Question

\(116 \mathrm{mg}\) of a compound on vapourisation in a Victor Meyer's apparatus displaces \(44.8 \mathrm{~mL}\) of air measured at STP. The molecular mass of the compound is: (a) \(58 \mathrm{~g}\) (b) \(48 \mathrm{~g}\) (c) \(116 \mathrm{~g}\) (d) \(44.8 \mathrm{~g}\)

Short answer

The molecular mass of the compound is 58 g (option a).

Step-by-step solution

Understanding the Problem

We are asked to find the molecular mass of a compound that has displaced a certain volume of air at standard temperature and pressure (STP). We know that 1 mole of a gas occupies 22.4 L at STP.

Convert mL to L

Convert the displaced volume from milliliters to liters to use the relation for molar volume. Given that the displaced volume is 44.8 mL, thus\[44.8 \text{ mL} = 0.0448 \text{ L}\]

Calculate Moles of the Displaced Air

Use the relationship that 1 mole of gas at STP occupies 22.4 L to find the moles of air displaced.\[\text{Moles of air} = \frac{\text{Volume of air displaced (L)}}{\text{Volume of 1 mole of gas at STP (22.4 L)}}\]\[= \frac{0.0448}{22.4} = 0.002 \text{ moles}\]

Determine Molar Mass

We know that 116 mg of compound corresponds to the calculated moles of displaced air. Convert 116 mg to grams:\[116 \text{ mg} = 0.116 \text{ g}\]The molar mass of the compound is given by:\[\text{Molar Mass} = \frac{\text{Mass of compound (g)}}{\text{Moles of gas}}\]\[= \frac{0.116}{0.002} = 58 \text{ g/mol}\]

Select the Correct Answer

From the calculations, the molecular mass of the compound is 58 g/mol. Therefore, the correct choice is (a) 58 g.

Key concepts

Victor Meyer's Apparatus

Victor Meyer's apparatus is a classic tool used in chemistry to determine the molecular masses of volatile substances. This apparatus works by measuring the amount of vapor displaced when a substance is vaporized, which can help in determining molar mass. The vaporization process occurs in a heated chamber, where the compound quickly changes from liquid or solid to gas.

The resulting vapor then displaces an equal volume of air, and this change is measured outside the chamber using this ingenious apparatus. By capturing the volume displaced, one can use calculations at standard temperature and pressure (STP) to determine the molecular mass. Using Victor Meyer's apparatus simplifies calculations by exploiting the direct relationship between gas volume and the amount of substance.

Molar Volume

Molar volume is a concept that refers to the volume occupied by one mole of a substance at a given temperature and pressure. At standard temperature and pressure (STP), which is 0 degrees Celsius and 1 atmosphere of pressure, one mole of any ideal gas occupies a volume of 22.4 liters.

This constant allows chemists to easily relate gases' physical properties to their chemical amounts. For instance, knowing that a mole of gas takes up 22.4 liters at STP allows us to calculate the amount of substance in moles based on the volume it occupies. This concept is pivotal in solving many problems in chemistry, such as determining molecular mass, as it lets you work backwards from a measured volume to the number of moles present.

Moles at STP

Understanding how to calculate moles at standard temperature and pressure (STP) is a fundamental skill in chemistry. To determine the number of moles of a gas at STP, you divide the gas's volume by the molar volume of 22.4 liters. For example, if you have a gas volume of 44.8 milliliters, you first need to convert this volume into liters so you can apply the molar volume relationship.

The step-by-step process involves calculating

• First, convert mL to liters: 44.8 mL = 0.0448 L
• Use the formula: moles = volume (L) / molar volume (L/mol)
• Conclusion: moles = 0.0448 L / 22.4 L/mol = 0.002 moles

This straightforward calculation allows you to move from a measurable physical property (volume) to the chemical concept of moles.

Unit Conversions

Unit conversions are essential in chemistry for ensuring that calculations are carried out with consistent units of measurement. Conversion of units helps in translating real-world measurements into relatable chemical quantities.

Examples of unit conversions commonly seen include:

• Milliliters to Liters: Often necessary for applying molar volume concepts, as seen with the conversion from 44.8 mL to 0.0448 L.
• Milligrams to Grams: Important for mass calculations, such as converting 116 mg to 0.116 g.
• Grams to Moles: Essential for determining molar mass, enabling the use of the formula: molar mass = mass/moles.

By mastering these conversions, students can tackle a wide range of problems in chemistry with greater ease and precision.