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1) That looks right. 2) Step 1: Moles=Mass/Mr, so it's 144/72= 2mol. Step 2: Stoichiometry means the ratio of oxygen to pentane is 1:8 so moles of oxygen is moles of pentane times 8. 2*8=16mol of oxygen. Step 3: 16= 9.6*10^24. 3) The ratio of oxygen to carbon in CO2 is 1:2. so it's 192/3 = 64.
They are the ratios of the number of moles of a reactant to the number of moles of a product. For example, in the equation: #2H_2# + #O_2# = #2H_2O#, There are two moles of #2H_2# and two moles of #2H_2O#, so the mole ratio of #2H_2# to #2H_2O# would be 2:2, which can be simplified to 1:1. There is, however, only one mole of #O_2# to two moles of #2H_2O#, so the mole ratio between these compounds would be 1:2.