Gaseous ammonia is injected into the exhaust stream of a coal-burning power plant to reduce the pollutant NO to N2 according to the reaction: 4 NH3(g) + 4 NO(g) + O2(g) → 4 N2(g) + 6 H2O(g). Suppose that the exhaust stream of a power plant has a flow rate of 335 L/s at a temperature of 955 K, and that the exhaust contains a partial pressure of NO of 22.4 torr. What should be the flow rate of ammonia delivered at 755 torr and 298 K into the stream to react completely with the NO if the ammonia is 65.2% pure (by volume)?

Verified step by step guidance

1. Convert the partial pressure of NO from torr to atm using the conversion factor: 1 atm = 760 torr.
2. Use the ideal gas law, PV = nRT, to calculate the moles of NO in the exhaust stream. Use the given flow rate, temperature, and converted pressure.
3. Determine the moles of NH3 needed to react with the moles of NO using the stoichiometry of the balanced chemical equation: 4 NH3 + 4 NO + O2 → 4 N2 + 6 H2O.
4. Calculate the volume of pure NH3 required at the given conditions (755 torr and 298 K) using the ideal gas law, considering the moles of NH3 needed.
5. Adjust the calculated volume of NH3 to account for the purity of the ammonia (65.2% pure by volume) to find the actual flow rate of the ammonia solution.

Key Concepts

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the balanced equation. It allows us to determine the proportions of substances involved in a reaction. In this case, the stoichiometric coefficients from the balanced equation indicate that four moles of ammonia react with four moles of nitric oxide, which is essential for calculating the required amount of ammonia to completely react with the given amount of NO.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is crucial for converting between different states of gases and calculating the flow rates and partial pressures in the problem. By applying the Ideal Gas Law, we can determine the number of moles of NO present in the exhaust stream and subsequently the amount of ammonia needed for the reaction.

Partial Pressure and Gas Mixtures

Partial pressure refers to the pressure exerted by a single component of a gas mixture. In this scenario, understanding the partial pressure of NO in the exhaust stream is vital for determining how much ammonia is needed for the reaction. The total pressure and the composition of the gas mixture influence the behavior of each gas, and knowing the purity of ammonia (65.2% by volume) is necessary to calculate the actual flow rate of ammonia required to achieve complete reaction with NO.