Question

nitrogen dioxide decomposes to nitric oxide and oxygen via the reaction,
$2no_2 \
ightarrow 2no + o_2$
in a particular experiment at 300 °c, $no_2$ drops from 0.0100 to 0.00650 m in 100s. the rate of appearance of $o_2$ for this period is ______ m/s.
$3.5 \times 10^{-3}$
$7.0 \times 10^{-3}$
$3.5 \times 10^{-5}$
$1.8 \times 10^{-5}$
$7.0 \times 10^{-5}$

Explanation:

Step1: Calculate rate of $\text{NO}_2$ disappearance

$$\text{Rate of disappearance of } \text{NO}_2 = -\frac{\Delta [\text{NO}_2]}{\Delta t} = -\frac{0.00650\ \text{M} - 0.0100\ \text{M}}{100\ \text{s}}$$
$$= -\frac{-0.00350\ \text{M}}{100\ \text{s}} = 3.5 \times 10^{-5}\ \text{M/s}$$

Step2: Relate to $\text{O}_2$ appearance rate

From reaction $2\text{NO}_2
ightarrow 2\text{NO} + \text{O}_2$, the rate relation is:
$$\text{Rate of appearance of } \text{O}_2 = \frac{1}{2} \times \text{Rate of disappearance of } \text{NO}_2$$
$$= \frac{1}{2} \times 3.5 \times 10^{-5}\ \text{M/s}$$

Answer:

$\boldsymbol{1.8 \times 10^{-5}}$ (Option: 1.8 x 10⁻⁵)