Question

A 132.10 mL glass vessel weighs 56.1035 g when evacuated and \(56.2445 \mathrm{g}\) when filled with the gaseous hydrocarbon acetylene at \(749.3 \mathrm{mmHg}\) and \(20.02^{\circ} \mathrm{C}\) What is the molar mass of acetylene? What conclusion can you draw about its molecular formula?

Short answer

The molar mass of acetylene is approximately 26.1 g/mol, which indicates that its molecular formula is \(C_2H_2\).

Step-by-step solution

Calculate Mass of Gas

First, calculate the mass of the gas in the container by subtracting the weight of the evacuated container from the weight of the container filled with acetylene: Mass (gas) = \(56.2445g - 56.1035g = 0.1410g\).

Convert Units

Convert pressure from mmHg to atm: \[Pressure (P) = \frac{749.3mmHg}{760 mmHg/atm} = 0.9859 atm\]. Convert temperature from Celsius to Kelvin: \[Temperature (T) = 20.02° C + 273.15 = 293.17 K\].

Calculate Moles

Use the Ideal Gas Law formula to calculate the number of moles (n). Rearrange the formula to calculate n as follows: n = PV/RT. \[n (acetylene) = \frac{(0.9859 atm)(0.13210 L)}{(0.0821 L.atm/mol.K)(293.17 K)} = 0.0054 mol\]

Calculate Molar Mass

Next, find the molar mass by dividing the mass by the number of moles. \[Molar mass = \frac{0.1410g}{0.0054 mol} = 26.1 g/mol \]

Determine Molecular Formula

The molecular formula of a compound is determined by the molar mass. The molar mass of acetylene (\(C_2H_2\)) is approximately 26 g/mol, so the empirical formula must be \(C_2H_2\)

Key concepts

Ideal Gas Law and Its Application

The Ideal Gas Law is a fundamental equation used in chemistry to relate the pressure, volume, temperature, and number of moles of a gas. The equation is given by\[ PV = nRT \]where:

• \( P \) is the pressure of the gas.
• \( V \) is the volume occupied by the gas.
• \( n \) is the number of moles of the gas.
• \( R \) is the ideal gas constant, commonly \( 0.0821 \) L·atm/mol·K.
• \( T \) is the temperature in Kelvin.

This law is essential for calculating the number of moles when other parameters are known.
For example, in the original exercise, converting given volumes and pressure conditions allowed us to use the Ideal Gas Law to solve for moles, providing critical information to further determine the molar mass of the gas involved. It’s crucial to always convert all parameters to their correct units before substituting into the equation to ensure a valid solution.

Understanding Molecular Formulas

A molecular formula provides the actual number of each type of atom in a molecule. It is derived from the molar mass and the simple empirical formula. To find a molecular formula, first determine the empirical formula, which provides the simplest whole-number ratio of atoms in the compound.
Given the molar mass, the molecular formula can be verified or deduced by dividing the obtained molar mass by the empirical mass.

• If the results show a whole number, you multiply the subscripts in the empirical formula by this number.
• Back to our example, with a molar mass of about 26 g/mol, which matches the molar mass of acetylene \( C_2H_2 \), its molecular formula perfectly aligns with its empirical formula.

Understanding molecular formulas helps clarify chemical compositions, enabling quantitative analysis of compounds.

Acetylene: A Brief Overview

Acetylene, represented chemically as \( C_2H_2 \), is a hydrocarbon and the simplest alkyne. Its structure comprises two carbon atoms joined by a triple bond, reflecting its classification in organic chemistry.
This molecule has intriguing applications in various industrial processes:

• As a fuel in oxy-acetylene welding and cutting due to its high-temperature flame.
• In organic synthesis as a precursor for many chemical reactions.

Practically, understanding the properties such as molar mass can assist in predicting behaviors and reactions with other compounds.
In experimental contexts like the one from the exercise, acetylene’s known molar mass helps confirming results of gas analysis, efficiently identifying or verifying the measured sample.