Final answer:
To find the molecular formula of the metal chloride, the amount of chlorine in the vapor is calculated and converted to moles. The molar ratio of metal to chlorine is used to determine the molecular formula. The molecular formula of the metal chloride is MCl, where M represents the metal.
Step-by-step explanation:
To find the molecular formula of the metal chloride, we need to calculate the molar mass of chlorine and determine the ratio of metal to chlorine.
First, we calculate the amount of chlorine in the vapor by multiplying the percentage of chlorine by the weight of the vapor. This gives us 0.57 g x 0.55 = 0.3135 g chlorine.
Next, we convert the mass of chlorine to moles using the molar mass of chlorine (35.45 g/mol). This gives us 0.3135 g / 35.45 g/mol = 0.00883 mol chlorine.
Finally, we use the molar ratio of metal to chlorine to determine the molecular formula. Since the weight of the vapor is 100 mL at STP, we can assume the volume is also 100 mL. This corresponds to 0.100 L of vapor. Using the ideal gas law, we can calculate the number of moles of the metal chloride. Assuming the metal chloride is a diatomic gas, we can use the molar volume at STP (22.4 L/mol). This gives us 0.100 L / 22.4 L/mol = 0.00446 mol of the metal chloride. Since the molar ratio of metal to chlorine is 1:1, the molecular formula of the metal chloride is MCl, where M represents the metal.