Question

A chloride of a metal (M) has \(65.5 \%\) of chlorine. \(100 \mathrm{ml}\) of vapour of the chloride of metal at STP weighs \(0.72 \mathrm{~g}\). The molecular formula of this metal chloride is: (a) \(\mathrm{MCl}_{3}\) (b) \(\mathrm{MCl}_{4}\) (c) \(\mathrm{M}_{2} \mathrm{Cl}_{3}\) (d) \(\mathrm{MCl}_{5}\)

Short answer

The molecular formula is \(\mathrm{MCl}_3\).

Step-by-step solution

Calculate Molar Volume at STP

At standard temperature and pressure (STP), the volume occupied by 1 mole of any gas is known to be 22.4 liters. Therefore, 100 ml of gas can be converted to liters by dividing by 1000, which gives us 0.1 liters. The key point here is that the given volume, 0.1 liters, is a fraction of the molar volume.

Calculate the Molar Mass of the Chloride

Given that 100 ml (0.1 liters) of the vapor weighs 0.72 grams, we can find the molar mass of the chloride. Since 22.4 liters (or 22400 ml) equals the molar volume, the molar mass can be calculated as follows: \[ \text{Molar mass} = \left( \frac{22.4 \text{ liters}}{0.1 \text{ liters}} \right) \times 0.72 \text{ g} \approx 161 \text{ g/mol}. \]

Key concepts

Molar Mass Calculation

Molar mass is a fundamental concept in chemistry, helping us understand the mass of a mole of a given compound. To compute the molar mass of a substance, we first need to determine how much one mole of the compound weighs. In our example, we start with 0.1 liters of chlorinated metal gas weighing 0.72 grams. At standard temperature and pressure (STP), 1 mole of any gas occupies 22.4 liters.
Thus, 0.1 liters of gas is merely a portion of a full mole, equating to part of the 22.4-liter molar volume.

• Given Weight: 0.72 grams for 0.1 liters of the gas
• Molar Volume at STP: 22.4 liters
• Calculation: To find the molar mass, use the conversion: \[\text{Molar mass} = \left(\frac{22.4 \text{ liters}}{0.1 \text{ liters}}\right) \times 0.72 \text{ g} \approx 161 \text{ g/mol}\]

This formula helps convert the sample gas's weight into a weight per mole format, essential for identifying the molecular formula.

Chloride Percentage Composition

Understanding the percentage composition of elements in a compound is crucial for determining its molecular formula. This method involves determining the weight percentage of each element within a compound. In the problem, the metal chloride contains 65.5% chlorine.
By recognizing this percentage, we gather insights into the compound's elemental structure.

• Percentage of Chlorine: 65.5%
• Contribution Towards Detection: The percentage allows the breakdown of the metal chloride's components, thus guiding us toward the molecular formula.

Knowing the percentage composition is paramount to distinguishing the exact elements in the compound. It helps in verifying the empirical formula, which can then be used to compute the exact molecular formula.

Gas Molar Volume at STP

The concept of molar volume refers to the volume occupied by one mole of a substance at a given temperature and pressure. At STP, which is 0°C (273.15 K) and 1 atmosphere pressure, a mole of any ideal gas fills 22.4 liters. This baseline allows easy conversions from experimental values to ideal moles.
When given any gas volume measurement, it's vital to convert it to liters if not already done, so as to align with the molar volume at STP.

• Standard Conversion: 1 mole = 22.4 liters at STP
• Application of STP Values: By using this constant, we can deduce unknown information like molar mass or the identification of a specific compound.

Utilizing this constant helps simplify calculations and reinforce the understanding of fundamental gas laws in chemistry, providing a solid foundation for further studies.