Question

Calculate each of the following: (a) Mass \% of I in strontium periodate (b) Mass \% of Mn in potassium permanganate

Short answer

Mass % of I in Sr(IO₄)₂ is 52.08%. Mass % of Mn in KMnO₄ is 34.77%.

Step-by-step solution

Write the chemical formulas

Identify the chemical formulas for strontium periodate and potassium permanganate. They are Sr(IO₄)₂ and KMnO₄, respectively.

Calculate the molar mass of Sr(IO₄)₂

Sum the atomic masses of each element in Sr(IO₄)₂. Sr: 1 x 87.62, I: 2 x 126.90, O: 8 x 16.00. \[\text{Molar mass of Sr(IO₄)_2} = 87.62 + 2 \times 126.90 + 8 \times 16.00 = 487.42 \ \text{g/mol}\]

Calculate the mass % of I in Sr(IO₄)₂

Use the formula for mass percent: \[\text{Mass \, %} = \left(\frac{\text{mass of I}}{\text{total molar mass}}\right) \times 100\] \[\text{Mass \, % of I} = \left(\frac{2 \times 126.90}{487.42}\right) \times 100 \approx 52.08 \ \%\]

Calculate the molar mass of KMnO₄

Sum the atomic masses of each element in KMnO₄. K: 1 x 39.10, Mn: 1 x 54.94, O: 4 x 16.00. \[\text{Molar mass of KMnO_4} = 39.10 + 54.94 + 4 \times 16.00 = 158.04 \ \text{g/mol}\]

Calculate the mass % of Mn in KMnO₄

Use the formula for mass percent: \[\text{Mass \, %} = \left(\frac{\text{mass of Mn}}{\text{total molar mass}}\right) \times 100\] \[\text{Mass \, % of Mn} = \left(\frac{54.94}{158.04}\right) \times 100 \approx 34.77 \ \%\]

Key concepts

Molar Mass

Understanding molar mass is fundamental for various calculations in chemistry. Molar mass is the mass of one mole of a substance (atoms, molecules, or ions) and is expressed in grams per mole (g/mol). To calculate the molar mass, sum the atomic masses of all atoms in a given molecular formula. For instance, to find the molar mass of Sr(IO₄)₂ and KMnO₄, you need to:

• Identify the atomic masses of each element (from the periodic table). For example, Sr has an atomic mass of 87.62 g/mol, I has an atomic mass of 126.90 g/mol, and O has an atomic mass of 16.00 g/mol.
• Sum the masses multiplied by the number of each type of atom in the formula. For Sr(IO₄)₂, the molar mass calculation is: 1*87.62 + 2*126.90 + 8*16.00 = 487.42 g/mol.
• For KMnO₄: 1*39.10 + 1*54.94 + 4*16.00 = 158.04 g/mol.

Calculating molar mass helps in determining other properties like density, volume, and in our case, mass percentage.

Mass Percentage

Mass percentage is a way to express the concentration of an element within a compound. To find the mass percent, use the formula: \(\text{Mass \%} = \left(\frac{\text{mass of element}}{\text{total molar mass}}\right) \times 100\).
Calculating mass percentage involves:

• Finding the total molar mass of the compound as discussed previously.
• Determining the mass contributed by the specific element of interest.
• For strontium periodate, Sr(IO₄)₂, the mass contributed by Iodine (I): 2 * 126.90 = 253.80 g/mol.
• For KMnO₄, the mass contributed by Manganese (Mn): 54.94 g/mol.
• Using the formula, for Sr(IO₄)₂, \(\text{Mass \% of I} = \left(\frac{253.80}{487.42}\right) \times 100 \approx 52.08\ \%\).
• For KMnO₄, \(\text{Mass \% of Mn} = \left(\frac{54.94}{158.04}\right) \times 100 \approx 34.77\ \%\).

Mass percentage is crucial for understanding the composition of compounds and for various practical applications in chemistry.

Chemical Formulas

Chemical formulas represent the elements in a compound and the ratio of atoms. There are different types of chemical formulas:

• Empirical Formula: Simplest whole-number ratio of atoms in a compound.
• Molecular Formula: Actual number of atoms of each element in a molecule.
• Structural Formula: Shows the arrangement of atoms within the molecule.

For example, in the given exercise:

• The empirical formula for strontium periodate is Sr(IO₄)₂, indicating 1 Sr atom, 2 I atoms, and 8 O atoms per molecule.
• The molecular formula for potassium permanganate is KMnO₄, indicating 1 K atom, 1 Mn atom, and 4 O atoms per molecule.

Understanding chemical formulas is essential for writing chemical equations, stoichiometry, and various other chemical calculations.