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How many moles of sodium cations, \(\mathrm{Na}^{+},\) are dissolved in a 1.0 \(\mathrm{L}\) sample of each solution listed below? a. 0.10 \(\mathrm{M} \mathrm{NaCl}\) b. 3.0 \(\mathrm{M} \mathrm{Na}_{2} \mathrm{SO}_{4}\) c. 0.30 \(\mathrm{M} \mathrm{Na}_{3} \mathrm{PO}_{4}\)

Short Answer

Expert verified
a. 0.10 moles; b. 6.0 moles; c. 0.90 moles

Step by step solution

01

Determine Moles of Sodium from NaCl

The concentration of NaCl is given as 0.10 M. Since NaCl dissociates into Na鈦 and Cl鈦 ions, each mole of NaCl will provide 1 mole of Na鈦. Therefore, in 1.0 L of 0.10 M NaCl, there are 0.10 moles of Na鈦.
02

Determine Moles of Sodium from Na鈧係O鈧

The concentration of Na鈧係O鈧 is given as 3.0 M. Na鈧係O鈧 dissociates into 2 Na鈦 ions and 1 SO鈧劼测伝 ion per mole. Thus, each mole of Na鈧係O鈧 provides 2 moles of Na鈦. In 1.0 L of 3.0 M Na鈧係O鈧, the moles of Na鈦 are calculated as 3.0 * 2 = 6.0 moles.
03

Determine Moles of Sodium from Na鈧働O鈧

The concentration of Na鈧働O鈧 is given as 0.30 M. Na鈧働O鈧 dissociates into 3 Na鈦 ions and 1 PO鈧劼斥伝 ion per mole. Each mole of Na鈧働O鈧 provides 3 moles of Na鈦. Therefore, in 1.0 L of 0.30 M Na鈧働O鈧, there are 0.30 * 3 = 0.90 moles of Na鈦.

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Key Concepts

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

Molarity
Molarity is a term used to describe the concentration of a solute in a solution. It鈥檚 represented by the symbol "M" and is defined as the number of moles of solute per liter of solution. The formula to find molarity, which you can denote as \( M \), is:
  • \( M = \frac{\text{moles of solute}}{\text{liters of solution}} \)
This concept is crucial in chemistry, especially when you need to calculate the amount of a substance in a solution. For example, if you have a 0.10 M NaCl solution, it means there are 0.10 moles of NaCl in every 1 liter of solution.
Understanding molarity can help you determine how concentrated a solution is, and it plays a vital role in stoichiometry, which is the study of the ratios of chemical substances consumed and produced in a chemical reaction.
Sodium ions
Sodium ions, denoted as \( \text{Na}^+ \), are positively charged particles that are extremely common in various chemical reactions and solutions. They result from the dissociation of sodium-containing compounds in water.
  • For example, when sodium chloride (NaCl) is dissolved in water, it dissociates into \( \text{Na}^+ \) and \( \text{Cl}^- \) ions.
  • Similarly, sodium sulfate (\( \text{Na}_2\text{SO}_4 \)) provides two \( \text{Na}^+ \) ions per formula unit upon dissolution.
These ions are significant in numerous biological and industrial applications. In the original exercise, the concentration of \( \text{Na}^+ \) in a solution depends on the stoichiometric coefficients when compounds like NaCl, \( \text{Na}_2\text{SO}_4 \), and \( \text{Na}_3\text{PO}_4 \) dissociate.
Knowing the concentration of sodium ions is important for understanding and controlling the chemical properties of the solution.
Chemical dissociation
Chemical dissociation is the process in which molecules split into smaller particles such as atoms, ions, or radicals. In the context of solutions, dissociation refers specifically to the breaking down of ionic compounds in water, resulting in free ions.
  • When \( \text{NaCl} \) is dissolved, it dissociates completely into \( \text{Na}^+ \) and \( \text{Cl}^- \) ions.
  • Similarly, \( \text{Na}_2\text{SO}_4 \) splits into 2 \( \text{Na}^+ \) and 1 \( \text{SO}_4^{2-} \) ion, while \( \text{Na}_3\text{PO}_4 \) yields 3 \( \text{Na}^+ \) ions and 1 \( \text{PO}_4^{3-} \) ion.
These reactions illustrate how ionic substances separate into their individual ions, allowing for various interactions and reactions in aqueous solutions.
Understanding how dissociation affects the concentration of components in a solution is crucial for accurately performing calculations in stoichiometry and is a fundamental concept in chemistry.

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