Question

\(0.30 \mathrm{~g}\) of a volatile liquid displaces \(90.0 \mathrm{~cm}^{3}\) of air at STP in the Victor Meyer's method. The molecular mass of the liquid is: (a) \(54.44 \mathrm{~g}\) (b) \(34.64 \mathrm{~g}\) (c) \(64.76 \mathrm{~g}\) (d) \(74.66 \mathrm{~g}\)

Short answer

The molecular mass is 74.66 g/mol, so option (d) is correct.

Step-by-step solution

Understand the Problem

The problem provides the mass of a volatile liquid and the volume of air displaced by its vapor at Standard Temperature and Pressure (STP). We are asked to determine the molecular mass of the liquid.

Recall the Ideal Gas Law

The Ideal Gas Law, \( PV = nRT \), relates the pressure \( P \), volume \( V \), number of moles \( n \), gas constant \( R \), and temperature \( T \). At STP, \( P = 1 \) atm and \( T = 273.15 \) K. The volume of one mole of gas at STP is \( 22.4 \) L.

Convert Units

Convert the volume of air displaced from \( \text{cm}^3 \) to liters: \[ \text{Volume (L)} = \frac{90.0 \, \text{cm}^3}{1000} = 0.090 \, \text{L} \]

Calculate Moles of Gas

Using the molar volume at STP (22.4 L), calculate the moles of gas displaced: \[ n = \frac{V}{\text{Molar Volume}} = \frac{0.090}{22.4} \approx 0.0040179 \, \text{moles} \]

Calculate Molecular Mass

The molecular mass (M) is the mass of the liquid divided by the moles of gas: \[ M = \frac{\text{Mass of liquid}}{n} = \frac{0.30 \, \text{g}}{0.0040179} \approx 74.66 \, \text{g/mol} \]

Identify the Correct Answer

Compare the calculated molecular mass with the given options. The closest match is \( 74.66 \, \text{g/mol} \), corresponding to option (d).

Key concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental principle used in chemistry to relate different properties of gases. It is expressed by the equation:\[ PV = nRT \]Where:

• \( P \) represents pressure, measured in atmospheres (atm).
• \( V \) stands for volume, commonly measured in liters (L).
• \( n \) is the number of moles of gas.
• \( R \) is the universal gas constant \( (0.0821 \, \frac{L \cdot atm}{K \cdot mol}) \).
• \( T \) is the temperature, measured in Kelvin (K).

At Standard Temperature and Pressure (STP), which is 0°C (273.15 K) and 1 atm, these conditions are commonly used to simplify gas calculations. The ideal gas law helps us understand how gas will behave under these predictable conditions.

molecular mass calculation

Molecular mass calculation is a method to determine the mass of one molecule of a substance. In the case of gases, we rely on the relationship between the mass of the gas and the number of moles it contains. With the Ideal Gas Law and the concept of molar volume, we can find the molecular mass using the formula:\[ M = \frac{\text{Mass of the Gas}}{n} \]Where:

• \( M \) is the molecular mass, typically measured in grams per mole (g/mol).
• The mass of the gas is the known weight of the substance, usually given in grams.
• \( n \) is the number of moles of gas, derived from the volume of gas displaced and its corresponding moles.

By accurately measuring the gas's mass and using volume displacement, we can precisely calculate its molecular mass. This process is crucial for understanding the properties and behaviors of substances at a molecular level.

molar volume at STP

Molar volume at Standard Temperature and Pressure (STP) is the volume occupied by one mole of any gas under standard conditions. At STP, the pressure is 1 atm, and the temperature is 273.15 K (0°C). Under these conditions: - One mole of an ideal gas occupies a volume of 22.4 liters. Molar volume is a critical concept because it provides a standardized measure for comparing gases under consistent conditions. It helps chemists predict how gases will expand, compress, or displace one another when confined to the same pressure and temperature. This concept plays a major role in calculations involving gases, including determining molecular mass or conducting stoichiometric calculations.

volume displacement method

The volume displacement method is a practical technique used to determine the volume of gas released by a liquid or substance. This method is especially significant in the Victor Meyer's method, often used in the determination of molecular weights. Here is how it typically works:

• A known mass of a volatile liquid is turned to vapor through heating.
• The vapor displaces an equivalent volume of air.
• By measuring the volume of displaced air, the volume of the gas can be determined.

The displaced volume of gas (in this case, 90.0 cm³) allows us to calculate the number of moles of the gas using the molar volume at STP. This step is critical in analyzing and interpreting the compound's molecular mass or any other gas-related property. Such accurate methods ensure chemists can draw precise conclusions about substances based on experimental data.