At `27^(@)C` it was observed in the hydrogenation of a reaction, the pressure of `H_(2)(g)` decreases form `10 atm` to `2 atm` in `10 min`. Calculate the rate of reaction in `M min^(-1)` (Given `R = 0.08 L atm K^(-1) mol^(-1)`)

Options

A. `0.02`
B. `0.03`
C. `0.04`
D. `0.05`

Explanation

To calculate the rate of reaction in M min^(-1) for the hydrogenation reaction, we will follow these steps:

### Step 1: Calculate the change in pressure of H₂
The initial pressure (P₁) of H₂ is 10 atm, and the final pressure (P₂) is 2 atm.

\[ \Delta P = P_1 - P_2 = 10 \, \text{atm} - 2 \, \text{atm} = 8 \, \text{atm} \]

### Step 2: Calculate the rate of reaction in atm/min
The time taken for this change is 10 minutes. The rate of reaction (R) can be calculated as:

\[ R = \frac{\Delta P}{\Delta t} = \frac{8 \, \text{atm}}{10 \, \text{min}} = 0.8 \, \text{atm/min} \]

### Step 3: Use the ideal gas law to convert atm/min to mol/min
The ideal gas law is given by:

\[ PV = nRT \]

From this, we can express the number of moles (n) per unit volume (V):

\[ \frac{n}{V} = \frac{P}{RT} \]

Rearranging gives us:

\[ n = \frac{PV}{RT} \]

### Step 4: Calculate the temperature in Kelvin
The temperature is given as 27°C. To convert this to Kelvin:

\[ T = 27 + 273 = 300 \, \text{K} \]

### Step 5: Substitute values into the equation
We know R = 0.08 L atm K^(-1) mol^(-1), and we have already calculated the pressure change rate (0.8 atm/min). To find the rate in moles per minute, we need to express it in terms of moles:

\[ \text{Rate in moles/min} = \frac{0.8 \, \text{atm/min}}{R \cdot T} \]

Substituting the values:

\[ \text{Rate in moles/min} = \frac{0.8 \, \text{atm/min}}{0.08 \, \text{L atm K}^{-1} \text{mol}^{-1} \cdot 300 \, \text{K}} \]

### Step 6: Calculate the final rate
Calculating the denominator:

\[ 0.08 \cdot 300 = 24 \, \text{L atm mol}^{-1} \]

Now substituting back:

\[ \text{Rate in moles/min} = \frac{0.8}{24} = 0.0333 \, \text{mol/min} \]

### Final Answer
The rate of reaction is approximately:

\[ \text{Rate} = 0.033 \, \text{mol/min} \]