Question

A. When 44.4 L of nitric oxide reacts with 31.2 L of oxygen at 448 K under a constant pressure of 1.605 atm, what is the theoretical yield (in g) of nitrogen dioxide?

B. If helium effuses through a porous barrier in 1.58 min, how much time (in min) would it take the same amount of ammonia to effuse through the same barrier under the same conditions?

C. Nitrogen and hydrogen react in the Haber process to form ammonia. All substances are in the gas phase. If 0.541 atm of nitrogen and 0.681 atm of hydrogen react, what is the partial pressure of ammonia (in mmHg) when this reaction goes 60.8 complete. The volume and temperature are constant.

D. What is the root mean square speed (in m/s) of nitrogen at 32^oC?

Answer 1

A.

Reaction is

2NO_(g) + O_2(g) 2NO_2(g)

2 mole of NO yields 2 moles of NO₂ and needs 1 mole of O₂

Number of moles of NO in 44.4L NO at 1.605atm,

n= PV÷(RT) ------- from universal gas equation.

n= (1.605× 44.4) ÷(0.082057×448) = 1.94 moles

Number of moles of Oxygen in 31.2L of O₂

n = (1.605×31.2)÷ (0.082057×448) = 1.36 moles.

1.94 moles of NO requires 1.94÷2 =.97 moles of oxygen molecules.

So limiting reagent is NO

So 1.94 moles of NO will yield 1.94 moles of NO₂ theorettheoretically.

Theoretical yield = molar mass × number of moles

= 46× 1.96 = 89.24 g

B

As per Graham's law of effusion, rate of effusion is inversely proportional to square-root of molecular mass.

If x amount of Helium effuses in 1.58 minutes

Then time for effusion of x amount of ammonia can be calculated by Graham's law of effusion.

So it takes 37.5 minutes  ammonia to effuse the same amount

C

3H₂+2N₂ 2NH₃

At constant volume and temperature, 3 atm H2 needs 2 atm N2.

0.681 atm H2 will require 0.681x(2÷3) = .454 atm N2.

So limiting reagent is H2

As per balanced equation, 2 atm NH3 is 100% completion of 3 atm of H2.

So, 0.681 atm partial pressure of H2 will require (2÷3)×0.681 = 0.454 atm NH3 for completion.

Then, 60.8% completion means (0.454÷100)×60.8 = 0.276 atm partial pressure of ammonia.

So partial pressure of ammonia at 60.8 % completion will be 0.276 atm.

D

Root mean square velocity of molecule of molecular mass M, at temperature T is given by