In-Depth Gas Law Problem

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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