[m_foysal_a]

I was wondering how i could construct an experiment to measure a volume of gas to prove which of these equations is true.

Equation 1: 2CuCo₃(s) =  Cu₂O(s) + 2CO₂(g) + 0.5O₂(g)

Equation 2: CuCO₃(s) = CuO(s) + CO₂(g)

Thank you.

[plu]

It seems that one of your equations produces oxygen gas while the other does not.  Have you thought about any tests for oxygen?  

[Mitch]

Do it in a flask, attach a deflated balloon and see if you can ignite the balloon.  

[movies]

If you want a quantitative measure of the gas produced, take a graduated cylinder and fill it, then invert it in a tank of water.  Run a tube from your reaction vessel into the inverted cylinder.  As the gas is produced it will bubble up into the cylinder and you can measure the volume of gas produced.  You can convert that to moles using the ideal gas law.

Chemistry is fun!!