Percentage Composition of MgCl2 (magnesium chloride)

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Percentage Composition of MgCl2 (magnesium chloride) To calculate the mass percent composition (or mass percent) of each atom in a compound, you must determine the atomic mass of each atom and the molecular mass of the compound. You know the atomic masses of the atoms from the Periodic Table, so you can calculate the formula mass for magnesium chloride: (24.31 amu) + 2 (35.45 amu) = 95.21 amu. Now you can calculate the mass percentage composition of each ion in magnesium chloride: – Magnesium ion: (24.31 amu) x 100 / 95.21 amu = 25.53% – Chloride ions: 2 (35.45 amu) x 100 / 95.21 amu = 74.47% Critical Thinking Questions: Ions are produced from atoms. Explain why we can use masses of the atoms to calculate the percentage composition of the ions in a compound. How many grams of chloride ions are in 100.00 grams of magnesium chloride? Model 1 Exercises: Show your work with unit conversions and correct significant figures. Hypochlorous acid (HCIO) is a weak acid that partially dissociates in water to hydrogen ions, H+, and hypochlorite ions, CIO-. Show your calculations to determine the mass percent of hydrogen ions, H+, and hypochlorite ions, CIO- in hypochlorous acid. According to the US Environmental Protection Agency, hypochlorous acid is an effective disinfectant against COVID-19 on surfaces. Hypochlorite ions are used to whiten clothes, lighten hair color, and as a broad-spectrum disinfectant and deodorizer. Use mass percent composition to find how many grams of hypochlorous acid (HCIO) has 10.288 grams of hypochlorite ions, CIO-. Use mass percent composition to find how many grams of magnesium chloride you need to have 14.89 grams of chloride ions. An 11.50 gram sample of ethanol contains 6.00 g of carbon and 1.51 g of hydrogen. The remainder must be oxygen, as ethanol only contains these three elements. What is the percent composition of each atom in ethanol?

The Correct Answer and Explanation is:

Percentage Composition of Magnesium Chloride (MgCl₂):

To calculate the mass percent composition of each element in magnesium chloride (MgCl₂), follow these steps:

  1. Calculate the Molar Mass of MgCl₂:
    • Magnesium (Mg) has an atomic mass of 24.31 amu.
    • Chlorine (Cl) has an atomic mass of 35.45 amu.
    Molar mass of MgCl₂ = 24.31 g/mol24.31 \, \text{g/mol}24.31g/mol + 2 × 35.45 g/mol35.45 \, \text{g/mol}35.45g/mol = 95.21 g/mol95.21 \, \text{g/mol}95.21g/mol
  2. Calculate the Mass Percent of Magnesium:
    • The mass percent of magnesium in MgCl₂ is given by:
    24.31 g/mol95.21 g/mol×100=25.53%\frac{24.31 \, \text{g/mol}}{95.21 \, \text{g/mol}} \times 100 = 25.53\%95.21g/mol24.31g/mol​×100=25.53%
  3. Calculate the Mass Percent of Chlorine:
    • There are two chlorine atoms in magnesium chloride, so their total mass is 2×35.45 g/mol=70.90 g/mol2 \times 35.45 \, \text{g/mol} = 70.90 \, \text{g/mol}2×35.45g/mol=70.90g/mol.
    • The mass percent of chlorine in MgCl₂ is:
    70.90 g/mol95.21 g/mol×100=74.47%\frac{70.90 \, \text{g/mol}}{95.21 \, \text{g/mol}} \times 100 = 74.47\%95.21g/mol70.90g/mol​×100=74.47%

Critical Thinking Questions:

  1. Why We Use Atomic Masses for Ions:
    • Ions are atoms that have either gained or lost electrons, and their atomic masses (in terms of grams per mole) are nearly identical to the masses of the neutral atoms. This means we can use the atomic mass to calculate the mass percent composition of ions in a compound because the mass of an ion is directly related to the mass of the atom it came from.
  2. Grams of Chloride Ions in 100.00 Grams of MgCl₂:
    • Since 74.47% of the mass of MgCl₂ is from chloride ions, we can calculate the amount of chloride ions in a 100.00 g sample:
    74.47100×100.00 g=74.47 g of chloride ions\frac{74.47}{100} \times 100.00 \, \text{g} = 74.47 \, \text{g of chloride ions}10074.47​×100.00g=74.47g of chloride ions

Hypochlorous Acid (HClO) Mass Percent Composition:

  1. Molar Mass of HClO:
    • Hydrogen (H) = 1.008 g/mol
    • Chlorine (Cl) = 35.45 g/mol
    • Oxygen (O) = 16.00 g/mol
    • Molar mass of HClO = 1.008 g/mol + 35.45 g/mol + 16.00 g/mol = 52.458 g/mol
  2. Mass Percent of Hydrogen Ions (H⁺):
    • The mass of hydrogen in HClO is 1.008 g/mol. So, the mass percent of H⁺ is:
    1.00852.458×100=1.92%\frac{1.008}{52.458} \times 100 = 1.92\%52.4581.008​×100=1.92%
  3. Mass Percent of Hypochlorite Ions (ClO⁻):
    • The mass of chlorine and oxygen in HClO is 35.45 g/mol+16.00 g/mol=51.45 g/mol35.45 \, \text{g/mol} + 16.00 \, \text{g/mol} = 51.45 \, \text{g/mol}35.45g/mol+16.00g/mol=51.45g/mol. So, the mass percent of ClO⁻ is:
    51.4552.458×100=98.08%\frac{51.45}{52.458} \times 100 = 98.08\%52.45851.45​×100=98.08%

Calculations for Given Masses:

  1. 10.288 Grams of Hypochlorite Ions in HClO:
    • Use the mass percent composition to calculate how many grams of hypochlorous acid contain 10.288 grams of ClO⁻. The mass percent of ClO⁻ is 98.08%.
    98.08100×x=10.288(where x is the mass of HClO)\frac{98.08}{100} \times x = 10.288 \quad \text{(where x is the mass of HClO)}10098.08​×x=10.288(where x is the mass of HClO) x=10.2880.9808=10.49 g of HClOx = \frac{10.288}{0.9808} = 10.49 \, \text{g of HClO}x=0.980810.288​=10.49g of HClO
  2. Grams of Magnesium Chloride Needed for 14.89 Grams of Chloride Ions:
    • The mass percent of chloride ions in magnesium chloride is 74.47%. To find how many grams of MgCl₂ contain 14.89 grams of chloride ions:
    74.47100×x=14.89\frac{74.47}{100} \times x = 14.8910074.47​×x=14.89 x=14.890.7447=20.00 g of MgCl₂x = \frac{14.89}{0.7447} = 20.00 \, \text{g of MgCl₂}x=0.744714.89​=20.00g of MgCl₂

Ethanol Percent Composition:

Given:

  • Mass of carbon (C) = 6.00 g
  • Mass of hydrogen (H) = 1.51 g
  • Mass of oxygen (O) = Total mass – (mass of C + mass of H) = 11.50−(6.00+1.51)=3.99 g of O11.50 – (6.00 + 1.51) = 3.99 \, \text{g of O}11.50−(6.00+1.51)=3.99g of O

Now, calculate the percent composition:

  1. Percent Composition of Carbon: 6.0011.50×100=52.17%\frac{6.00}{11.50} \times 100 = 52.17\%11.506.00​×100=52.17%
  2. Percent Composition of Hydrogen: 1.5111.50×100=13.13%\frac{1.51}{11.50} \times 100 = 13.13\%11.501.51​×100=13.13%
  3. Percent Composition of Oxygen: 3.9911.50×100=34.70%\frac{3.99}{11.50} \times 100 = 34.70\%11.503.99​×100=34.70%

So, the percent composition of ethanol is:

  • Carbon: 52.17%
  • Hydrogen: 13.13%
  • Oxygen: 34.70%

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