Advanced Topics (more challenging questions in Atkins\' and beyond Atkins\') A f

Question

Advanced Topics (more challenging questions in Atkins' and beyond Atkins') A flask of volume 5.00 L is evacuated and 43.78 g of solid dinitrogen tetroxide, N_2O_4, is introduced at -19 degree C. The sample is then warmed to 25 degree C, during which time the N_2O_4 vaporizes and some of it dissociates to form brown gas NO_2. The pressure slowly increases until it stabilizes at 2.96 atm. (a) Please write a balanced equation for this reaction. (b) If the gas in the flask at 25 degree C were all N_2O_4, what would the pressure be? (c) If all the gas in the flask were converted into NO_2, what would the pressure be? (d) What are the mole fractions of N_2O_4 and NO_2 once the pressure stabilizes at 2.96 atm?

Explanation / Answer

a) N2O4 (g) <---------> 2NO2(g)

b) mass of N2O4 = 43.78g

Molar mass of N2O4 = 92g

No of moles, n= 43.78/92 = 0.47587

PV = nRT

Pressure, P = nRT/V

=0.47587 × 0.082057(lit atm/mol K) × 298.15K/5L

= 2.33atm

c) No of moles of N2O4 = 0.47587

According to stoichiometry 1 mol of N2O4 give 2 mol of NO2. So, 0.47587 mol of N2O4 give 0.95174 mol of NO2

Applying in ideal gas equation

P = (0.95174 × 0.082057 × 298.15)/5

=4.66atm

d) n = PV/RT

=( 2.96 × 5)/(0.082057 ×298.15)

= 0.60493

Conversion = (100/0.47587)×0.12906=27.12%

Mole fraction of N2O4 = 0.7288

Mole fraction of NO2 = 0.2712

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