Final answer:
To determine the new volume of the gas at 450 K and 2.4 moles from an initial state of 250 K and 3 moles in a 500 mL container, we used the combined gas law and found that the final volume would be 720 mL.
Step-by-step explanation:
Given a gas sample originally at 250 K and 3 moles in a 500 mL container, to find the new volume of the gas when the moles change to 2.4 and the temperature changes to 450 K at constant pressure, we can use the combined gas law as follows: V1/T1 = V2/T2 (where V1 and T1 are the initial volume and temperature, and V2 and T2 are the final volume and temperature, respectively).
We start by calculating the initial conditions in terms of moles and volume to equalize the molar amounts:
- V1 for the initial 3 moles is 500 mL (given).
- To find the V1 for 2.4 moles at the initial temperature (250 K), we use direct proportion since the pressure is constant: V1 = 500 mL * (2.4 moles / 3 moles) = 400 mL
Now we apply the combined gas law to find the new volume at the final temperature (450 K):
- (400 mL / 250 K) = V2 / 450 K
- V2 = (400 mL * 450 K) / 250 K
- V2 = 720 mL
Thus, the final volume of the gas, when the temperature is raised to 450 K and the moles are changed to 2.4 moles while keeping the pressure constant, would be 720 mL.