Suppose that the exhaust stream of an automobile has a flow rate of 2.55 L/s at 655 K and contains a partial pressure of NO of 12.4 torr. What total mass of urea is necessary to react completely with the NO formed during 8.0 hours of driving?

Verified step by step guidance

1. Convert the flow rate from liters per second (L/s) to liters per hour (L/h) by multiplying by the number of seconds in an hour.
2. Calculate the total volume of the exhaust stream over 8.0 hours using the flow rate in L/h.
3. Use the ideal gas law, PV = nRT, to find the number of moles of NO in the exhaust stream. Remember to convert the pressure from torr to atm and use the appropriate value for R (0.0821 L·atm/mol·K).
4. Determine the stoichiometry of the reaction between urea and NO. The balanced chemical equation is: 2 NO + (NH2)2CO → N2 + CO2 + 2 H2O.
5. Calculate the mass of urea needed using the stoichiometry from the balanced equation and the molar mass of urea (60.06 g/mol).

Key Concepts

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 essential for calculating the amount of gas present in a given volume and temperature, which is necessary to determine the moles of NO in the exhaust stream.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions based on balanced chemical equations. Understanding stoichiometry is crucial for determining how much urea is needed to react with the given amount of NO, as it allows for the conversion between moles of reactants and products.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole. Knowing the molar mass of urea is necessary to convert the number of moles calculated from stoichiometry into a total mass, which is required to answer the question about the total mass of urea needed.