Final answer:
By applying Avogadro's principle under constant temperature and pressure conditions, we find that the contracted container containing the 1.25 original moles plus the additional gas added equals 2.00 moles of gas.
Step-by-step explanation:
To solve the problem regarding the flexible container holding gas, we need to apply the Ideal Gas Law, which states that PV=nRT. However, since we are dealing with the same gas under constant temperature and pressure conditions (as we added more gas without changing those conditions), we can simplify this application to Boyle's law and Avogadro's principle combined, which relate volume and moles directly since pressure and temperature are held constant.
In this case, the volume of the container decreases from 25.0 L to 10.0 L as more gas is added. We are told that the container originally had 1.25 moles of gas. The moles of gas are directly proportional to the volume, so we can set up the following ratio:
1.25 moles / 25.0 L = x moles / 10.0 L
Solving for x gives:
x = (1.25 moles * 10.0 L) / 25.0 L
x = 0.50 moles
This calculation tells us how many moles would occupy 10.0 L at the original concentration. Since the container is now at 10.0 L but started with 1.25 moles, the additional gas added must have made up the difference between 0.50 moles and 1.25 moles.
Therefore, the number of moles added is:
1.25 moles - 0.50 moles = 0.75 moles
To find the total moles in the contracted container, we simply add the original moles to the moles added:
1.25 moles + 0.75 moles = 2.00 moles
The contracted container thus contains 2.00 moles of gas.