A certen amount of gas at `25^(@)C` and at a pressure of 0.80 atm is kept in a glass vessel. Suppose that the vessel can withstand a pressure of 2.0 atm. How high can you raise the temperature of the gas without bursting the vessel?

Options

A. `745^(@)C`
B. `472^(@)C`
C. `500^(@)C`
D. None of these

Explanation

To solve the problem, we will use the ideal gas law and the relationship between pressure and temperature. Here’s the step-by-step solution:

### Step 1: Identify the given values
- Initial temperature (T1) = 25°C
- Initial pressure (P1) = 0.80 atm
- Maximum pressure (P2) = 2.0 atm

### Step 2: Convert the initial temperature to Kelvin
To use the ideal gas law, we need to convert the temperature from Celsius to Kelvin:
\[ T1 = 25 + 273 = 298 \, K \]

### Step 3: Use the relationship between pressure and temperature
According to Gay-Lussac's law, the pressure of a gas is directly proportional to its temperature when the volume is constant. This can be expressed as:
\[ \frac{P1}{P2} = \frac{T1}{T2} \]

### Step 4: Rearrange the equation to solve for T2
We can rearrange the equation to find T2:
\[ T2 = T1 \times \frac{P2}{P1} \]

### Step 5: Substitute the known values into the equation
Now, substitute the values we have:
\[ T2 = 298 \, K \times \frac{2.0 \, atm}{0.80 \, atm} \]

### Step 6: Calculate T2
Calculating the right side:
\[ T2 = 298 \, K \times 2.5 = 745 \, K \]

### Step 7: Convert T2 back to Celsius
To find the temperature in Celsius, we convert it back from Kelvin:
\[ T2 = 745 \, K - 273 = 472 \, °C \]

### Conclusion
The maximum temperature to which the gas can be raised without bursting the vessel is **472°C**.

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