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## Q. 5.11

The combustion of acetylene with pure oxygen produces a very high-temperature flame used for welding and cutting metals. Calculate the volume of  $O_{2}$  (in liters) required for the complete combustion of 7.64 L of acetylene ($C_{2}H_{2}$) measured at the same temperature and pressure.

$2C_{2}H_{2}(g) + 5O_{2}(g) → 4CO_{2}(g) + 2H_{2}O(l)$

Strategy Note that the temperature and pressure of $O_{2}$ and  $C_{2}H_{2}$ are the same. Which gas law do we need to relate the volume of the gases to the moles of gases?

## Verified Solution

According to Avogadro’s law, at the same temperature and pressure, the number of moles of gases is directly related to volume. From the equation, we have 5 mol  $O_{2} \bumpeq 2 mol C_{2}H_{2}$ ; therefore, we can also write 5 $L O_{2} \bumpeq 2 L C_{2}H_{2}$ . The volume of $O_{2}$  that will react with 7.64 L  $C_{2}H_{2}$ is given by

volume of $O_{2}=7.64 \cancel{L C_{2}H_{2}}\times \frac{5 L O_{2}}{2 \cancel{L C_{2}H_{2}}}$

=19.1  L