A student forgot to add the reaction mixture to the round bottomed open flask at `27^(@) C` and put it on the flame After a lapse of time he realized his mistake using a pyrometer he found the temperature of the flask was `477^(@)C` What fraction of air would have been expelled out ? .

Explanation

To solve the problem of how much air was expelled from the flask when it was heated from 27°C to 477°C, we can use the ideal gas law and the relationship between volume and temperature. Here’s a step-by-step solution:

### Step 1: Convert Temperatures to Kelvin
First, we need to convert the given temperatures from Celsius to Kelvin.

- Initial temperature (T1) = 27°C = 27 + 273 = 300 K
- Final temperature (T2) = 477°C = 477 + 273 = 750 K

### Step 2: Set Up the Volume-Temperature Relationship
According to Charles's Law, the volume of a gas is directly proportional to its temperature (in Kelvin) when pressure is constant. This can be expressed as:

\[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \]

Where:
- \( V_1 \) is the initial volume of the air in the flask.
- \( V_2 \) is the final volume of the air after heating.

### Step 3: Solve for Final Volume (V2)
Rearranging the equation to solve for \( V_2 \):

\[ V_2 = V_1 \cdot \frac{T_2}{T_1} \]

Substituting the values:

\[ V_2 = V_1 \cdot \frac{750}{300} = V_1 \cdot 2.5 \]

### Step 4: Calculate the Volume of Air Expelled
The volume of air expelled can be calculated as the difference between the final volume and the initial volume:

\[ \text{Volume expelled} = V_2 - V_1 \]

Substituting \( V_2 \):

\[ \text{Volume expelled} = (V_1 \cdot 2.5) - V_1 = V_1 \cdot (2.5 - 1) = V_1 \cdot 1.5 \]

### Step 5: Calculate the Fraction of Air Expelled
To find the fraction of air that was expelled, we divide the volume expelled by the final volume:

\[ \text{Fraction expelled} = \frac{\text{Volume expelled}}{V_2} = \frac{V_1 \cdot 1.5}{V_1 \cdot 2.5} = \frac{1.5}{2.5} \]

This simplifies to:

\[ \text{Fraction expelled} = \frac{3}{5} \]

### Conclusion
The fraction of air that would have been expelled from the flask is \( \frac{3}{5} \).

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