Which of the following statements about substances X and Y is true, assuming both behave as ideal gases under identical conditions?

• A. At the same temperature and pressure, 1 mole of X has a lower volume than 1 mole of Y.
• B. At the same temperature and pressure, 1 mole of X occupies the same volume as 1 mole of Y.
• C. At the same temperature and pressure, 1 mole of X contains fewer molecules than 1 mole of Y.
• D. At the same temperature and pressure, 1 mole of X has a higher pressure than 1 mole of Y.

Answer: (B)

Verified step by step guidance

1. Recall the Ideal Gas Law, which states that for an ideal gas, the volume \(V\) is related to the number of moles \(n\), temperature \(T\), and pressure \(P\) by the equation: \[ V = \frac{nRT}{P} \] where \(R\) is the ideal gas constant.
2. Understand that under identical conditions of temperature \(T\) and pressure \(P\), and for the same number of moles \(n\), the volume \(V\) of any ideal gas will be the same regardless of the type of gas.
3. Recognize that 1 mole of any ideal gas contains the same number of molecules, given by Avogadro's number (\$6.022 \times 10^{23}$ molecules), so the number of molecules in 1 mole of X and 1 mole of Y is equal.
4. Note that since the volume depends only on \(n\), \(T\), and \(P\) (and \(R\) is a constant), the volume occupied by 1 mole of gas X and 1 mole of gas Y at the same temperature and pressure must be equal.
5. Conclude that statements claiming different volumes, different numbers of molecules, or different pressures for 1 mole of gases X and Y under identical conditions are incorrect, and the true statement is that 1 mole of X occupies the same volume as 1 mole of Y.