To determine the temperature at which a 5L balloon will expand to a volume of 12.5L, we can use Charles's Law, which states that for a fixed amount of gas at constant pressure, the volume is directly proportional to its absolute temperature (measured in Kelvin):

$\frac{V_1}{T_1} = \frac{V_2}{T_2}$

Given:

• Initial volume, $V_1 = 5 \, \text{L}$
• Final volume, $V_2 = 12.5 \, \text{L}$
• Initial temperature, $T_1 = 0^\circ \text{C} = 273.15 \, \text{K}$

Step 1: Rearrange Charles's Law to solve for $T_2$

$T_2 = \frac{V_2 \cdot T_1}{V_1}$

Step 2: Substitute the known values

$T_2 = \frac{12.5 \, \text{L} \times 273.15 \, \text{K}}{5 \, \text{L}}$

$T_2 = \frac{3414.375}{5} = 682.875 \, \text{K}$

Step 3: Convert $T_2$ from Kelvin to Celsius

$T_2 (\text{°C}) = 682.875 \, \text{K} - 273.15 = 409.725 \, \text{°C}$

Conclusion

The balloon must be heated to approximately 409.73°C for its volume to expand from 5L to 12.5L at constant pressure.

Would you like additional details on this calculation or further assistance?

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Here are some related questions to consider:

1. How does pressure affect the final volume in similar gas law calculations?
2. What happens to the balloon volume if the temperature remains constant but pressure changes?
3. How would adding more gas to the balloon impact the temperature needed for expansion?
4. Can this expansion be achieved in a real-world setting without causing the balloon to burst?
5. How would Charles’s Law apply if this were a different gas, such as a real gas like CO₂?

Tip: Remember to always convert Celsius to Kelvin when using gas law equations, as Kelvin is the standard absolute temperature scale for these calculations.