Question

What volume of O2 is required to completely burn 15cm3 of pentane? Equation - C5H12 + O2 - CO2 + H2O.​

Answer 1

The volume of
`\rm O_2` required would be
`120\; \rm cm^(3)`, assuming that both the pentane and the
`\rm O_2\!` in this question are ideal gases and are under the same temperature and pressure.

Step-by-step explanation:

Balance the equation for the reaction:

`\rm ?\; C_(5)H_(12) + ?\; O_2 \to ?\; CO_(2) + ?\; H_(2)O`.

Start by setting the coefficient of the molecule with the largest number of atoms to
`1`.

In the combustion of alkanes (including pentane,) consider setting the coefficient of the alkane to
`1\!`.

`\rm 1\; C_(5)H_(12) + ?\; O_2 \to ?\; CO_(2) + ?\; H_(2)O`.

Number of carbon atoms among the reactants:
`5`.

Number of hydrogen atoms among the products:
`12`.

By the conservation of atoms, there would need to be the same number of carbon and hydrogen atoms (along with the oxygen atoms) among the products.

Hence, the coefficient of
`\rm CO_2` would be
`5` while the coefficient of
`\rm H_2O` would be
`12 / 2 = 6`.

`\rm 1\; C_(5)H_(12) + ?\; O_2 \to 5\; CO_(2) + 6\; H_(2)O`.

There would be
`5 * 2 + 6 * 1 = 16` oxygen atoms among the products. Also by the conservation of atoms, there would be the same number of oxygen atoms among the reactants.

Hence, the coefficient of
`\rm O_2` would be
`16 / 2 = 8`.

`\rm 1\; C_(5)H_(12) + 8\; O_2 \to 5\; CO_(2) + 6\; H_(2)O`.

The ratio between the coefficient of
`\rm O_2` and
`\rm C_(5)H_(12)` in the balanced equation is:

`\displaystyle \frac{n({\rm O_2})}{n({\rm C_(5)H_(12)})} = (8)/(1) = 8`.

In other words, it would take eight
`\rm O_2` molecules to react with one
`\rm C_(5)H_(12)` molecule.

Assume that both
`\rm O_2` and
`\rm C_(5)H_(12)` are ideal gases. Under the same temperature and pressure, the volume of the two gases would be proportional to the number of molecules in each gas:

`\displaystyle \frac{V({\rm O_2})}{V({\rm C_(5)H_(12)})} = \frac{n({\rm O_2})}{n({\rm C_(5)H_(12)})} = (8)/(1) = 8`.

In other words, it would take
`8\; \rm cm^(3)` of
`\rm O_2` to react with
`1\; \rm cm^(3)` of
`\rm C_(5)H_(12)` under these assumptions. It would then take
`8 * 15\; \rm cm^(3) = 120\; \rm cm^(3)` of
`\rm O_2\!` to react with
`15\; \rm cm^(3)\!` of
`\rm C_(5)H_(12)\!`.