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For the reaction, N2O5(g)→2NO2(g)+12O2(g)\text{N}_2\text{O}_5(g) \rightarrow 2\text{NO}_2(g) + \frac{1}{2}\text{O}_2(g) the value of the rate of disappearance of N2O5\text{N}_2\text{O}_5 is given as 6.25×10−3 mol L−1s−16.25 \times 10^{-3} \text{ mol L}^{-1}\text{s}^{-1}. The rate of formation of NO2\text{NO}_2 and O2\text{O}_2 is given respectively as:

A

6.25×10−3 mol L−1s−16.25 \times 10^{-3} \text{ mol L}^{-1}\text{s}^{-1} and 6.25×10−3 mol L−1s−16.25 \times 10^{-3} \text{ mol L}^{-1}\text{s}^{-1}

B

1.25×10−2 mol L−1s−11.25 \times 10^{-2} \text{ mol L}^{-1}\text{s}^{-1} and 3.125×10−3 mol L−1s−13.125 \times 10^{-3} \text{ mol L}^{-1}\text{s}^{-1}

C

6.25×10−3 mol L−1s−16.25 \times 10^{-3} \text{ mol L}^{-1}\text{s}^{-1} and 3.125×10−3 mol L−1s−13.125 \times 10^{-3} \text{ mol L}^{-1}\text{s}^{-1}

D

1.25×10−2 mol L−1s−11.25 \times 10^{-2} \text{ mol L}^{-1}\text{s}^{-1} and 6.25×10−3 mol L−1s−16.25 \times 10^{-3} \text{ mol L}^{-1}\text{s}^{-1}

Step-by-Step Solution

For the given reaction: N2O5(g)→2NO2(g)+12O2(g)\text{N}_2\text{O}_5(g) \rightarrow 2\text{NO}_2(g) + \frac{1}{2}\text{O}_2(g) The rate of the reaction is related to the rates of disappearance and formation of species as follows: Rate=−d[N2O5]dt=12d[NO2]dt=11/2d[O2]dt=2d[O2]dt\text{Rate} = -\frac{d[\text{N}_2\text{O}_5]}{dt} = \frac{1}{2} \frac{d[\text{NO}_2]}{dt} = \frac{1}{1/2} \frac{d[\text{O}_2]}{dt} = 2 \frac{d[\text{O}_2]}{dt} Given the rate of disappearance of N2O5\text{N}_2\text{O}_5: −d[N2O5]dt=6.25×10−3 mol L−1s−1-\frac{d[\text{N}_2\text{O}_5]}{dt} = 6.25 \times 10^{-3} \text{ mol L}^{-1}\text{s}^{-1}

Rate of formation of NO2\text{NO}_2: d[NO2]dt=2×(−d[N2O5]dt)=2×6.25×10−3=12.5×10−3=1.25×10−2 mol L−1s−1\frac{d[\text{NO}_2]}{dt} = 2 \times \left( -\frac{d[\text{N}_2\text{O}_5]}{dt} \right) = 2 \times 6.25 \times 10^{-3} = 12.5 \times 10^{-3} = 1.25 \times 10^{-2} \text{ mol L}^{-1}\text{s}^{-1}

Rate of formation of O2\text{O}_2: d[O2]dt=12×(−d[N2O5]dt)=12×6.25×10−3=3.125×10−3 mol L−1s−1\frac{d[\text{O}_2]}{dt} = \frac{1}{2} \times \left( -\frac{d[\text{N}_2\text{O}_5]}{dt} \right) = \frac{1}{2} \times 6.25 \times 10^{-3} = 3.125 \times 10^{-3} \text{ mol L}^{-1}\text{s}^{-1}

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