Question

Wetlands can play a significant role in removing fertilizer residues from rain runoff and groundwater; one way they do this is through denitrification, which converts nitrate ions to nitrogen gas: $$2NO − 3​(aq)+5CO(g)+2H+(aq) N2​(g)+H2​O(l)+5CO2​(g) Suppose 375.00 g of NO3- flows into a swamp each day. What volume of N2 would be produced each day at 17°C and 1.00 atm if the denitrification process were complete? What volume of CO2 would be produced each day? Suppose the gas mixture produced by the decomposition reaction is trapped in a container at 17°C; what is the density of the mixture assuming Ptotal = 1.00 atm? Please report all of your answers to 2 decimal places. volume of N2 ___ L volume of CO2 ___ L density ___ g/L

Answer 1

first of all we need to write the balanced chemical reaction:

2NO^-₃(aq) + 5CO(g) + 2H+(aq) -----> N₂​(g)+H₂​O(l)+5CO₂​(g)

we see that all the atoms are balanced and hence the reaction

now we need to write stoichometric conversion factor for N₂ to NO^-₃ which is 1 mole N₂ / 2 mole NO^-₃

and CO₂ toNO^-₃ is 5 mole CO₂ / 2 mole NO^-₃

molar mass of NO₃^- is 62.00 g/mol

moles of NO₃^- = mass / molar mass = 375g/62.00 g/mol = 6.05 moles

using stoichiometric conversion factor N₂ produced is 1 mole N₂ / 2 mole NO^-₃ x 6.05 mole NO^-₃

   = 3.025 mole N₂

mass of N₂ produced = moles x molar mass = 3.025 x 28 = 84.7 g

simlarly for CO₂ = 5 mole CO₂ / 2 mole NO^-₃ x 6.05 mole NO^-₃ = 15.125 moles CO₂

mass of CO₂ produced = 15.125 x 44 = 665.5g

total mass = 750.2g

converting moles to volume using ideal gas equation

17^oC = 17 + 273 = 290K

V_N2 = nRT/P = 3.025 x 0.0821 x 290/1 = 72.02 L

for V_CO2 = 15.125 x 0.0821 x 290/1 = 360.11 L

density = mass/volume

750.2g/(72.02 + 360.11)

density = 1.74 g/L