## Chemistry Tutorial

*In-Depth Gas Law Problem *

#### Intro

Gas law problems are very useful in everyday life, so it is nice to be able to navigate them and all their possibilities.

#### Sample Problem

Knowing the molar mass of O2 is 32g/mol and at STP 1 mol of gas occupies 22.4L, how much volume will 50kg of O2 occupy?

What happens if I increase the pressure 10x what it was initially, what temperature would I need for the O2 to be at to occupy 100L?

#### Solution

Start with converting 50Kg O2 to grams O2 –> 50,000g O2

Then using the molar mass of O2 (32g/mol) and the mass of O2 –> 1562.5 mols O2

Then use the STP relationship (1 mol O2/22.4L) to get final volume –> **35000 L O2**

Remember STP: 273K and 1 atm, so 10x initial pressure –> 10 atm

Now we have a pressure (10 atm), mols (1562.5mols), volume (100L), R (.0821 L*atm/mol*K), and we must solve for T using PV = nRT

T = (PV/nR) = (10 atm * 100 L)/(1562.5 mols * .0821 L*atm/mol*K) –> **7.79 K**

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