When an equation stoichiometry problem involves two gases at the same temperature and pressure, a shortcut can be used. This shortcut employs the coefficients from the balanced equation to create a volume ratio that converts directly from volume of one gas to volume of another. The following hypothetical case illustrates the underlying logic.

Consider two gases, A and B, at the same temperature and pressure. The ratio of their volume to the moles of gas can be determined from the ideal gas equation.

If the two gases are at the same temperature and pressure, the V/n ratio for each gas must be the same.

If we rearrange the equation above, we see that the volume ratio of two gases at the same temperature and pressure is equal to their molar ratio.

The molar ratio of the two gases is constructed from the coefficients in the balanced equation. Because the molar ratio is equal to the volume ratio for gases at the same temperature and pressure, the coefficients from the balanced equation can also be used to generate a factor that converts directly from volume of one gas to volume of another, as in the following example.

 

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 gas at the same temperature and pressure?

Solution:

The unit 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.