Suppose there are two known compounds containing the generic elements X and Y. You have a 1.00-g sample of each compound. One sample contains 0.29 g of X and the other contains 0.38 g of X. Identify plausible sets of formulas for these two compounds. Check all that apply.

XY and X2Y
X4Y2 and X3Y
X2Y3 and X3Y3
X2Y and X3Y
X3Y and X4Y
XY and X3Y
XY3 and XY4

X3Y and X4Y2

X4Y2

X2Y
X2Y2

To determine the plausible sets of formulas for the two compounds, we need to consider the ratio of X to Y in each compound based on the given masses.

Compound 1:
- Contains 0.29 g of X and 0.71 g of Y.
- Possible formulas:
- XY (0.29 g X, 0.71 g Y)
- X3Y (0.87 g X, 0.13 g Y) -> Not plausible based on the given mass of X

Compound 2:
- Contains 0.38 g of X and 0.62 g of Y.
- Possible formulas:
- X4Y2 (1.52 g X, 1.24 g Y) -> Not plausible based on the given mass of X
- X2Y3 (0.76 g X, 1.86 g Y) -> Not plausible based on the given mass of X
- X4Y (0.38 g X, 0.62 g Y)
- X3Y (0.38 g X, 0.62 g Y)

Therefore, the plausible sets of formulas for these two compounds are:
1. XY and X3Y
2. XY and X3Y

To solve this problem, we need to compare the amount of each element (X and Y) in both compounds to identify plausible sets of formulas. Here's how we can do that:

Sample 1 contains 0.29 g of X:
- This indicates that there is more than one X atom present because 0.29 g is not an exact atomic mass.
- Therefore, XY and X2Y are plausible formulas since they contain at least one X atom.

Sample 2 contains 0.38 g of X:
- Similarly, this also indicates that there is more than one X atom present.
- X2Y3 and X3Y3 are plausible formulas since they contain at least one X atom.

Now, let's check each option:

XY and X2Y: These formulas match up with the observations made for both samples, so this is a plausible set of formulas.

X4Y2 and X3Y: While Sample 1 can be explained by X4Y2, Sample 2 cannot be explained by X3Y, so this set is not valid.

X2Y3 and X3Y3: Sample 2 can be explained by X2Y3 or X3Y3, so this is a valid set of formulas as well.

X2Y and X3Y: Sample 1 can be explained by X2Y, and Sample 2 can be explained by X3Y, so this is a plausible set of formulas.

X3Y and X4Y: Sample 1 can be explained by X3Y, but Sample 2 cannot be explained by X4Y, so this set is not valid.

XY and X3Y: Sample 1 can be explained by XY, and Sample 2 can be explained by X3Y, so this is a plausible set of formulas.

XY3 and XY4: None of the samples can be explained by either of these formulas, so this set is not valid.

Based on the above analysis, the plausible sets of formulas are: XY and X2Y, X2Y3 and X3Y3, X2Y and X3Y, and XY and X3Y.