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pentane gas (c5h12) combusts with oxygen gas (o2) to form water (h2o) and carbon dioxide (co2). write a balanced chemical equation for this reaction and explain the scientific principle (statement) that requires the balancing of an equation to make it conform to reality.

The scientific principle you're referring to here is the law of conservation of mass. The unbalanced equation would be:

C5H12 + O2 --> H2O + CO2

We need the same number of each atom on both sides for mass to be conserved. Start with C because it only appears once on both sides. We have 5 on the left, so we need 5 on the right:

C5H12 + O2 --> H2O + 5CO2

Now we can do the same with H. There are 12 on the left, but only 2 on the right:

C5H12 + O2 --> 6H2O + 5CO2

Finally we can balance the O's. There are 2 on the left, but 16 on the right. Your final balanced equation will be:

C5H12 + 8O2 --> 6H2O + 5CO2