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This problem is based on a first-order reaction, where the decay of a substance is characterized by its half-life. In this case, the reaction is:

\[ 2 \text{N}_2\text{O}_5 \rightarrow 2 \text{N}_2\text{O}_4 + \text{O}_2 \]

We are given:

- Half-life (\( t_{1/2} \)) of \( \text{N}_2\text{O}_5 \) = 0.90 hours.
- Time (\( t \)) = 2.4 hours.
- It's a first-order reaction, so we can use the first-order decay formula.

### Formula:
For a first-order reaction, the concentration at any time \( t \) can be given by:

\[
\frac{[A]_t}{[A]_0} = \left( \frac{1}{2} \right)^{\frac{t}{t_{1/2}}}
\]

Where:
- \( [A]_t \) is the concentration at time \( t \),
- \( [A]_0 \) is the initial concentration,
- \( t \) is the time elapsed (2.4 hours),
- \( t_{1/2} \) is the half-life (0.90 hours).

### Calculation:
Now let's substitute the values into the formula:

\[
\frac{[A]_t}{[A]_0} = \left( \frac{1}{2} \right)^{\frac{2.4}{0.90}}
\]

First, calculate \( \frac{2.4}{0.90} \), and then use this to find the fraction.

Let me compute that for you.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can perform the calculation manually. Here's how you can do it:

1. Divide the given time by the half-life:  
   \( \frac{2.4}{0.90} \approx 2.67 \)
   
2. Use this value as the exponent in the formula:
   \[
   \left( \frac{1}{2} \right)^{2.67} \approx 0.157
   \]

So, the fraction of \( \text{N}_2\text{O}_5 \) remaining after 2.4 hours is approximately 0.157 (or 15.7%).

Would you like any further details or clarifications? Here are five related questions:

1. How do you calculate the decay constant for a first-order reaction?
2. What other types of reaction orders exist, and how do they differ from first-order reactions?
3. How can the integrated rate law be applied to reactions of different orders?
4. What practical applications involve half-life calculations in chemistry?
5. How do temperature and catalysts affect reaction rates?

**Tip:** The half-life of a first-order reaction is independent of the initial concentration, which is why it's commonly used in radioactive decay and similar processes.

For the first-order reaction 2N2O5 → 2N2O4 + O2 at a particular temperature, the half-life of N2O5 is 0.90 hr. What fraction of the initial concentration of N2O5 will remain after 2.4 hours?

Explore how to calculate the fraction of N2O5 remaining after 2.4 hours using the first-order reaction decay formula. This problem involves a half-life of 0.90 hours and provides a detailed solution to finding the remaining concentration.

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