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Chapter 5

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?

WhatsApp Image 2022-10-10 at 18.42.10

Step-by-Step

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