A

Step 1: Identify the initial conditions of the system. We have a container of volume 1 m³, divided into two equal parts. One part contains an ideal gas at 300 K, while the other part is a vacuum, meaning it contains no gas.

Step 2: Understand the process after removing the partition. When the partition is removed, the ideal gas expands freely into the vacuum. This process is known as free expansion.

Step 3: Analyze the thermodynamic principles involved. Since the system is thermally isolated, there is no heat exchange with the surroundings (Q = 0). In addition, in a free expansion, no work is done on or by the gas (W = 0).

Step 4: Apply the first law of thermodynamics, which states: \( \Delta U = Q - W \). In this case, we have \( \Delta U = 0 - 0 = 0 \), implying that the internal energy of the gas remains unchanged.

Step 5: For an ideal gas, the internal energy is related to temperature. Since the internal energy remains constant, so does the temperature.

Step 6: Therefore, the final temperature of the gas after the partition is removed and it expands into the vacuum will remain at 300 K.

Therefore, the final answer is 300 K.