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[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

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[ACTION NAME]

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# Your action step 2

# Your action step 3

...

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According to the law of active masses, the rate of the direct reaction is expressed by the equation:

$$
\mathrm{v}=\mathrm{k} \cdot \mathrm{C}_{\mathrm{CO}}{ }^{2} \cdot \mathrm{C}_{\mathrm{O}_2}
$$

If the reaction volume is decreased or the pressure is increased, the concentration of reacting substances increases.

If the reaction volume is increased or the pressure is decreased, the concentration of reacting substances decreases.

When the reaction volume is reduced by a factor of 3, the concentration of reacting substances increases by a factor of 3. The expression for the rate of the direct reaction is:

$$
\begin{gathered}
v_{2}=k\left(3 \mathrm{C}_{C O}\right)^{2} \cdot 3 \mathrm{C}_{O_2}=27 k \mathrm{C}_{C O}^{2} \mathrm{C}_{O_2} \\
\frac{v_{2}}{v_{1}}=\frac{27 k \mathrm{C}_{C O}^{2} \mathrm{C}_{O_2}}{k \mathrm{C}_{C O}^{2} \mathrm{C}_{O_2}}=27
\end{gathered}
$$

Present the answer in LaTex format: \boxed{Your answer}
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