According to the following reaction, disappearance rate of oxygen is 5.75 x 10-2 mol L-1 s-1. Determine formation rate of dinitrogen pentaoxide (g)?

4 NO2(g) + O2(g) → 2 N2O5(g)

Question

According to the following reaction, disappearance rate of oxygen is 5.75 x 10-2 mol L-1 s-1. Determine  formation rate of dinitrogen pentaoxide (g)?

4 NO2(g) + O2(g) → 2 N2O5(g)

BlackTom AI · Accepted Answer

Question restatement: Given the reaction 4 NO2(g) + O2(g) → 2 N2O5(g), the disappearance rate of O2 is 5.75 x 10^-2 mol L^-1 s^-1. Find the formation rate of N2O5(g). The answer options are: 0.0225, 0.1150, 0.0575, 0.0450, 0.180 mol L^-1 s^-1.

Step-by-step analysis of each option:

Option 0: 0.0225 mol L^-1 s^-1. To assess this, consider the reaction stoichiometry. The rate of reaction r is related to each species by r = - (1/coeff) d[species]/dt. For O2, coeff = 1, so r = - d[O2]/dt. Given -d[O2]/dt = 5.75 x 10^-2, r = 5.75 x 10^-2 s^-1 (units M s^-1). The rate of formation of N2O5 is d[N2O5]/dt = 2 r = 2 × 5.75 x 10^-2 = 0.115. This option 0.0225 is too small by a factor of about 5, so it is inconsistent with the stoichiometry.

Option 1: 0.1150 mol L^-1 s^-1. This matches the calculation: d[N2O5]/dt = 2 r with r = -d[O2]/dt = 5.75 x 10^-2, so d[N2O5]/dt = 2 × 5.75 x 10^-2 = 0.115. It aligns exactly with the stoichiometric relationship between O2 consumption and N2O5 formation, so this option is correct based on the stoichiometric coefficients.

Option 2: 0.0575 mol L^-1 s^-1. This value is equal to r itself (the rate derived from O2 disappearance), not the formation rate of N2O5, which comes from the 2:1 ratio between N2O5 formation and O2 consumption. Since the product side has coefficient 2, the formation rate must be twice r, not equal to r. Hence this is incorrect.

Option 3: 0.0450 mol L^-1 s^-1. This is neither equal to r nor to 2r, and shows a mistaken factor likely from misapplying the stoichiometric coefficients. It does not satisfy the relationship d[N2O5]/dt = 2 × (-d[O2]/dt). Therefore this option is incorrect.

Option 4: 0.180 mol L^-1 s^-1. This is larger than the computed 0.115 by a factor of about 1.56. It would correspond to multiplying by 3.125 or misapplying coefficients or rates. Since the correct relation is d[N2O5]/dt = 2 × (-d[O2]/dt) = 2 × 0.0575? No: -d[O2]/dt is 0.0575? Wait: given the problem states the disappearance rate of O2 is 5.75 x 10^-2, which is 0.0575. Then r = 0.0575, and d[N2O5]/dt = 0.1150, not 0.180. Therefore this option is incorrect.

Summary: The only option that faithfully follows from the stoichiometry 4 NO2 + O2 → 2 N2O5 and the given -d[O2]/dt = 5.75 x 10^-2 is d[N2O5]/dt = 2 × (5.75 x 10^-2) = 0.1150 mol L^-1 s^-1. The other choices either misapply the stoichiometric factors or misinterpret the rate relationships.

According to the following reaction, disappearance rate of oxygen is 5.75 x 10-2 mol L-1 s-1. Determine formation rate of dinitrogen pentaoxide (g)? 4 NO2(g) + O2(g) → 2 N2O5(g) Single choice

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