The work done in open vessel at 300 K, when 56 g iron reacts with dilute HCI is

Options

A. 600 cal
B. 300 cal
C. 150 cal
D. 100 cal

Answer

To solve the problem of calculating the work done when 56 g of iron reacts with dilute HCl at 300 K, we can follow these steps:

### Step 1: Calculate the number of moles of iron
The molar mass of iron (Fe) is approximately 56 g/mol.

Using the formula:
\[ n = \frac{\text{mass}}{\text{molar mass}} \]
Substituting the values:
\[ n = \frac{56 \text{ g}}{56 \text{ g/mol}} = 1 \text{ mole} \]

### Step 2: Use the ideal gas law to find the work done
The work done (W) in a chemical reaction at constant pressure can be calculated using the formula:
\[ W = -P \Delta V \]
However, for reactions involving gases, we can also use the ideal gas equation:
\[ PV = nRT \]
Where:
- \(P\) = pressure
- \(V\) = volume
- \(n\) = number of moles
- \(R\) = ideal gas constant
- \(T\) = temperature in Kelvin

### Step 3: Substitute values into the work done equation
For this problem, we can express the work done as:
\[ W = nRT \]
Given:
- \(n = 1 \text{ mole}\)
- \(R = 2 \text{ cal/K mole}\) (since the answer is required in calories)
- \(T = 300 \text{ K}\)

Substituting these values:
\[ W = 1 \text{ mole} \times 2 \text{ cal/K mole} \times 300 \text{ K} \]
\[ W = 600 \text{ calories} \]

### Conclusion
The work done when 56 g of iron reacts with dilute HCl at 300 K is **600 calories**.