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Chapter 3: Problem 21

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

Short Answer

Expert verified
Mass % of I in Sr(IO鈧�)鈧� is 52.08%. Mass % of Mn in KMnO鈧� is 34.77%.

Step by step solution

01

Write the chemical formulas

Identify the chemical formulas for strontium periodate and potassium permanganate. They are Sr(IO鈧�)鈧� and KMnO鈧�, respectively.
02

Calculate the molar mass of Sr(IO鈧�)鈧�

Sum the atomic masses of each element in Sr(IO鈧�)鈧�. Sr: 1 x 87.62, I: 2 x 126.90, O: 8 x 16.00. \[\text{Molar mass of Sr(IO鈧�)_2} = 87.62 + 2 \times 126.90 + 8 \times 16.00 = 487.42 \ \text{g/mol}\]
03

Calculate the mass % of I in Sr(IO鈧�)鈧�

Use the formula for mass percent: \[\text{Mass \, %} = \left(\frac{\text{mass of I}}{\text{total molar mass}}\right) \times 100\] \[\text{Mass \, % of I} = \left(\frac{2 \times 126.90}{487.42}\right) \times 100 \approx 52.08 \ \%\]
04

Calculate the molar mass of KMnO鈧�

Sum the atomic masses of each element in KMnO鈧�. K: 1 x 39.10, Mn: 1 x 54.94, O: 4 x 16.00. \[\text{Molar mass of KMnO_4} = 39.10 + 54.94 + 4 \times 16.00 = 158.04 \ \text{g/mol}\]
05

Calculate the mass % of Mn in KMnO鈧�

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

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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(IO鈧�)鈧� and KMnO鈧�, 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(IO鈧�)鈧�, the molar mass calculation is: 1*87.62 + 2*126.90 + 8*16.00 = 487.42 g/mol.
  • For KMnO鈧�: 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(IO鈧�)鈧�, the mass contributed by Iodine (I): 2 * 126.90 = 253.80 g/mol.
  • For KMnO鈧�, the mass contributed by Manganese (Mn): 54.94 g/mol.
  • Using the formula, for Sr(IO鈧�)鈧�, \(\text{Mass \% of I} = \left(\frac{253.80}{487.42}\right) \times 100 \approx 52.08\ \%\).
  • For KMnO鈧�, \(\text{Mass \% of Mn} = \left(\frac{54.94}{158.04}\right) \times 100 \approx 34.77\ \%\).
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(IO鈧�)鈧�, indicating 1 Sr atom, 2 I atoms, and 8 O atoms per molecule.
  • The molecular formula for potassium permanganate is KMnO鈧�, 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.

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Most popular questions from this chapter

Hydroxyapatite, \(\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3}(\mathrm{OH}),\) is the main mineral component of dental enamel, dentin, and bone. Coating the compound on metallic implants (such as titanium alloys and stainless steels) helps the body accept the implant. When placed in bone voids, the powder encourages natural bone to grow into the void. Hydroxyapatite is prepared by adding aqueous phosphoric acid to a dilute slurry of calcium hydroxide. (a) Write a balanced equation for this preparation. (b) What mass (g) of hydroxyapatite could form from \(100 . \mathrm{g}\) of \(85 \%\) phosphoric acid and \(100 . \mathrm{g}\) of calcium hydroxide?

Chromium(III) oxide reacts with hydrogen sulfide \(\left(\mathrm{H}_{2} \mathrm{~S}\right)\) gas to form chromium(III) sulfide and water: $$ \mathrm{Cr}_{2} \mathrm{O}_{3}(s)+3 \mathrm{H}_{2} \mathrm{~S}(g) \longrightarrow \mathrm{Cr}_{2} \mathrm{~S}_{3}(s)+3 \mathrm{H}_{2} \mathrm{O}(l) $$ To produce \(421 \mathrm{~g}\) of \(\mathrm{Cr}_{2} \mathrm{~S}_{3},\) how many (a) moles of \(\mathrm{Cr}_{2} \mathrm{O}_{3}\) and (b) grams of \(\mathrm{Cr}_{2} \mathrm{O}_{3}\) are required?

Chlorine gas can be made in the laboratory by the reaction of hydrochloric acid and manganese(IV) oxide: $$ 4 \mathrm{HCl}(a q)+\mathrm{MnO}_{2}(s) \longrightarrow \mathrm{MnCl}_{2}(a q)+2 \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{Cl}_{2}(g) $$ When 1.82 mol of \(\mathrm{HCl}\) reacts with excess \(\mathrm{MnO}_{2}\), how many (a) moles of \(\mathrm{Cl}_{2}\) and (b) grams of \(\mathrm{Cl}_{2}\) form?

Why might the expression " 1 mol of chlorine" be confusing? What change would remove any uncertainty? For what other elements might a similar confusion exist? Why?

Lead can be prepared from galena [lead(II) sulfide] by first roasting the galena in oxygen gas to form lead(II) oxide and sulfur dioxide. Heating the metal oxide with more galena forms the molten metal and more sulfur dioxide. (a) Write a balanced equation for each step. (b) Write an overall balanced equation for the process. (c) How many metric tons of sulfur dioxide form for every metric ton of lead obtained?
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