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Chapter 6: Problem 23

How many moles of ions are in \(1.75 \mathrm{~mol}\) of \(\mathrm{K}_{2} \mathrm{SO}_{4} ?\)

Short Answer

Expert verified
There are 5.25 moles of ions in 1.75 mol of \(\mathrm{K}_{2}\mathrm{SO}_{4}.\)

Step by step solution

01

Identify the Compound

The compound provided is potassium sulfate, \(\mathrm{K}_{2}\mathrm{SO}_{4}.\) This compound is composed of potassium ions \(\mathrm{K}^+,\) sulfate ions \(\mathrm{SO}_{4}^{2-},\) and contains no overall charge.
02

Determine Ion Composition

In each formula unit of \(\mathrm{K}_{2}\mathrm{SO}_{4},\) there are 2 potassium ions \(\mathrm{K}^+\) and 1 sulfate ion \(\mathrm{SO}_{4}^{2-}.\) Thus, each unit contributes 3 ions in total.
03

Calculate Total Moles of Ions

The number of moles of ions can be found by multiplying the total number of ions per molecule by the given moles of the compound. Since there are 3 ions per molecule, for \(1.75\) moles of \(\mathrm{K}_{2}\mathrm{SO}_{4},\) the total moles of ions is calculated as \(3 \times 1.75 = 5.25\) moles.

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Key Concepts

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

Potassium Sulfate
Potassium sulfate is a chemical compound with the formula \(\mathrm{K}_{2}\mathrm{SO}_{4}\). It is commonly used in fertilizers because it provides essential nutrients like potassium and sulfur to plants. Potassium sulfate is a white crystalline salt that dissolves well in water, making it easy to apply in agricultural settings.
This compound is highly valued for being chlorine-free, which is beneficial for sensitive crops. Overall, it's an important substance in various applications, thanks to its nutrient content and physical properties.
Chemical Formula
The chemical formula \(\mathrm{K}_{2}\mathrm{SO}_{4}\) of potassium sulfate provides insights into its composition and structure. A chemical formula represents the elements present in a compound and their ratios. In \(\mathrm{K}_{2}\mathrm{SO}_{4}\), each molecule contains:
  • Two potassium (\(\mathrm{K}\)) atoms
  • One sulfur (\(\mathrm{S}\)) atom
  • Four oxygen (\(\mathrm{O}\)) atoms
This formula helps us understand the stoichiometry of the compound and is essential for performing calculations related to the compound鈥檚 properties and behavior.
Ion Composition
In the context of potassium sulfate, its ion composition plays a crucial role in understanding its chemical nature. Potassium sulfate dissociates into ions when dissolved in water. This process involves:
  • Two potassium ions, \(\mathrm{K}^+\)
  • One sulfate ion, \(\mathrm{SO}_{4}^{2-}\)
Each unit of \(\mathrm{K}_{2}\mathrm{SO}_{4}\) provides a total of three ions. This is key to calculating how many ions are generated from a given amount of the compound.
Molar Calculations
Performing molar calculations helps us determine the quantity of ions in a substance. With potassium sulfate, if you have \(1.75\) moles of \(\mathrm{K}_{2}\mathrm{SO}_{4}\), you can calculate the total moles of ions by multiplying the moles of the compound by the number of ions per formula unit.
For \(\mathrm{K}_{2}\mathrm{SO}_{4}\), this means:
  • 3 ions per formula unit \((2 \ \mathrm{K}^+ + 1 \ \mathrm{SO}_{4}^{2-})\)
  • \(3 \times 1.75 = 5.25\) moles of ions
These calculations are fundamental in chemistry to quantify how substances behave in reactions and solutions.

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Most popular questions from this chapter

Calculate the molecular mass of the following substances: (a) Ibuprofen, \(\mathrm{C}_{13} \mathrm{H}_{18} \mathrm{O}_{2}\) (a drug used as for pain relief) (b) Phenobarbital, \(\mathrm{C}_{12} \mathrm{H}_{12} \mathrm{~N}_{2} \mathrm{O}_{3}\) (a drug used as a sedative, hypnotic, and antiseizure medication)

Acetylsalicylic acid, the active ingredient in aspirin, is prepared from salicylic acid by reaction with acetic anhydride. $$\mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{3}+\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{3} \quad \longrightarrow \quad \mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4} \quad+\quad \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}_{2}$$ (salicylic acid) (acetic anhydride) (acetylsalicylic acid) (acetic acid) (a) Calculate the theoretical yield if \(47 \mathrm{~g}\) of salicylic acid is reacted with \(25 \mathrm{~g}\) of acetic anhydride. (b) What is the percent yield if only \(35 \mathrm{~g}\) is obtained?

When table sugar (sucrose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\) ) is heated, it decomposes to form \(\mathrm{C}\) and \(\mathrm{H}_{2} \mathrm{O}\). (a) Write a balanced equation for the process. (b) How many grams of carbon are formed by the breakdown of \(60.0 \mathrm{~g}\) of sucrose? (c) How many grams of water are formed when \(6.50 \mathrm{~g}\) of carbon are formed?

At elevated temperatures in an automobile engine, \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) can react to yield NO, an important cause of air pollution. (a) Write a balanced equation for the reaction. (b) How many moles of \(\mathrm{N}_{2}\) are needed to react with \(7.50 \mathrm{~mol}\) of \(\mathrm{O}_{2} ?\) (c) How many moles of \(\mathrm{NO}\) can be formed when \(3.81 \mathrm{~mol}\) of \(\mathrm{N}_{2}\) reacts? (d) How many moles of \(\mathrm{O}_{2}\) must react to produce \(0.250 \mathrm{~mol}\) of \(\mathrm{NO} ?\)

How many molecules of ascorbic acid (vitamin \(\left.\mathrm{C}, \mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6}\right)\) are in a \(500 \mathrm{mg}\) tablet? (Hint: First calculate molar mass, then use it as a conversion factor to convert mass to moles).
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