Calculate the work done when 112 g iron reacts with dilute HCl at 300 K. The reaction is carried out in an open container
(At mass of Fe = 56)

Options

A. 600 cal
B. 300 cal
C. 200 cal
D. -1200 cal

Answer

To calculate the work done when 112 g of iron reacts with dilute HCl at 300 K in an open container, we can follow these steps:

### Step 1: Calculate the number of moles of iron (Fe)
The number of moles (n) can be calculated using the formula:
\[ n = \frac{\text{mass of substance}}{\text{molar mass}} \]
Given:
- Mass of iron (Fe) = 112 g
- Molar mass of iron (Fe) = 56 g/mol

Substituting the values:
\[ n = \frac{112 \, \text{g}}{56 \, \text{g/mol}} = 2 \, \text{mol} \]

### Step 2: Calculate the work done (W)
The work done in a chemical reaction at constant pressure can be calculated using the formula:
\[ W = -P \Delta V \]
However, we can relate this to the ideal gas law:
\[ PV = nRT \]
Thus, the work done can be expressed as:
\[ W = -nRT \]
Where:
- \( R = 8.314 \, \text{J/(mol K)} \)
- \( T = 300 \, \text{K} \)

### Step 3: Substitute the values into the work formula
Now substituting the values of \( n \), \( R \), and \( T \):
\[ W = -2 \, \text{mol} \times 8.314 \, \text{J/(mol K)} \times 300 \, \text{K} \]
Calculating this gives:
\[ W = -2 \times 8.314 \times 300 = -4988.4 \, \text{J} \]

### Step 4: Convert Joules to calories
To convert Joules to calories, we use the conversion factor:
\[ 1 \, \text{cal} = 4.184 \, \text{J} \]
Thus:
\[ W = \frac{-4988.4 \, \text{J}}{4.184 \, \text{J/cal}} \approx -1193.3 \, \text{cal} \]

### Step 5: Round to significant figures
Rounding to significant figures, we can express the work done as approximately:
\[ W \approx -1200 \, \text{cal} \]

### Final Answer
The work done when 112 g of iron reacts with dilute HCl at 300 K is approximately \(-1200 \, \text{cal}\).

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