
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system

To reduce the reaction rate, it is necessary to increase the system volume, thereby decreasing the pressure and reducing the concentration of the gaseous component - $\mathrm{NH}_{3}$. The concentration of $\mathrm{Br}_{2}$ will remain constant.

The initial forward reaction rate was:

$$
\mathrm{v}_1 = \mathrm{k} \cdot [\mathrm{NH}_{3}]^8 \cdot [\mathrm{Br}_{2}]
$$

When the concentration of ammonia is increased, the forward reaction rate becomes:

$$
\begin{gathered}
\mathrm{v}_2 = \mathrm{k} \cdot (x \cdot [\mathrm{NH}_{3}])^8 \cdot [\mathrm{Br}_{2}] = \mathrm{k} \cdot x^8 \cdot [\mathrm{NH}_{3}]^8 \cdot [\mathrm{Br}_{2}] \\
\mathrm{v}_2 / \mathrm{v}_1 = \mathrm{k} \cdot x^8 \cdot [\mathrm{NH}_{3}]^8 \cdot [\mathrm{Br}_{2}] / \mathrm{k} \cdot [\mathrm{NH}_{3}]^8 \cdot [\mathrm{Br}_{2}] = 60
\end{gathered}
$$

After canceling out all the constants, we get:

$$
x^8 = 60 \\
x = 1.66
$$

Therefore, to reduce the reaction rate by 60 times, the volume must be increased by a factor of 1.66.

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