Gaseous ammonia is injected into the exhaust stream of a...

Gaseous ammonia is injected into the exhaust stream of a coalburning power plant to reduce the pollutant $\mathrm{NO}$ to $\mathrm{N}_{2}$ according to the reaction: $$ 4 \mathrm{NH}_{3}(g)+4 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightarrow 4 \mathrm{~N}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g) $$ Suppose that the exhaust stream of a power plant has a flow rate of $335 \mathrm{~L} / \mathrm{s}$ at a temperature of $955 \mathrm{~K}$, and that the exhaust contains a partial pressure of $\mathrm{NO}$ of $22.4$ torr. What should be the flow rate of ammonia delivered at 755 torr and $298 \mathrm{~K}$ into the stream to react completely with the $\mathrm{NO}$ if the ammonia is $65.2 \%$ pure (by volume)?

Gaseous ammonia is injected into the exhaust stream of a coalburning power plant to reduce the pollutant $\mathrm{NO}$ to $\mathrm{N}_{2}$ according to the reaction:
$$
4 \mathrm{NH}_{3}(g)+4 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightarrow 4 \mathrm{~N}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)
$$
Suppose that the exhaust stream of a power plant has a flow rate of $335 \mathrm{~L} / \mathrm{s}$ at a temperature of $955 \mathrm{~K}$, and that the exhaust contains a partial pressure of $\mathrm{NO}$ of $22.4$ torr. What should be the flow rate of ammonia delivered at 755 torr and $298 \mathrm{~K}$ into
the stream to react completely with the $\mathrm{NO}$ if the ammonia is $65.2 \%$ pure (by volume)?

Key Concepts

Gas Purity Calculation

When a gas is not pure, its effective amount is reduced by its percentage of purity. Calculating the flow rate based on the impurity level ensures that sufficient reactive gas is delivered. In this example, the delivered ammonia's volume is adjusted to account for the fact that only a fraction of it is the desired reactive component.

Flow Rate Conversion

This involves adjusting volumetric flow rates from one set of conditions (e.g., temperature and pressure) to another. The conversion typically relies on the ideal gas law and is necessary to accurately relate the flow rate of gases in different operational environments like those at the power plant exhaust and the ammonia supply.

Ideal Gas Law

The ideal gas law (PV = nRT) is crucial for relating the pressure, volume, temperature, and number of moles of a gas. It allows one to calculate the molar flow rate of a gas stream under specified conditions and subsequently determine how the gas behaves when transferred between different temperature and pressure regimes.

Reaction Stoichiometry

This concept involves using the balanced chemical equation to understand the molar relationships between reactants and products. In this context, the stoichiometric coefficients indicate how many moles of ammonia are required to react completely with a given number of moles of nitric oxide, enabling the calculation of the necessary amount of ammonia for pollutant reduction.

Partial Pressure

Partial pressure refers to the pressure exerted by an individual gas in a mixture, as if it alone occupied the entire volume. It is an important concept for determining the effective concentration of reactive species, such as nitric oxide in the exhaust stream, which directly influences the calculation of its molar flow rate.

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