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# Basic Math/Algebra

So yes, we do expect you to be able to do basic math and algebra. We will not make you do calculus or differential equations - just some plain ol' algebra. This means you might memorize an equation with some variables in it and we tell you a few of them - then you calculate for the missing one. Here is an example and the solution...

#### gas law type question

A given sample of an ideal gas at 300 K occupies 20.2 L at a pressure of 1.50 atm. How many moles of gas are in this sample?

**Solution: ** Use the ideal gas law! \(\longrightarrow PV = nRT\)

Now put in all the known values (\(P,V,T,R\)) and solve for the unknown value (\(n\)).

\[(1.50\;{\rm atm})(20.2\;{\rm L}) = n(0.08206\;{\rm L\;atm/mol \,K})(300\;{\rm K})\]

\[{(1.50)(20.2)\over (0.08206)(300)} = n\]

\[ 1.23\;{\rm mol} = n\]

Not too bad, right? 1.23 moles of ideal gas is the answer and we just substituted into the equation and then did a little algebra to solve. You might get longer questions to solve - meaning more numbers and math... but, it will not be harder algebra. Just don't get lost along the way to the answer.

In the above example I dropped all units after the first line. The units DO work out to end up with only moles for the units of \(n\). Sometimes I drop units in examples in order to show the pure math and not let units clutter my page. You might want to drag the units along for the ride though - in case you get lost. Units will often help lead you to the right way to do the math.