A metal chloride contains 55.0% of chlorine by weight. 100 mL vapours of the metal chloride at STP weigh 0.57g. The molecular formula of the metal chloride is (Given: Atomic mass of chlorine is 35.5u)
 

We are given that a metal chloride contains 55.0% chlorine by weight. We need to find the molecular formula of the metal chloride. To do this, we can use the following data provided:

• The chlorine content is 55.0% by weight.
• The volume of the vapor is 100 mL at STP, and it weighs 0.57 g.
• The atomic mass of chlorine (Cl) is 35.5 g/mol.

Step 1: Determine the mass of chlorine in the given sample

We know that 55% of the metal chloride by weight is chlorine. Therefore, the mass of chlorine in 0.57 g of the metal chloride can be calculated as:

        Mass of chlorine = 55.0% × 0.57 g = 0.3135 g

Step 2: Determine the moles of chlorine in the sample

Using the atomic mass of chlorine (35.5 g/mol), we can calculate the number of moles of chlorine in the 0.3135 g of chlorine:

        Moles of chlorine = Mass of chlorine / Atomic mass of chlorine
                           = 0.3135 g / 35.5 g/mol
                           ≈ 0.00883 mol

Step 3: Determine the volume of the sample in moles

At STP (Standard Temperature and Pressure), 1 mole of any gas occupies 22.4 liters or 22,400 mL. Therefore, we can find the number of moles in the 100 mL of metal chloride vapor as follows:

        Moles of metal chloride = Volume of vapor / Molar volume
                                 = 100 mL / 22400 mL/mol
                                 ≈ 0.00446 mol

Step 4: Calculate the molecular formula of the metal chloride

Since the metal chloride contains chlorine (Cl) and a metal (M), we can use the ratio of the number of moles of chlorine to the total moles in the sample to deduce the formula. The number of moles of the metal chloride is 0.00446 mol, and the moles of chlorine is 0.00883 mol. The metal chloride formula involves a simple ratio between the metal and chlorine atoms. By calculating the ratio of chlorine to metal, we find:

        Moles of chlorine per mole of metal chloride ≈ 2