Final answer:
Using Charles's Law, we can determine that the new volume of methane gas when cooled from 51 °C to 24 °C at constant pressure is approximately 11.3 liters.
Step-by-step explanation:
The question is asking how the volume of a methane gas sample changes when it is cooled at constant pressure from 51 °C to 24 °C. This scenario is primarily an application of Charles's Law, which states that the volume of a gas is directly proportional to its temperature (in Kelvin) when the pressure and the number of moles are kept constant. To find the new volume, we'll use the formula:
V1 / T1 = V2 / T2,
where V1 is the initial volume, T1 is the initial temperature in Kelvin, V2 is the final volume, and T2 is the final temperature in Kelvin. Remember to convert the Celsius temperatures to Kelvin by adding 273.15. We can then rearrange the formula to solve for V2:
V2 = (V1 × T2) / T1
Calculating the values, we get:
V2 = (12.4 L × (24 + 273.15) K) / (51 + 273.15) K
V2 = (12.4 L × 297.15 K) / 324.15 K
V2 ≈ 11.3 liters
Therefore, the volume of the gas sample when cooled to 24 °C at constant pressure will be approximately 11.3 liters.