The van der Waals constant for hydrogen is `0.025 N-m^(4) //m o l^(2)`. What is the internal pressure of hydrogen if `V = 22.4 xx 10^(-3) m^(3) ` ?

Explanation

To find the internal pressure of hydrogen using the given van der Waals constant and volume, we can follow these steps:

### Step 1: Identify the given values
- Van der Waals constant for hydrogen, \( a = 0.025 \, \text{N m}^4/\text{mol}^2 \)
- Volume, \( V = 22.4 \times 10^{-3} \, \text{m}^3 \)

### Step 2: Use the formula for internal pressure
The internal pressure \( P \) can be calculated using the formula:
\[ P = \frac{a}{V^2} \]

### Step 3: Calculate \( V^2 \)
First, we need to calculate \( V^2 \):
\[ V^2 = (22.4 \times 10^{-3})^2 = 0.00050276 \, \text{m}^6 \]

### Step 4: Substitute the values into the formula
Now, substitute the values of \( a \) and \( V^2 \) into the formula for internal pressure:
\[ P = \frac{0.025}{0.00050276} \]

### Step 5: Perform the calculation
Calculating the above expression:
\[ P \approx 49.82 \, \text{N/m}^2 \]

### Final Answer
The internal pressure of hydrogen is approximately \( 49.82 \, \text{N/m}^2 \).

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