For the thermal decomposition of acetaldehyde, `CH_(3)CHO(g)to CH_(4)(g)+CO(g)`, the following rate data were obtained :
`{:("Experiment",,,"Initial pressure (torr)",,,"Initial rate of increase in total pressure (torr)"),(" "1,,," "300,,," "0.61(r_(1))),(" "2,,," "200,,," "0.27(r_(2))):}`
Predict the order of reaction.

Explanation

To determine the order of the reaction for the thermal decomposition of acetaldehyde, we will use the provided rate data from two experiments.

### Step-by-Step Solution:

1. **Identify the Rate Law**:
The rate of a reaction can generally be expressed as:
\[ \text{Rate} = k [\text{A}]^n \]
where \( k \) is the rate constant, \( [\text{A}] \) is the concentration (or pressure in this case) of the reactant, and \( n \) is the order of the reaction.

2. **Set Up the Ratios**:
From the data provided:
- Experiment 1: Initial pressure \( P_1 = 300 \) torr, Rate \( R_1 = 0.61 \)
- Experiment 2: Initial pressure \( P_2 = 200 \) torr, Rate \( R_2 = 0.27 \)

We can write the rate expressions for both experiments:
\[ R_1 = k (P_1)^n \quad \text{and} \quad R_2 = k (P_2)^n \]

3. **Form the Ratio of Rates**:
Taking the ratio of the rates from both experiments gives:
\[ \frac{R_1}{R_2} = \frac{k (P_1)^n}{k (P_2)^n} \]
The \( k \) cancels out:
\[ \frac{R_1}{R_2} = \frac{(P_1)^n}{(P_2)^n} \]

4. **Substitute the Values**:
Substitute \( R_1 = 0.61 \), \( R_2 = 0.27 \), \( P_1 = 300 \), and \( P_2 = 200 \):
\[ \frac{0.61}{0.27} = \frac{(300)^n}{(200)^n} \]

5. **Simplify the Equation**:
This simplifies to:
\[ \frac{0.61}{0.27} = \left(\frac{300}{200}\right)^n \]
\[ \frac{0.61}{0.27} = \left(\frac{3}{2}\right)^n \]

6. **Calculate the Left Side**:
Calculate \( \frac{0.61}{0.27} \):
\[ \frac{0.61}{0.27} \approx 2.26 \]

7. **Set Up the Equation**:
Now we have:
\[ 2.26 = \left(\frac{3}{2}\right)^n \]

8. **Take Logarithms**:
To solve for \( n \), take the logarithm of both sides:
\[ \log(2.26) = n \log\left(\frac{3}{2}\right) \]

9. **Calculate \( n \)**:
Rearranging gives:
\[ n = \frac{\log(2.26)}{\log\left(\frac{3}{2}\right)} \]
Using a calculator:
\[ n \approx \frac{0.354}{0.176} \approx 2.01 \]

10. **Conclusion**:
Since \( n \approx 2 \), we conclude that the order of the reaction is **2**.