Given Information:
- Pressure of gas X (1 g) at 300K = 2 ATM
- Pressure of gas X (1 g) + gas Y (2 g) at 300K = 3 ATM

To find:
The relationship between the molar mass of gas X and gas Y.

Solution:

1. Calculate the number of moles of gas X:
- The molar mass of gas X can be calculated using the ideal gas equation: PV = nRT
- Rearranging the equation, we have n = PV / RT, where P is the pressure, V is the volume, R is the ideal gas constant, and T is the temperature.
- Here, the pressure (P) is given as 2 ATM, the volume (V) is not mentioned but remains constant, the temperature (T) is given as 300K, and R is a constant.
- Therefore, we can calculate the number of moles of gas X present using the given information.

2. Calculate the number of moles of gas Y:
- Similar to gas X, we can calculate the number of moles of gas Y using the ideal gas equation.
- Here, the pressure (P) is given as 3 ATM (after introducing gas Y), the volume (V) is the same as before, the temperature (T) is given as 300K, and R is a constant.
- Therefore, we can calculate the number of moles of gas Y present using the given information.

3. Determine the relationship between the molar masses of X and Y:
- The molar mass of a substance is the mass of one mole of that substance.
- To find the relationship between the molar masses of gas X and gas Y, we need to compare the number of moles of each gas.
- Let's assume the molar mass of gas X is MX and the molar mass of gas Y is MY.
- From step 1, we know that the number of moles of gas X is equal to the mass of gas X divided by its molar mass, which can be written as nX = mX / MX.
- From step 2, we know that the number of moles of gas Y is equal to the mass of gas Y divided by its molar mass, which can be written as nY = mY / MY.
- We can equate the number of moles of gas X and gas Y since they are present in the same vessel at the same temperature: nX = nY.
- Substituting the expressions for the number of moles from step 1 and step 2, we get mX / MX = mY / MY.
- Cross-multiplying the equation, we get mX * MY = mY * MX.
- Simplifying the equation, we get MX / MY = mY / mX.

Conclusion:
The relationship between the molar mass of gas X (MX) and gas Y (MY) is MX / MY = mY / mX.

Under the same condition of temp. and volume. The pressure will be proportion to their moles. Initially pressure Pa=2 which is proportion to 1/Ma( here 1 is given mass) ....1Final pressure Pb=3=1/Ma+2/Mb [total moles] ..2Divide eq 1 by eq 22/3=1/Ma[(Ma xMb) /(Mb+2Ma)After Simplifying Ma/Mb=1/4Hope that this should be the answer...