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To determine the rate law for the reaction, let's analyze the information provided:

### Reaction:
\[
\text{CHCl}_3 (g) + \text{Cl}_2 (g) \rightarrow \text{CCl}_4 (g) + \text{HCl} (g)
\]

### Given Information:
1. **Tripling the concentration of \(\text{Cl}_2\)** increases the rate by a factor of **1.7** (which is stated to be the square root of 3).
2. **Tripling the concentration of \(\text{CHCl}_3\)** increases the rate by a factor of **3**.

### Rate Law Expression:
The general form of the rate law for this reaction is:
\[
\text{Rate} = k[\text{CHCl}_3]^m[\text{Cl}_2]^n
\]
Where:
- \( k \) is the rate constant,
- \( m \) is the order with respect to \(\text{CHCl}_3\),
- \( n \) is the order with respect to \(\text{Cl}_2\).

### Determining the Orders \( m \) and \( n \):

1. **Effect of \(\text{Cl}_2\) Concentration:**
   - Tripling the concentration of \(\text{Cl}_2\) increases the rate by a factor of 1.7.
   - Mathematically: \( 3^n = 1.7 \).
   - Since \(1.7\) is approximately the square root of \(3\), this implies that \(n = \frac{1}{2}\).

2. **Effect of \(\text{CHCl}_3\) Concentration:**
   - Tripling the concentration of \(\text{CHCl}_3\) increases the rate by a factor of 3.
   - Mathematically: \( 3^m = 3 \).
   - This implies \( m = 1 \).

### Rate Law:
Given the determined values of \( m \) and \( n \):
\[
\text{Rate} = k[\text{CHCl}_3]^1[\text{Cl}_2]^{1/2}
\]
Or more simply:
\[
\text{Rate} = k[\text{CHCl}_3][\text{Cl}_2]^{1/2}
\]

This is the rate law for the given reaction.

Would you like to dive deeper into any specific aspect of this problem or have any questions?

### Related Questions:
1. What are the units of the rate constant \( k \) for this reaction?
2. How does the reaction order affect the shape of the rate vs. concentration graph?
3. Can you explain the physical meaning of a half-order reaction with respect to \(\text{Cl}_2\)?
4. How would the rate change if both \(\text{CHCl}_3\) and \(\text{Cl}_2\) concentrations were doubled?
5. What experimental methods can be used to determine the rate law of a reaction?

### Tip:
Remember that reaction orders are not always integers. They can be fractions, and their values are determined experimentally, not from the stoichiometry of the reaction.

Trichloromethane and chlorine gas react according to the following equation:
CHCl3 (g) + Cl2 (g) → CCl4 (g) + HCl (g)

Tripling the concentration of Cl2 increases the rate by a factor of 1.7 (the square root of 3), and tripling the concentration of CHCl3 increases the rate by a factor of 3.
Determine the rate law for the reaction.

Determine the rate law for the reaction of CHCl3 and Cl2. Tripling Cl2 increases the rate by 1.7, and tripling CHCl3 increases it by 3. Analyze the rate law expression and solve for reaction orders.

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