The temperature of 4.0 mol of an ideal gas occupying `5dm^(3)` at 3.32 bar `(R="0.083 bar dm"^(3)K^(-1)"mol"^(-1))` is `nxx10K`. The value of n is

Explanation

To find the value of \( n \) in the temperature expression \( n \times 10^k \) for the given ideal gas, we will use the Ideal Gas Law equation:

### Step-by-Step Solution:

1. **Identify Given Values:**
- Number of moles, \( n = 4.0 \, \text{mol} \)
- Volume, \( V = 5 \, \text{dm}^3 \)
- Pressure, \( P = 3.32 \, \text{bar} \)
- Ideal Gas Constant, \( R = 0.083 \, \text{bar} \, \text{dm}^3 \, \text{K}^{-1} \, \text{mol}^{-1} \)

2. **Use the Ideal Gas Law:**
The Ideal Gas Law is given by the equation:
\[ PV = nRT \]
Rearranging the equation to solve for temperature \( T \):
\[ T = \frac{PV}{nR} \]

3. **Substitute the Known Values:**
Now, substitute the values into the equation:
\[ T = \frac{(3.32 \, \text{bar}) \times (5 \, \text{dm}^3)}{(4.0 \, \text{mol}) \times (0.083 \, \text{bar} \, \text{dm}^3 \, \text{K}^{-1} \, \text{mol}^{-1})} \]

4. **Calculate the Numerator:**
Calculate the numerator:
\[ 3.32 \times 5 = 16.6 \, \text{bar} \, \text{dm}^3 \]

5. **Calculate the Denominator:**
Calculate the denominator:
\[ 4.0 \times 0.083 = 0.332 \, \text{bar} \, \text{dm}^3 \, \text{K}^{-1} \, \text{mol}^{-1} \]

6. **Calculate Temperature \( T \):**
Now, divide the numerator by the denominator:
\[ T = \frac{16.6}{0.332} \approx 50 \, \text{K} \]

7. **Express Temperature in the Required Form:**
We know that the temperature can be expressed as \( T = n \times 10^k \). Here, we have:
\[ 50 \, \text{K} = n \times 10^1 \]
This implies:
\[ n = \frac{50}{10} = 5 \]

### Final Answer:
The value of \( n \) is \( 5 \).

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