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Chapter 2: Problem 1

If the rate with respect to \(\mathrm{O}_{2}, \mathrm{NO}\) and \(\mathrm{NO}_{2}\) are respectively $$ \frac{-\Delta\left[\mathrm{O}_{2}\right]}{\Delta \mathrm{t}}, \frac{-1}{2}, \frac{\Delta[\mathrm{NO}]}{\Delta \mathrm{t}}, \frac{+1}{2} \frac{\Delta\left[\mathrm{NO}_{2}\right]}{\Delta \mathrm{t}} $$ then the corresponding chemical equation is \(2 \mathrm{NO}\) \(+\mathrm{O}_{2} \rightarrow 2 \mathrm{NO}_{2}\)

Short Answer

Expert verified
Answer: The balanced chemical equation is 2 NO + O₂ → 2 NO₂.

Step by step solution

01

Identify the rate of change expressions for each species

We are given the rates of change for \(\mathrm{O}_{2}\), \(\mathrm{NO}\), and \(\mathrm{NO}_{2}\) as follows: 1. \(\frac{-\Delta\left[\mathrm{O}_{2}\right]}{\Delta \mathrm{t}}\) 2. \(\frac{-\Delta[\mathrm{NO}]}{2\Delta \mathrm{t}}\) 3. \(\frac{\Delta\left[\mathrm{NO}_{2}\right]}{\Delta \mathrm{t}}\)
02

Determine the stoichiometric coefficients

We can use these rate expressions to determine the stoichiometric coefficients in the balanced equation. 1. For \(\mathrm{O}_2\) : The rate expression is \(\frac{-\Delta\left[\mathrm{O}_{2}\right]}{\Delta \mathrm{t}}\). The negative sign indicates that it is being consumed in the reaction, and its coefficient is 1 (since there is no other factor in the expression). 2. For \(\mathrm{NO}\) : The rate expression is \(\frac{-\Delta[\mathrm{NO}]}{2\Delta \mathrm{t}}\). The negative sign indicates that it is being consumed in the reaction, and its coefficient is 2 (since there is a factor of 2 in the denominator). 3. For \(\mathrm{NO}_2\) : The rate expression is \(\frac{\Delta\left[\mathrm{NO}_{2}\right]}{\Delta \mathrm{t}}\). The positive sign indicates that it is being produced in the reaction, and its coefficient is 1 (since there is no other factor in the expression).
03

Write the balanced chemical equation

Using the stoichiometric coefficients determined in Step 2, we can write the balanced chemical equation as: $$2 \mathrm{NO} \ + \ \mathrm{O}_2 \ \rightarrow \ 2 \mathrm{NO}_2$$

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Most popular questions from this chapter

For each of the questions, four choices have been provided. Select the correct alternative. For a particular reaction, \(A+B \rightarrow C\) was studied at \(25^{\circ} \mathrm{C}\). The following results are obtained: $$ \begin{array}{|c|c|c|} \hline \begin{array}{c} {[\mathrm{A}]} \\ \text { mole } / \mathrm{I} \end{array} & \begin{array}{c} {[\mathrm{B}]} \\ \text { moles } / \mathrm{I} \end{array} & \begin{array}{c} \text { Rate } \\ \left(\mathrm{mole} \mathrm{I}^{-1} \mathrm{~s}^{-1}\right) \end{array} \\ \hline 9 \times 10^{-5} & 1.5 \times 10^{-2} & 0.06 \\ \hline 9 \times 10^{-5} & 3 \times 10^{-3} & 0.012 \\ \hline 3 \times 10^{-5} & 3 \times 10^{-3} & 0.004 \\ \hline 6 \times 10^{-5} & \mathrm{x} & 0.024 \\ \hline \end{array} $$ Then the value of \(\mathrm{x}\) is ________ (a) \(6 \times 10^{-3} \mathrm{~m} \ell^{-1}\) (b) \(3 \times 10^{-3} \mathrm{~m} \ell^{-1}\) (c) \(4.5 \times 10^{-3} \mathrm{~m} \ell^{-1}\) (d) \(9 \times 10^{-3} \mathrm{~m} \ell^{-1}\)

Threshold energy \(=\) Energy of normal molecules \(+\) Activation energy.

For each of the questions, four choices have been provided. Select the correct alternative. For a reaction \(\mathrm{A}+\mathrm{B} \rightarrow \mathrm{C}\), the rate law is written as \(\mathrm{r}=\mathrm{k}[\mathrm{A}]^{2}[\mathrm{~B}] .\) Doubling the concentrations of both of "A" and "B" increases the rate of reaction by (a) 2 times (b) 4 times (c) 8 times (d) 16 times

For a reaction \(2 \mathrm{~A}+\mathrm{B} \rightarrow 2 \mathrm{AB}\), it is found that doubling the concentration of both the reactants increases the rate to eight times that of initial rate but doubling the concentration of \(\mathrm{B}\) alone doubles the rate. Then the order of the reaction with respect to \(A\) and \(B\) is (a) 0,3 (b) 0,2 (c) 2,1 (d) 2,2

In the reaction \(\mathrm{N}_{2} \mathrm{O}_{4} \rightleftarrows 2 \mathrm{NO}_{2}\), the degree of dissociation of \(\mathrm{N}_{2} \mathrm{O}_{4}\) increases with (a) increase in pressure (b) decrease in temperature (c) increase in volume (d) presence of catalyst
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