Solution: To find the rate of formation of \( NO_2 \), we first need to determine the change in concentration of \( N_2O_4 \) over the given time period.
Initial concentration of \( N_2O_4 \): \([N_2O_4]_0 = 3 \, \text{mol L}^{-1}\)
Final concentration after 30 minutes: \([N_2O_4] = 2.75 \, \text{mol L}^{-1}\)
The change in concentration of \( N_2O_4 \) over 30 minutes is:
\[ \Delta [N_2O_4] = [N_2O_4]_0 - [N_2O_4] = 3 - 2.75 = 0.25 \, \text{mol L}^{-1} \]
According to the reaction:
\[ 2N_2O_4 \rightarrow 4NO_2 \]
For every 2 moles of \( N_2O_4 \) that decompose, 4 moles of \( NO_2 \) are formed, so the ratio is:
\[ \frac{4 \, \text{mol} \, NO_2}{2 \, \text{mol} \, N_2O_4} = 2 \]
The change in concentration of \( NO_2 \) formed is:
\[ \Delta [NO_2] = 2 \times \Delta [N_2O_4] = 2 \times 0.25 = 0.50 \, \text{mol L}^{-1} \]
The rate of formation of \( NO_2 \) over 30 minutes is:
\[ \text{Rate} = \frac{\Delta [NO_2]}{\Delta t} = \frac{0.50 \, \text{mol L}^{-1}}{30 \, \text{min}} = \frac{0.50}{30} \, \text{mol L}^{-1} \text{min}^{-1} = \frac{1}{60} \, \text{mol L}^{-1} \text{min}^{-1} \]
Given \( x \times 10^{-3} = \frac{1}{60} \), we can find \( x \):
\[ x = \frac{1}{60} \times 1000 = 16.67 \approx 17 \]
Thus, the value of \( x \) is: 17
A(g) $ \rightarrow $ B(g) + C(g) is a first order reaction.
The reaction was started with reactant A only. Which of the following expression is correct for rate constant k ?
Rate law for a reaction between $A$ and $B$ is given by $\mathrm{R}=\mathrm{k}[\mathrm{A}]^{\mathrm{n}}[\mathrm{B}]^{\mathrm{m}}$. If concentration of A is doubled and concentration of B is halved from their initial value, the ratio of new rate of reaction to the initial rate of reaction $\left(\frac{\mathrm{r}_{2}}{\mathrm{r}_{1}}\right)$ is
For $\mathrm{A}_{2}+\mathrm{B}_{2} \rightleftharpoons 2 \mathrm{AB}$ $\mathrm{E}_{\mathrm{a}}$ for forward and backward reaction are 180 and $200 \mathrm{~kJ} \mathrm{~mol}^{-1}$ respectively. If catalyst lowers $\mathrm{E}_{\mathrm{a}}$ for both reaction by $100 \mathrm{~kJ} \mathrm{~mol}^{-1}$. Which of the following statement is correct?
Match List-I with List-II: List-I