Question

A metal chloride contains 55% by mass of chlorine. 100 mL of vapours gives 0.57 gm of chlorine at STP. Calculate the molecular mass of metal chloride. (Nearest integer)

Answer 1

We are given that a metal chloride contains 55% by mass of chlorine. 100 mL of vapors gives 0.57 gm of chlorine at STP. We are required to calculate the molecular mass of the metal chloride. 

Step 1: Use the given data to find the moles of chlorine gas (Cl₂) at STP.
At STP (Standard Temperature and Pressure), 1 mole of any gas occupies 22.4 liters (22400 mL). Thus, the volume of chlorine gas is 100 mL, which corresponds to: \[ \text{Moles of Cl}_2 = \frac{\text{Volume}}{\text{Molar Volume}} = \frac{100}{22400} = 0.004464 \text{ moles of Cl}_2. \] Since chlorine (Cl₂) consists of two chlorine atoms, the moles of chlorine atoms will be: \[ \text{Moles of Cl} = 2 \times \text{Moles of Cl}_2 = 2 \times 0.004464 = 0.008928 \text{ moles of Cl}. \] 

Step 2: Calculate the mass of chlorine atoms.
We are told that the mass of chlorine obtained is 0.57 gm, which corresponds to 0.008928 moles of chlorine. The molar mass of chlorine (Cl) is 35.5 g/mol. Hence, the mass of chlorine (0.008928 moles) is: \[ \text{Mass of Cl} = 0.008928 \times 35.5 = 0.317 g. \] 

Step 3: Determine the total mass of the metal chloride.
Since the metal chloride contains 55% chlorine by mass, we can write: \[ \text{Mass of metal chloride} = \frac{\text{Mass of chlorine}}{55\%} = \frac{0.57}{0.55} = 1.036 \text{ grams}. \] 

Step 4: Calculate the molecular mass of the metal chloride.
The molecular mass of the metal chloride is the sum of the metal's atomic mass and the chlorine's atomic mass. Let \( M \) be the atomic mass of the metal. We know the mass of chlorine is 0.57 g, and the mass of the chloride is 1.036 g, so the mass of the metal in the chloride is: \[ \text{Mass of metal} = 1.036 - 0.57 = 0.466 \text{ grams}. \] Therefore, the molecular mass of the metal chloride is: \[ \text{Molecular mass} = M + 35.5. \] Now, to find the atomic mass of the metal, we use the mass of metal (0.466 g) and the number of moles of chlorine (0.008928 moles of Cl). The number of moles of metal in the chloride is the same as the number of moles of chlorine since it's a 1:1 ratio in the metal chloride formula. \[ \text{Moles of metal} = 0.008928 \text{ moles}. \] Therefore, the atomic mass of the metal \( M \) is: \[ M = \frac{0.466}{0.008928} \approx 52.2. \] 

Step 5: Calculate the molecular mass.
The molecular mass of the metal chloride is: \[ \text{Molecular mass} = 52.2 + 35.5 = 87.7. \] The nearest integer is 88. 

Final Answer:
The molecular mass of the metal chloride is approximately 88.