Percentage Composition of MgCl2

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Model I: 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, we first determine the formula mass of the compound. The formula of magnesium chloride is MgCl2\text{MgCl}_2MgCl2​, which consists of one magnesium atom and two chloride ions.

  1. Magnesium Mass:
    From the Periodic Table, the atomic mass of magnesium (Mg) is 24.31 amu. Since there’s only one magnesium atom in the formula, the total mass contributed by magnesium is: 1×24.31=24.31 amu1 \times 24.31 = 24.31 \, \text{amu}1×24.31=24.31amu
  2. Chlorine Mass:
    The atomic mass of chlorine (Cl) is 35.45 amu. Since there are two chlorine atoms in the formula, the total mass contributed by chlorine is: 2×35.45=70.90 amu2 \times 35.45 = 70.90 \, \text{amu}2×35.45=70.90amu
  3. Total Molecular Mass of MgCl₂:
    Add the mass of magnesium and chlorine: 24.31+70.90=95.21 amu24.31 + 70.90 = 95.21 \, \text{amu}24.31+70.90=95.21amu
  4. Mass Percent of Magnesium:
    The mass percent of magnesium in magnesium chloride is calculated by dividing the mass of magnesium by the total molecular mass and multiplying by 100: 24.3195.21×100=25.53%\frac{24.31}{95.21} \times 100 = 25.53\%95.2124.31​×100=25.53%
  5. Mass Percent of Chlorine:
    Similarly, the mass percent of chlorine is calculated by dividing the mass of chlorine by the total molecular mass and multiplying by 100: 70.9095.21×100=74.47%\frac{70.90}{95.21} \times 100 = 74.47\%95.2170.90​×100=74.47%

Critical Thinking Question:

Why can we use the masses of atoms to calculate the percentage composition of ions in a compound?

We can use the atomic masses of elements to calculate the mass percent composition of ions because the total mass of the compound is the sum of the masses of its constituent ions. When magnesium chloride dissociates in water, it forms magnesium ions (Mg2+\text{Mg}^{2+}Mg2+) and chloride ions (Cl−\text{Cl}^-Cl−), but the mass percent of these ions in the solid compound (before dissociation) is the same as the mass percent of magnesium and chlorine in the molecular formula of MgCl₂.

Since the ions come from the atoms of the compound, we use the atomic masses of the elements in the compound to determine the mass percent composition of each ion.

Mass Percent of Hypochlorous Acid (HCIO):

To find the mass percent composition of hydrogen ions (H+\text{H}^+H+) and hypochlorite ions (ClO−\text{ClO}^-ClO−) in hypochlorous acid, we start by calculating the formula mass of HCIO\text{HCIO}HCIO.

  1. Hydrogen Mass:
    The atomic mass of hydrogen (H) is 1.008 amu. Since there is one hydrogen atom in the formula, the total mass contributed by hydrogen is: 1×1.008=1.008 amu1 \times 1.008 = 1.008 \, \text{amu}1×1.008=1.008amu
  2. Chlorine Mass:
    The atomic mass of chlorine is 35.45 amu. Since there is one chlorine atom in the formula, the total mass contributed by chlorine is: 1×35.45=35.45 amu1 \times 35.45 = 35.45 \, \text{amu}1×35.45=35.45amu
  3. Oxygen Mass:
    The atomic mass of oxygen (O) is 16.00 amu. Since there is one oxygen atom in the formula, the total mass contributed by oxygen is: 1×16.00=16.00 amu1 \times 16.00 = 16.00 \, \text{amu}1×16.00=16.00amu
  4. Total Molecular Mass of HCIO:
    Add the masses of hydrogen, chlorine, and oxygen: 1.008+35.45+16.00=52.458 amu1.008 + 35.45 + 16.00 = 52.458 \, \text{amu}1.008+35.45+16.00=52.458amu
  5. Mass Percent of Hydrogen:
    The mass percent of hydrogen is calculated by dividing the mass of hydrogen by the total molecular mass of HCIO\text{HCIO}HCIO and multiplying by 100: 1.00852.458×100=1.92%\frac{1.008}{52.458} \times 100 = 1.92\%52.4581.008​×100=1.92%
  6. Mass Percent of Chlorine:
    Similarly, the mass percent of chlorine is: 35.4552.458×100=67.57%\frac{35.45}{52.458} \times 100 = 67.57\%52.45835.45​×100=67.57%
  7. Mass Percent of Oxygen:
    The mass percent of oxygen is: 16.0052.458×100=30.47%\frac{16.00}{52.458} \times 100 = 30.47\%52.45816.00​×100=30.47%

Mass Percent Composition of Ethanol:

For ethanol (C₂H₅OH), we know that the total mass is 11.50 g, which consists of carbon (C), hydrogen (H), and oxygen (O). The mass of each element is provided as:

  • Carbon: 6.00 g
  • Hydrogen: 1.51 g
  • The remaining mass must be oxygen.

To find the mass of oxygen: Mass of Oxygen=11.50−(6.00+1.51)=3.99 g\text{Mass of Oxygen} = 11.50 – (6.00 + 1.51) = 3.99 \, \text{g}Mass of Oxygen=11.50−(6.00+1.51)=3.99g

  1. Mass Percent of Carbon:
    The mass percent of carbon is: 6.0011.50×100=52.17%\frac{6.00}{11.50} \times 100 = 52.17\%11.506.00​×100=52.17%
  2. Mass Percent of Hydrogen:
    The mass percent of hydrogen is: 1.5111.50×100=13.13%\frac{1.51}{11.50} \times 100 = 13.13\%11.501.51​×100=13.13%
  3. Mass Percent of Oxygen:
    The mass percent of oxygen is: 3.9911.50×100=34.70%\frac{3.99}{11.50} \times 100 = 34.70\%11.503.99​×100=34.70%

Summary of Results:

  • Magnesium Chloride (MgCl₂):
    • Magnesium: 25.53%
    • Chlorine: 74.47%
  • Hypochlorous Acid (HCIO):
    • Hydrogen: 1.92%
    • Chlorine: 67.57%
    • Oxygen: 30.47%
  • Ethanol (C₂H₅OH):
    • Carbon: 52.17%
    • Hydrogen: 13.13%
    • Oxygen: 34.70%

These mass percent compositions help understand the relative amounts of each element in the compounds, which is essential in chemical analysis and various applications.

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