Problem 35 - Chemistry Matter and Change

Question

Calculate the molar mass of each molecular compound. \begin{equation}a. \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} \quad \text { b. HCN } \quad \text { c. } \mathrm{CCl}_{4}\end{equation}

Step-by-Step Solution

Answer

a. 46.07 g/mol, b. 27.03 g/mol, c. 153.81 g/mol.

Step 1: Identify Atomic Masses for C₂H₅OH

The molecular formula for ethanol (\(\mathrm{C}_2\mathrm{H}_5\mathrm{OH}\)\u00a0) consists of the elements carbon (C), hydrogen (H), and oxygen (O). The standard atomic masses are approximately: C = 12.01 g/mol, H = 1.008 g/mol, and O = 16.00 g/mol.

Step 2: Calculate Molar Mass of C₂H₅OH

Ethanol has 2 carbon atoms, 6 hydrogen atoms, and 1 oxygen atom. The calculation is:\[2(12.01\, \text{g/mol for C}) + 6(1.008\, \text{g/mol for H}) + 1(16.00\, \text{g/mol for O}) = 24.02 + 6.048 + 16.00 = 46.068\,\text{g/mol}\]

Step 3: Identify Atomic Masses for HCN

The molecular formula for hydrogen cyanide (\(\mathrm{HCN}\)\u00a0) consists of hydrogen (H), carbon (C), and nitrogen (N). The standard atomic masses are approximately: H = 1.008 g/mol, C = 12.01 g/mol, and N = 14.01 g/mol.

Step 4: Calculate Molar Mass of HCN

Hydrogen cyanide has 1 hydrogen atom, 1 carbon atom, and 1 nitrogen atom. The calculation is:\[1(1.008\, \text{g/mol for H}) + 1(12.01\, \text{g/mol for C}) + 1(14.01\, \text{g/mol for N}) = 1.008 + 12.01 + 14.01 = 27.028\,\text{g/mol}\]

Step 5: Identify Atomic Masses for CCl₄

The molecular formula for carbon tetrachloride (\(\mathrm{CCl}_4\)\u00a0) consists of carbon (C), and chlorine (Cl). The standard atomic masses are approximately: C = 12.01 g/mol, and Cl = 35.45 g/mol.

Step 6: Calculate Molar Mass of CCl₄

Carbon tetrachloride has 1 carbon atom and 4 chlorine atoms. The calculation is:\[1(12.01\, \text{g/mol for C}) + 4(35.45\, \text{g/mol for Cl}) = 12.01 + 141.8 = 153.81\,\text{g/mol}\]

Key Concepts

Ethanol Molar Mass

To find the molar mass of ethanol, it's essential to know the molecular composition of ethanol, which is represented by the chemical formula \(\mathrm{C}_2\mathrm{H}_5\mathrm{OH}\). This tells us the molecule consists of:

• 2 Carbon (C) atoms
• 6 Hydrogen (H) atoms
• 1 Oxygen (O) atom

First, identify the atomic masses of each element. Generally, they are:

• Carbon (C) is approximately \(12.01\, \text{g/mol}\)
• Hydrogen (H) is approximately \(1.008\, \text{g/mol}\)
• Oxygen (O) is approximately \(16.00\, \text{g/mol}\)

Next, to calculate the total molar mass for ethanol, compute the sum of all the individual elements:\[2 \times 12.01 + 6 \times 1.008 + 1 \times 16.00 = 46.068\, \text{g/mol}\]This sum gives ethanol a molar mass of approximately \(46.068\, \text{g/mol}\). Understanding the molecular structure helps frame why ethanol's molar mass turns out to be this number.

Hydrogen Cyanide Molar Mass

Hydrogen cyanide, with the formula \(\mathrm{HCN}\), requires calculating its molar mass by looking at the atomic composition:

• 1 Hydrogen (H) atom
• 1 Carbon (C) atom
• 1 Nitrogen (N) atom

The atomic masses are approximately:

• Hydrogen (H): \(1.008\, \text{g/mol}\)
• Carbon (C): \(12.01\, \text{g/mol}\)
• Nitrogen (N): \(14.01\, \text{g/mol}\)

Calculating the molar mass involves adding:\[1 \times 1.008 + 1 \times 12.01 + 1 \times 14.01 = 27.028\, \text{g/mol}\]This calculation shows that hydrogen cyanide has a molar mass of around \(27.028\, \text{g/mol}\), providing insight into its constituent atomic weights.

Carbon Tetrachloride Molar Mass

Carbon tetrachloride has the formula \(\mathrm{CCl}_4\), indicating its molecular make-up as:

• 1 Carbon (C) atom
• 4 Chlorine (Cl) atoms

The approximate atomic masses are:

• Carbon (C): \(12.01\, \text{g/mol}\)
• Chlorine (Cl): \(35.45\, \text{g/mol}\)

Calculating its molar mass requires:\[1 \times 12.01 + 4 \times 35.45 = 153.81\, \text{g/mol}\]Thus, carbon tetrachloride's molar mass is about \(153.81\, \text{g/mol}\). Each step shows how the mass contributions of chlorine are significant in reaching the total molar mass.

Atomic Mass

Understanding "atomic mass" is key to mastering molar mass calculations. Atomic mass is the weight of one atom of an element, typically expressed in units of grams per mole. It’s a critical parameter and differs for each type of atom, obtained through relative comparisons based on carbon-12 as a standard. This standardization allows chemists:

• To compare different elements easily.
• To calculate molar masses precisely.

Atomic mass is noted on the periodic table as an average of all isotopes of an element. To apply it: - Calculate the molar mass of a compound by summing the atomic masses of constituent atoms. This concept makes complex molecular calculations feasible by using simple arithmetic when performing mass summation. Knowing atomic masses is fundamental for further chemical computations and understanding reactions.