Final answer:
Using Avogadro's Law and the reference molar mass of hydrogen, the relative molecular mass of gas A is determined to be 8 grams per mole and for gas B, it is 20 grams per mole.
Step-by-step explanation:
To calculate the relative molecular mass of gases A and B, we use the data for hydrogen as a reference because hydrogen has a known molar mass of approximately 2 grams per mole (since it's diatomic H2). If a cylinder filled with 50 grams of hydrogen, this is equivalent to 50 grams / 2 grams per mole = 25 moles of hydrogen.
Assuming ideal gas behavior and that equal volumes of gases at the same temperature and pressure contain an equal number of moles (Avogadro's Law), we can deduce that gases A and B are also in the same amount of moles since they occupy the same volume under the same conditions. Therefore, if 50 grams of hydrogen equals 25 moles, then 200 grams of gas A and 500 grams of gas B would also equal 25 moles each, given that the pressure and temperature are the same.
To find the molar mass of gas A, we take the mass of gas A (200 grams) and divide it by the number of moles (25 moles) to obtain the molar mass of gas A, which is 200 grams / 25 moles = 8 grams per mole. Similarly, the molar mass of gas B would be 500 grams / 25 moles = 20 grams per mole.
This gives us the relative molecular masses of A and B as 8 and 20, respectively.