Final answer:
After converting the mass of sulfur and oxygen to moles using their relative atomic masses, the simplest whole number ratio of moles reveals that the formula for the mystery gas is SO2. Therefore, the value of x is 2.
Step-by-step explanation:
Relative atomic mass and understanding stoichiometry are crucial in answering this question. Since the mystery gas contains equal masses of sulfur and oxygen, and we are given the relative atomic masses of both elements (sulfur = 32, oxygen = 16), we can determine the molar ratio of sulfur to oxygen in the compound. As 2.7 mg of sulfur is equal to 2.7/32 moles and 2.7 mg of oxygen is equal to 2.7/16 moles, we use the ratio of the moles of oxygen to sulfur to find the empirical formula of the compound, which in turn reveals the value of x in the formula.
Firstly, convert the mass to moles for each element: for sulfur, 2.7 mg / 32 = 0.084375 moles, and for oxygen, 2.7 mg / 16 = 0.16875 moles. Now, we determine the simplest whole number ratio by dividing each mole value by the smaller of the two: for sulfur and oxygen, 0.084375/0.084375 = 1 and 0.16875/0.084375 = 2 respectively. Thus, the value of x in the compound's formula, which is SXOx, is 2.
In conclusion, the formula of the compound is SO2, indicating that the value of x is 2.