Question

The emission of NO₂ by fossil fuel combustion can be prevented by injecting gaseous urea into the combustion mixture. The urea reduces NO (which oxidizes in air to form NO₂) according to the following reaction: 2CO(NH₂)₂(g)+4NO(g)+O₂(g)→4N₂(g)+2CO₂(g)+4H₂O(g) Suppose that the exhaust stream of an automobile has a flow rate of 2.37 L/s at 657 K and contains a partial pressure of NO of 14.0 torr .What total mass of urea is necessary to react completely with the NO formed during 8.1 hours of driving?Express answer in g.

Answer 1

There is 709.1 grams of urea needed.

Step-by-step explanation:

Step 1: The balanced equation:

2CO(NH2)2(g)+4NO(g)+O2(g)→4N2(g)+2CO2(g)+4H2O(g)

Step 2: Data given

The exhaust stream of an automobile has a flow rate of 2.37 L/s

This happens at a temperature of 657 Kelvin

The partial pressure of NO is 14.0 torr

Step 3: Calculating the volume during 8.1 hours

V = 2.37L/s ∙ 8.1hr ∙3600s/hr = 69109.2L = 69.1092m³

Step 4: Calculate the partial pressure of nitric oxide:

p = 14 torr ∙ 101325Pa/760torr = 1866.5Pa

Step 5: Calculating number of moles of NO

⇒ We use the ideal gas law P*V=n*R*T

n(NO) = P*V/R*T

with P= The partial pressure of NO = 1866.5 Pa

with V =the volume of NO = 69.1092m³

with R = the gas constant = 8.314472 Pa*m³/mol*K

with T = 657 Kelvin

n(NO) = 1866.5Pa ∙ 69.1092m³ / (8.314472Pa*m³/mol*K ∙ 657K)

= 23.61 mol es

Step 6: Calculate moles of urea

Since there is consumed 2 moles of urea per 4 moles of nitric oxide.

This means for 24.432 moles of NO, there is consumed 23.61 /2 = 11.806 moles of urea.

Step 7: Calculate mass of urea

m(CO(NH₂)₂) = 11.806 moles ∙ 60.06g/moles = 709.07g

There is 709.1 grams of urea needed.