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EXAMPLE Equation Stoichiometry with Gases at the Same Temperature and Pressure:

Nitric acid, which is used in the manufacture of fertilizers and explosives, can be made from ammonia, NH3, and oxygen, O2. The three-step process is summarized in the following net reaction:

NH3(g) + 2O2(g)    HNO3(l) + H2O(l)

What is the minimum volume of oxygen gas at 22.4 C and 271 kPa that would react completely with 875 L NH3 at the same temperature and pressure?

### Solution:

The dimensional analysis sequences laid out below show the use of two different values of R as conversion factor. Notice that all of the numbers cancel except the coefficients from the balanced equation.

or

Shortcut: Because the gases are at the same temperature and pressure, the molar ratio constructed from the coefficients in the balanced equation is equal to the volume ratio of the gases expressed in liters. Therefore, it is the only factor necessary to convert the volume of one gas into the stoichiometrically equivalent volume of the other.

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