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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(IO₄)₂ is 52.08%. Mass % of Mn in KMnO₄ 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(IO₄)₂ and KMnO₄, respectively.
02

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. \[\text{Molar mass of Sr(IO₄)_2} = 87.62 + 2 \times 126.90 + 8 \times 16.00 = 487.42 \ \text{g/mol}\]
03

Calculate the mass % of I in Sr(IO₄)₂

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

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. \[\text{Molar mass of KMnO_4} = 39.10 + 54.94 + 4 \times 16.00 = 158.04 \ \text{g/mol}\]
05

Calculate the mass % of Mn in KMnO₄

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

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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(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.

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Most popular questions from this chapter

Seawater is approximately \(4.0 \%\) by mass dissolved ions, \(85 \%\) of which are from \(\mathrm{NaCl}\). (a) Find the mass \(\%\) of \(\mathrm{NaCl}\) in seawater. (b) Find the mass \% of \(\mathrm{Na}^{+}\) ions and of \(\mathrm{Cl}^{-}\) ions in seawater.

Many metals react with oxygen gas to form the metal oxide. For example, calcium reacts as follows: $$ 2 \mathrm{Ca}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CaO}(s) $$ You wish to calculate the mass (g) of calcium oxide that can be prepared from \(4.20 \mathrm{~g}\) of \(\mathrm{Ca}\) and \(2.80 \mathrm{~g}\) of \(\mathrm{O}_{2}\). (a) What amount (mol) of CaO can be produced from the given mass of Ca? (b) What amount (mol) of CaO can be produced from the given mass of \(\mathrm{O}_{2} ?\) (c) Which is the limiting reactant? (d) How many grams of CaO can be produced?

Cocaine \(\left(\mathrm{C}_{17} \mathrm{H}_{21} \mathrm{O}_{4} \mathrm{~N}\right)\) is a natural substance found in \(\operatorname{coca}\) leaves, which have been used for centuries as a local anesthetic and stimulant. Illegal cocaine arrives in the United States either as the pure compound or as the hydrochloride salt \(\left(\mathrm{C}_{17} \mathrm{H}_{21} \mathrm{O}_{4} \mathrm{NHCl}\right)\). At \(25^{\circ} \mathrm{C},\) the salt is very soluble in water \((2.50 \mathrm{~kg} / \mathrm{L}),\) but cocaine is much less so \((1.70 \mathrm{~g} / \mathrm{L})\) (a) What is the maximum mass (g) of the hydrochloride salt that can dissolve in \(50.0 \mathrm{~mL}\) of water? (b) If the solution from part (a) is treated with \(\mathrm{NaOH}\), the salt is converted to cocaine. How much more water (L) is needed to dissolve it?

When powdered zinc is heated with sulfur, a violent reaction occurs, and zinc sulfide forms: $$ \mathrm{Zn}(s)+\mathrm{S}_{8}(s) \longrightarrow \mathrm{ZnS}(s)[\text { unbalanced }] $$ Some of the reactants also combine with oxygen in air to form zinc oxide and sulfur dioxide. When \(83.2 \mathrm{~g}\) of Zn reacts with \(52.4 \mathrm{~g}\) of \(\mathrm{S}_{8}\), \(104.4 \mathrm{~g}\) of \(\mathrm{ZnS}\) forms. (a) What is the percent yield of \(\mathrm{ZnS}\) ? (b) If all the remaining reactants combine with oxygen, how many grams of each of the two oxides form?

Various nitrogen oxides, as well as sulfur oxides, contribute to acidic rainfall through complex reaction sequences. Nitrogen and oxygen combine during the high-temperature combustion of fuels in air to form nitrogen monoxide gas, which reacts with more oxygen to form nitrogen dioxide gas. In contact with water vapor, nitrogen dioxide forms aqueous nitric acid and more nitrogen monoxide. (a) Write balanced equations for these reactions. (b) Use the equations to write one overall balanced equation that does not include nitrogen monoxide and nitrogen dioxide. (c) How many metric tons (t) of nitric acid form when \(1350 \mathrm{t}\) of atmospheric nitrogen is consumed \((1 \mathrm{t}=1000 \mathrm{~kg}) ?\)
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