Question

the mole - practice ques

1. using the periodic table, calculate the molar mass of the following substances:

a) xef₄ (ans.207.29g/mol)
b) h₂so₃ (ans.82.09g/mol)
c) baso₄ (ans.233.39g/mol)
d) nh₄no₃ (ans.80.06g/mol)
e) fe₃fe(cn)₆₂ (ans.591.49g/mol)

1. calculate the number of moles in the following:

a) 5.6 g koh (ans. 0.1mol)
b) 174 g mno₂ (ans. 2.0mol)
c) 0.58 g li₃po₄ (ans. 5.0×10⁻³mol)
d) 1.0 g co₂ (ans. 0.023mol)

1. calculate the mass of the following:

a) 4.0 mol h₂so₄ (ans.3.9×10² g)
b) 2.5 mol mgco₃ (ans.2.1×10²g)
c) 0.50 mol fecl₂ (ans.63g)
d) 1.80 mol al₂(so₄)₃ (ans.616g)

Answer:

To solve these problems, we'll use the concepts of molar mass, moles, and mass calculations. Molar mass is the sum of the atomic masses of all atoms in a compound. The formula relating mass (\(m\)), moles (\(n\)), and molar mass (\(M\)) is \(n = \frac{m}{M}\) (for moles from mass) and \(m = n \times M\) (for mass from moles).

Problem 1a: Molar Mass of \(XeF_4\)

Step 1: Identify Atomic Masses

From the periodic table:

• Atomic mass of \(Xe\) (Xenon) ≈ \(131.29\) g/mol
• Atomic mass of \(F\) (Fluorine) ≈ \(19.00\) g/mol

Step 2: Calculate Molar Mass

\(XeF_4\) has 1 \(Xe\) atom and 4 \(F\) atoms.
Molar mass \(M = 131.29 + (4 \times 19.00)\)
\(M = 131.29 + 76.00 = 207.29\) g/mol

Problem 1b: Molar Mass of \(H_2SO_3\)

Step 1: Identify Atomic Masses

• \(H\) (Hydrogen) ≈ \(1.01\) g/mol
• \(S\) (Sulfur) ≈ \(32.07\) g/mol
• \(O\) (Oxygen) ≈ \(16.00\) g/mol

Step 2: Calculate Molar Mass

\(H_2SO_3\) has 2 \(H\), 1 \(S\), and 3 \(O\) atoms.
\(M = (2 \times 1.01) + 32.07 + (3 \times 16.00)\)
\(M = 2.02 + 32.07 + 48.00 = 82.09\) g/mol

Problem 1c: Molar Mass of \(BaSO_4\)

Step 1: Identify Atomic Masses

• \(Ba\) (Barium) ≈ \(137.33\) g/mol
• \(S\) (Sulfur) ≈ \(32.07\) g/mol
• \(O\) (Oxygen) ≈ \(16.00\) g/mol

Step 2: Calculate Molar Mass

\(BaSO_4\) has 1 \(Ba\), 1 \(S\), and 4 \(O\) atoms.
\(M = 137.33 + 32.07 + (4 \times 16.00)\)
\(M = 137.33 + 32.07 + 64.00 = 233.40\) g/mol (close to 233.39 due to rounding)

Problem 1d: Molar Mass of \(NH_4NO_3\)

Step 1: Identify Atomic Masses

• \(N\) (Nitrogen) ≈ \(14.01\) g/mol
• \(H\) (Hydrogen) ≈ \(1.01\) g/mol
• \(O\) (Oxygen) ≈ \(16.00\) g/mol

Step 2: Calculate Molar Mass

\(NH_4NO_3\) has 2 \(N\), 4 \(H\), and 3 \(O\) atoms.
\(M = (2 \times 14.01) + (4 \times 1.01) + (3 \times 16.00)\)
\(M = 28.02 + 4.04 + 48.00 = 80.06\) g/mol

Problem 1e: Molar Mass of \(Fe_3[Fe(CN)_6]_2\)

Step 1: Identify Atomic Masses

• \(Fe\) (Iron) ≈ \(55.85\) g/mol
• \(C\) (Carbon) ≈ \(12.01\) g/mol
• \(N\) (Nitrogen) ≈ \(14.01\) g/mol

Step 2: Calculate Molar Mass

First, analyze the formula:

• \(Fe_3\): 3 \(Fe\) atoms
• \([Fe(CN)_6]_2\): 2 \(Fe\) atoms, 12 \(C\) atoms, 12 \(N\) atoms

Total \(Fe\) atoms: \(3 + 2 = 5\)
Total \(C\) atoms: \(12\)
Total \(N\) atoms: \(12\)

Molar mass \(M = (5 \times 55.85) + (12 \times 12.01) + (12 \times 14.01)\)
\(M = 279.25 + 144.12 + 168.12 = 591.49\) g/mol

Problem 2a: Moles of \(5.6\) g \(KOH\)

Step 1: Molar Mass of \(KOH\)

• \(K\) (Potassium) ≈ \(39.10\) g/mol
• \(O\) (Oxygen) ≈ \(16.00\) g/mol
• \(H\) (Hydrogen) ≈ \(1.01\) g/mol

\(M = 39.10 + 16.00 + 1.01 = 56.11\) g/mol

Step 2: Calculate Moles

Using \(n = \frac{m}{M}\):
\(n = \frac{5.6}{56.11} \approx 0.1\) mol

Problem 2b: Moles of \(174\) g \(MnO_2\)

Step 1: Molar Mass of \(MnO_2\)

• \(Mn\) (Manganese) ≈ \(54.94\) g/mol
• \(O\) (Oxygen) ≈ \(16.00\) g/mol

\(M = 54.94 + (2 \times 16.00) = 54.94 + 32.00 = 86.94\) g/mol

Step 2: Calculate Moles

\(n = \frac{174}{86.94} \approx 2.0\) mol

Problem 2c: Moles of \(0.58\) g \(Li_3PO_4\)

Step 1: Molar Mass of \(Li_3PO_4\)

• \(Li\) (Lithium) ≈ \(6.94\) g/mol
• \(P\) (Phosphorus) ≈ \(30.97\) g/mol
• \(O\) (Oxygen) ≈ \(16.00\) g/mol

\(M = (3 \times 6.94) + 30.97 + (4 \times 16.00)\)
\(M = 20.82 + 30.97 + 64.00 = 115.79\) g/mol

Step 2: Calculate Moles

\(n = \frac{0.58}{115.79} \approx 5.0 \times 10^{-3}\) mol

Problem 2d: Moles of \(1.0\) g \(CO_2\)

Step 1: Molar Mass of \(CO_2\)

• \(C\) (Carbon) ≈ \(12.01\) g/mol
• \(O\) (Oxygen) ≈ \(16.00\) g/mol

\(M = 12.01 + (2 \times 16.00) = 44.01\) g/mol

Step 2: Calculate Moles

\(n = \frac{1.0}{44.01} \approx 0.023\) mol

Problem 3a: Mass of \(4.0\) mol \(H_2SO_4\)

Step 1: Molar Mass of \(H_2SO_4\)

• \(H\): \(1.01\) g/mol, \(S\): \(32.07\) g/mol, \(O\): \(16.00\) g/mol

\(M = (2 \times 1.01) + 32.07 + (4 \times 16.00)\)
\(M = 2.02 + 32.07 + 64.00 = 98.09\) g/mol

Step 2: Calculate Mass

Using \(m = n \times M\):
\(m = 4.0 \times 98.09 \approx 392.36\) g (≈ \(3.9 \times 10^2\) g)

Problem 3b: Mass of \(2.5\) mol \(MgCO_3\)

Step 1: Molar Mass of \(MgCO_3\)

• \(Mg\) (Magnesium) ≈ \(24.31\) g/mol
• \(C\) (Carbon) ≈ \(12.01\) g/mol
• \(O\) (Oxygen) ≈ \(16.00\) g/mol

\(M = 24.31 + 12.01 + (3 \times 16.00) = 24.31 + 12.01 + 48.00 = 84.32\) g/mol

Step 2: Calculate Mass

\(m = 2.5 \times 84.32 = 210.8\) g (≈ \(2.1 \times 10^2\) g)

Problem 3c: Mass of \(0.50\) mol \(FeCl_2\)

Step 1: Molar Mass of \(FeCl_2\)

• \(Fe\) (Iron) ≈ \(55.85\) g/mol
• \(Cl\) (Chlorine) ≈ \(35.45\) g/mol

\(M = 55.85 + (2 \times 35.45) = 55.85 + 70.90 = 126.75\) g/mol

Step 2: Calculate Mass

\(m = 0.50 \times 126.75 = 63.375\) g (≈ \(63\) g)

Problem 3d: Mass of \(1.80\) mol \(Al_2(SO_4)_3\)

Step 1: Molar Mass of \(Al_2(SO_4)_3\)

• \(Al\) (Aluminum) ≈ \(26.98\) g/mol
• \(S\) (Sulfur) ≈ \(32.07\) g/mol
• \(O\) (Oxygen) ≈ \(16.00\) g/mol

\(Al_2(SO_4)_3\) has 2 \(Al\), 3 \(S\), and 12 \(O\) atoms:
\(M = (2 \times 26.98) + (3 \times 32.07) + (12 \times 16.00)\)
\(M = 53.96 + 96.21 + 192.00 = 342.17\) g/mol

Step 2: Calculate Mass

\(m = 1.80 \times 342.17 \approx 615.906\) g (≈ \(616\) g)

Final Answers (Summarized)

1a) \(207.29\) g/mol
1b) \(82.09\) g/mol
1c) \(233.39\) g/mol
1d) \(80.06\) g/mol
1e) \(591.49\) g/mol
2a) \(0.1\) mol
2b) \(2.0\) mol
2c) \(5.0 \times 10^{-3}\) mol
2d) \(0.023\) mol
3a) \(3.9 \times 10^2\) g
3b) \(2.1 \times 10^2\) g
3c) \(63\) g
3d) \(616\) g