4} * 760) / (1.013 * 10^{5}) = 180

2.4 * 10^{4} |
760 mm Hg = | 180 mm Hg |

1.013 * 10^{5} |

**Step 9:**

What is the complete answer?

COMPLETE ANSWER: 180 mm Hg

**PRACTICE PROBLEMS**: Give the requested units of pressure for the questions below.

How many atmospheres is 360 torr?

Answer: 0.473atm

How many mm Hg is 2.3atm?

Answer: 1748 mm Hg

5.9atm is how many Pa?

Answer: 5.98 * 10^{5} Pa

824 mm Hg is how many atmospheres?

Answer: 1.08atm